From 58ad8bbcfc5bafc92e753507e4be4559537f0f60 Mon Sep 17 00:00:00 2001 From: mattansb <35330040+mattansb@users.noreply.github.com> Date: Fri, 26 Jul 2019 14:05:04 +0300 Subject: [PATCH 01/21] Update bayesfactor_parameters.R #200 --- R/bayesfactor_parameters.R | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/R/bayesfactor_parameters.R b/R/bayesfactor_parameters.R index e197c249b..a79600fce 100644 --- a/R/bayesfactor_parameters.R +++ b/R/bayesfactor_parameters.R @@ -274,7 +274,7 @@ bayesfactor_parameters.data.frame <- function(posterior, prior = NULL, class(bf_val) <- unique(c( "bayesfactor_parameters", - "see_bayesfactor_savagedickey", + "see_bayesfactor_parameters", class(bf_val) )) From 1458dc35276fe8fb99c0befad967e94604d35073 Mon Sep 17 00:00:00 2001 From: Dominique Makowski Date: Tue, 30 Jul 2019 08:22:59 +0800 Subject: [PATCH 02/21] Update README.md --- README.md | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/README.md b/README.md index fa23171e1..64352e335 100644 --- a/README.md +++ b/README.md @@ -86,7 +86,9 @@ describe_posterior(rnorm(1000)) [**`map_estimate()`**](https://easystats.github.io/bayestestR/reference/map_estimate.html) find the **Highest Maximum A Posteriori (MAP)** estimate of a posterior, -*i.e.,* the most probable value. +*i.e.*, the value associated with the highest probability density (the +“peak” of the posterior distribution). In other words, it is an +estimation of the *mode* for continuous parameters. ``` r map_estimate(rnorm(1000, 1, 1)) @@ -236,9 +238,8 @@ vignette](https://easystats.github.io/bayestestR/articles/bayes_factors.html). computes a Bayesian equivalent of the p-value, related to the odds that a parameter (described by its posterior distribution) has against the null hypothesis (*h0*) using Mills’ (2014, 2017) *Objective Bayesian -Hypothesis Testing* framework. It is mathematically based on the density -at the Maximum A Priori (MAP) and corresponds to the density value at 0 -divided by the density of the MAP estimate. +Hypothesis Testing* framework. It corresponds to the density value at 0 +divided by the density at the Maximum A Posteriori (MAP). ``` r p_map(rnorm(1000, 1, 1)) From 83a2fa88eb97a839c9ec619d4432cc91d438727b Mon Sep 17 00:00:00 2001 From: Dominique Makowski Date: Tue, 30 Jul 2019 08:48:08 +0800 Subject: [PATCH 03/21] CONTRIBUTING guide aims to be general to easystats --- .github/CONDUCT.md | 73 ++++++++++++++++++++++++++ .github/CONTRIBUTING.md | 52 ++++++++++++++++++ .github/ISSUE_TEMPLATE/bug_report.md | 24 +++++++++ .github/ISSUE_TEMPLATE/feature-idea.md | 11 ++++ .github/ISSUE_TEMPLATE/question.md | 7 +++ .github/PULL_REQUEST_TEMPLATE.md | 7 +++ 6 files changed, 174 insertions(+) create mode 100644 .github/CONDUCT.md create mode 100644 .github/CONTRIBUTING.md create mode 100644 .github/ISSUE_TEMPLATE/bug_report.md create mode 100644 .github/ISSUE_TEMPLATE/feature-idea.md create mode 100644 .github/ISSUE_TEMPLATE/question.md create mode 100644 .github/PULL_REQUEST_TEMPLATE.md diff --git a/.github/CONDUCT.md b/.github/CONDUCT.md new file mode 100644 index 000000000..30f74c5d5 --- /dev/null +++ b/.github/CONDUCT.md @@ -0,0 +1,73 @@ +# Contributor Covenant Code of Conduct + +## Our Pledge + +In the interest of fostering an open and welcoming environment, we as +contributors and maintainers pledge to making participation in our project and +our community a harassment-free experience for everyone, regardless of age, body +size, disability, ethnicity, gender identity and expression, level of experience, +nationality, personal appearance, race, religion, or sexual identity and +orientation. + +## Our Standards + +Examples of behavior that contributes to creating a positive environment +include: + +* Using welcoming and inclusive language +* Being respectful of differing viewpoints and experiences +* Gracefully accepting constructive criticism +* Focusing on what is best for the community +* Showing empathy towards other community members + +Examples of unacceptable behavior by participants include: + +* The use of sexualized language or imagery and unwelcome sexual attention or + advances +* Trolling, insulting/derogatory comments, and personal or political attacks +* Public or private harassment +* Publishing others' private information, such as a physical or electronic + address, without explicit permission +* Other conduct which could reasonably be considered inappropriate in a + professional setting + +## Our Responsibilities + +Project maintainers are responsible for clarifying the standards of acceptable +behavior and are expected to take appropriate and fair corrective action in +response to any instances of unacceptable behavior. + +Project maintainers have the right and responsibility to remove, edit, or +reject comments, commits, code, wiki edits, issues, and other contributions +that are not aligned to this Code of Conduct, or to ban temporarily or +permanently any contributor for other behaviors that they deem inappropriate, +threatening, offensive, or harmful. + +## Scope + +This Code of Conduct applies both within project spaces and in public spaces +when an individual is representing the project or its community. Examples of +representing a project or community include using an official project e-mail +address, posting via an official social media account, or acting as an appointed +representative at an online or offline event. Representation of a project may be +further defined and clarified by project maintainers. + +## Enforcement + +Instances of abusive, harassing, or otherwise unacceptable behavior may be +reported by contacting the project team at [INSERT EMAIL ADDRESS]. All +complaints will be reviewed and investigated and will result in a response that +is deemed necessary and appropriate to the circumstances. The project team is +obligated to maintain confidentiality with regard to the reporter of an incident. +Further details of specific enforcement policies may be posted separately. + +Project maintainers who do not follow or enforce the Code of Conduct in good +faith may face temporary or permanent repercussions as determined by other +members of the project's leadership. + +## Attribution + +This Code of Conduct is adapted from the [Contributor Covenant][homepage], version 1.4, +available at https://www.contributor-covenant.org/version/1/4/code-of-conduct.html + +[homepage]: https://www.contributor-covenant.org diff --git a/.github/CONTRIBUTING.md b/.github/CONTRIBUTING.md new file mode 100644 index 000000000..cec30249a --- /dev/null +++ b/.github/CONTRIBUTING.md @@ -0,0 +1,52 @@ +# Contribution Guidelines + +easystats guidelines 0.1.0 + +**All people are very much welcome to contribute to code, documentation, testing and suggestions.** + +This package aims at being beginner-friendly. Even if you're new to this open-source way of life, new to coding and github stuff, we encourage you to try submitting pull requests (PRs). + +- **"I'd like to help, but I'm not good enough with programming yet"** + +It's alright, don't worry! You can always dig in the code, in the documentation or tests. There are always some typos to fix, some docs to improve, some details to add, some code lines to document, some tests to add... **Even the smaller PRs are appreciated**. + +- **"I'd like to help, but I don't know where to start"** + +You can look around the **issue section** to find some features / ideas / bugs to start working on. You can also open a new issue **just to say that you're there, interested in helping out**. We might have some ideas adapted to your skills. + +- **"I'm not sure if my suggestion or idea is worthwile"** + +Enough with the impostor syndrom! All suggestions and opinions are good, and even if it's just a thought or so, it's always good to receive feedback. + +- **"Why should I waste my time with this? Do I get any credit?"** + +Software contributions are getting more and more valued in the academic world, so it is a good time to collaborate with us! Authors of substantial contributions will be added within the **authors** list. We're also very keen on including them to eventual academic publications. + + +**Anyway, starting is the most important! You will then enter a *whole new world, a new fantastic point of view*... So fork this repo, do some changes and submit them. We will then work together to make the best out of it :)** + + +## Code + +- Please document and comment your code, so that the purpose of each step (or code line) is stated in a clear and understandable way. +- Before submitting a change, please read the [**R style guide**](https://style.tidyverse.org/) to keep some consistency in code formatting. +- Regarding the style guide, note this exception: we put readability and clarity before everything. Thus, we like underscores and full names (prefer `model_performance` over `modelperf` and `interpret_odds_logistic` over `intoddslog`). +- Before you start to code, make sure you're on the `dev` branch (the most "advanced"). Then, you can create a new branch named by your feature (e.g., `feature_lightsaber`) and do your changes. Finally, submit your branch to be merged into the `dev` branch. Then, every now and then, the dev branch will merge into `master`, as a new package version. + +## Checks to do before submission + +- Make sure **documentation** (roxygen) is good +- Make sure to add **tests** for the new functions +- Run: + + - `styler::style_pkg()`: Automatic style formatting + - `lintr::lint_package()`: Style checks + - `devtools::check()`: General checks + + + +## Useful Materials + +- [Understanding the GitHub flow](https://guides.github.com/introduction/flow/) + + diff --git a/.github/ISSUE_TEMPLATE/bug_report.md b/.github/ISSUE_TEMPLATE/bug_report.md new file mode 100644 index 000000000..e43c61a3b --- /dev/null +++ b/.github/ISSUE_TEMPLATE/bug_report.md @@ -0,0 +1,24 @@ +--- +name: Bug report +about: Create a report to help us improve + +--- + +**Describe the bug** +A description of what the bug is. + +**To Reproduce** +Steps to reproduce the behaviour: +1. Go to '...' +2. Click on '....' +3. Scroll down to '....' +4. See error + +**Expected behaviour** +A clear and concise description of what you expected to happen. + +**Screenshots** +If applicable, add screenshots to help explain your problem. + +**Specifiations (please complete the following information):** + - Package Version [e.g. 0.2.1] diff --git a/.github/ISSUE_TEMPLATE/feature-idea.md b/.github/ISSUE_TEMPLATE/feature-idea.md new file mode 100644 index 000000000..16e9032e9 --- /dev/null +++ b/.github/ISSUE_TEMPLATE/feature-idea.md @@ -0,0 +1,11 @@ +--- +name: Feature idea +about: Suggest an idea for this project + +--- + +**Describe the solution you'd like** +A clear and concise description of what you want to happen. + +**How could we do it?** +A description of actual ways of implementing a feature. diff --git a/.github/ISSUE_TEMPLATE/question.md b/.github/ISSUE_TEMPLATE/question.md new file mode 100644 index 000000000..86e22377f --- /dev/null +++ b/.github/ISSUE_TEMPLATE/question.md @@ -0,0 +1,7 @@ +--- +name: Question +about: You didn't understand something? + +--- + +**Question and context** diff --git a/.github/PULL_REQUEST_TEMPLATE.md b/.github/PULL_REQUEST_TEMPLATE.md new file mode 100644 index 000000000..4d3b055de --- /dev/null +++ b/.github/PULL_REQUEST_TEMPLATE.md @@ -0,0 +1,7 @@ +# Description + +This PR aims at adding this feature... + +# Proposed Changes + +I changed the `foo` function so that ... From 98fa54c9877234d9b6b40ab96c2e6d216b401c25 Mon Sep 17 00:00:00 2001 From: Dominique Makowski Date: Tue, 30 Jul 2019 08:53:54 +0800 Subject: [PATCH 04/21] protect brms reference --- paper/paper.bib | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.bib b/paper/paper.bib index 811e22d66..43d53ad20 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -218,7 +218,7 @@ @article{burkner2017brms volume = {80}, number = {1}, author = {Paul-Christian Bürkner}, - title = {brms: An R Package for Bayesian Multilevel Models Using Stan}, + title = {{brms}: An R Package for Bayesian Multilevel Models Using Stan}, journal = {Journal of Statistical Software} } From feae6aff8fc1dcfa5002bf455bb294d0209d50f1 Mon Sep 17 00:00:00 2001 From: Dominique Makowski Date: Tue, 30 Jul 2019 09:02:31 +0800 Subject: [PATCH 05/21] hopefully fix Kruschke's fullname (does anyone has any idea what would that happen tho?) --- paper/paper.bib | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/paper/paper.bib b/paper/paper.bib index 43d53ad20..d70cc6b75 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -52,7 +52,7 @@ @article{kruschke2018rejecting volume = {1}, number = {2}, pages = {270--280}, - author = {John K. Kruschke}, + author = {Kruschke, John K}, title = {Rejecting or Accepting Parameter Values in Bayesian Estimation}, journal = {Advances in Methods and Practices in Psychological Science} } @@ -363,7 +363,7 @@ @book{kruschke2015doing year = 2015, publisher = {Elsevier}, pages = {399--416}, - author = {John K. Kruschke}, + author = {Kruschke, John K}, title = {Stan}, booktitle = {Doing Bayesian Data Analysis} } @@ -487,7 +487,7 @@ @article{kruschke2012time volume = {15}, number = {4}, pages = {722--752}, - author = {John K. Kruschke and Herman Aguinis and Harry Joo}, + author = {Kruschke, John K and Herman Aguinis and Harry Joo}, title = {The Time Has Come: Bayesian methods for data analysis in the organizational sciences}, journal = {Organizational Research Methods} } @@ -543,7 +543,7 @@ @article{kruschke2010believe volume = {14}, number = {7}, pages = {293--300}, - author = {John K. Kruschke}, + author = {Kruschke, John K}, title = {What to believe: Bayesian methods for data analysis}, journal = {Trends in Cognitive Sciences} } From 1290ab38842802d495d1bfd20c7041b4df99b9e0 Mon Sep 17 00:00:00 2001 From: Dominique Makowski Date: Tue, 30 Jul 2019 09:09:06 +0800 Subject: [PATCH 06/21] typos --- paper/paper.md | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 2da481aa0..2fdfcae7b 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -49,7 +49,7 @@ The following demonstration of functions is accompanied by figures to illustrate **bayestestR** offers two functions to compute point-estimates from posterior distributions: `map_estimate()` and `point_estimate()`, the latter providing options to calculate the mean, median or MAP estimate of a posterior distribution. [`map_estimate()`](https://easystats.github.io/bayestestR/reference/map_estimate.html) is a convenient function to calculate the **Maximum A Posteriori** (MAP) estimate directly. -The **posterior mean** minimizes expected _squared_ error, whereas the **posterior median** minimizes expected _absolute_ error (i.e. the difference of estimates from true values over samples). The **MAP estimate** corresponds to the most probable value of a posterior distribution. +The **posterior mean** minimizes expected _squared_ error, whereas the **posterior median** minimizes expected _absolute_ error (i.e., the difference of estimates from true values over samples). The **MAP estimate** corresponds to the most probable value of a posterior distribution. ``` r set.seed(1) @@ -96,14 +96,14 @@ eti(posterior) ## Null-Hypothesis Significance Testing (NHST) -The Bayesian framework allows to neatly delineate and quantify different aspects of hypothesis testing, including effect *existence* and *significance*, and different indices have been developped to describe them. +The Bayesian framework allows one to neatly delineate and quantify different aspects of hypothesis testing, including effect *existence* and *significance*, and different indices have been developed to describe them. ### ROPE and Test for Practical Equivalence [`rope()`](https://easystats.github.io/bayestestR/reference/rope.html) computes the proportion of the HDI (default to the 89% HDI) of a posterior distribution that lies within a Region Of Practical Equivalence (the **ROPE**; see figure 3, panel A). -Statistically, the probability of a posterior distribution of being different from 0 does not make much sense (the probability of it being different from a single point being infinite). Therefore, the idea underlining ROPE is to let the user define an area around the null value enclosing values that are *equivalent to the null* value for practical purposes [@kruschke2018bayesian; @kruschke2018rejecting]. Nevertheless, in the absence of user-provided values, **bayestestR** will automatically find an appropriate range for the ROPE using the [`rope_range()`](https://easystats.github.io/bayestestR/reference/rope_range.html) function. +Statistically, the probability of a posterior distribution of being different from 0 does not make much sense (the probability of it being different from a single point being infinite). Therefore, the idea underlining ROPE is to let the user define an area around the null value enclosing values that are *equivalent to the null* value for practical purposes [@kruschke2018bayesian; @kruschke2018rejecting]. In the absence of user-provided values, **bayestestR** will automatically find an appropriate range for the ROPE using the [`rope_range()`](https://easystats.github.io/bayestestR/reference/rope_range.html) function. ``` r rope(distribution_normal(1000, mean = 1), range = c(-0.5, 0.5)) @@ -147,7 +147,7 @@ p_direction(distribution_normal(100, 0.4, 0.2)) ### Bayes Factor -[**`bayesfactor_parameters()`**](https://easystats.github.io/bayestestR/reference/bayesfactor_parameters.html) computes Bayes factors against the null (either a point or an interval), bases on prior and posterior samples of a single parameter. This Bayes factor indicates the degree by which the mass of the posterior distribution has shifted further away from or closer to the null value(s) (relative to the prior distribution), thus indicating if the null value has become less or more likely given the observed data. +[**`bayesfactor_parameters()`**](https://easystats.github.io/bayestestR/reference/bayesfactor_parameters.html) computes Bayes factors against the null (either a point or an interval), based on prior and posterior samples of a single parameter. This Bayes factor indicates the degree by which the mass of the posterior distribution has shifted further away from or closer to the null value(s) (relative to the prior distribution), thus indicating if the null value has become less or more likely given the observed data. When the null is an interval, the Bayes factor is computed by comparing the prior and posterior odds of the parameter falling within or outside the null; When the null is a point, a Savage-Dickey density ratio is computed, which is also an approximation of a Bayes factor comparing the marginal likelihoods of the model against a model in which the tested parameter has been restricted to the point null [@wagenmakers2010bayesian]. From 7680fed7bbdfa5cc2fbe5864170a13ca3e08db30 Mon Sep 17 00:00:00 2001 From: Dominique Makowski Date: Tue, 30 Jul 2019 09:52:55 +0800 Subject: [PATCH 07/21] in-text figures reference --- paper/paper.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 2fdfcae7b..22c24fe0a 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -47,7 +47,7 @@ The following demonstration of functions is accompanied by figures to illustrate ## Indices of Centrality: Point-estimates -**bayestestR** offers two functions to compute point-estimates from posterior distributions: `map_estimate()` and `point_estimate()`, the latter providing options to calculate the mean, median or MAP estimate of a posterior distribution. [`map_estimate()`](https://easystats.github.io/bayestestR/reference/map_estimate.html) is a convenient function to calculate the **Maximum A Posteriori** (MAP) estimate directly. +**bayestestR** offers two functions to compute point-estimates from posterior distributions: `map_estimate()` and `point_estimate()`, the latter providing options to calculate the mean, median or MAP estimate of a posterior distribution (see **Figure 1**). [`map_estimate()`](https://easystats.github.io/bayestestR/reference/map_estimate.html) is a convenient function to calculate the **Maximum A Posteriori** (MAP) estimate directly. The **posterior mean** minimizes expected _squared_ error, whereas the **posterior median** minimizes expected _absolute_ error (i.e., the difference of estimates from true values over samples). The **MAP estimate** corresponds to the most probable value of a posterior distribution. @@ -71,10 +71,10 @@ point_estimate(posterior, centrality = "map") ## Quantifying Uncertainty: The Credible Interval (CI) -In order to measure the uncertainty associated with the estimation, **bayestestR** provides two functions: `eti()`, the Equal-Tailed Interval **ETI**, and `hdi()`, the **Highest Density Interval (HDI)**. Both indices (accessible via the `method` argument in the `ci()` function) can be used in the context of Bayesian posterior characterisation as **Credible Interval (CI)**. +In order to measure the uncertainty associated with the estimation, **bayestestR** provides two functions: `eti()`, the **Equal-Tailed Interval (ETI)**, and `hdi()`, the **Highest Density Interval (HDI)**. Both indices (accessible via the `method` argument in the `ci()` function) can be used in the context of Bayesian posterior characterisation as **Credible Interval (CI)**. [`hdi()`](https://easystats.github.io/bayestestR/reference/hdi.html) -computes the HDI of a posterior distribution, i.e., the interval which contains all points within the interval have a higher probability density than points outside the interval. HDIs have a particular property: Unlike an equal-tailed interval (computed by [`eti()`](https://easystats.github.io/bayestestR/reference/eti.html)) that typically exclude 2.5% from each tail of the distribution, the HDI is *not* equal-tailed and therefore always includes the mode(s) of posterior distributions. +computes the HDI of a posterior distribution, i.e., the interval which contains all points within the interval have a higher probability density than points outside the interval (see **Figure 2**). HDIs have a particular property: Unlike an equal-tailed interval (computed by [`eti()`](https://easystats.github.io/bayestestR/reference/eti.html)) that typically exclude 2.5% from each tail of the distribution, the HDI is *not* equal-tailed and therefore always includes the mode(s) of posterior distributions. By default, `hdi()` and `eti()` return the 89% intervals (`ci = 0.89`), deemed to be more stable than, for instance, 95% intervals. An effective sample size of at least 10.000 is recommended if 95% intervals should be computed [@kruschke2015doing]. Moreover, 89 is the highest prime number that does not exceed the already unstable and arbritrary 95% threshold [@mcelreath2018statistical]. @@ -101,7 +101,7 @@ The Bayesian framework allows one to neatly delineate and quantify different asp ### ROPE and Test for Practical Equivalence -[`rope()`](https://easystats.github.io/bayestestR/reference/rope.html) computes the proportion of the HDI (default to the 89% HDI) of a posterior distribution that lies within a Region Of Practical Equivalence (the **ROPE**; see figure 3, panel A). +[`rope()`](https://easystats.github.io/bayestestR/reference/rope.html) computes the proportion of the HDI (default to the 89% HDI) of a posterior distribution that lies within a Region Of Practical Equivalence (the **ROPE**; see **Figure 3**, panel A). Statistically, the probability of a posterior distribution of being different from 0 does not make much sense (the probability of it being different from a single point being infinite). Therefore, the idea underlining ROPE is to let the user define an area around the null value enclosing values that are *equivalent to the null* value for practical purposes [@kruschke2018bayesian; @kruschke2018rejecting]. In the absence of user-provided values, **bayestestR** will automatically find an appropriate range for the ROPE using the [`rope_range()`](https://easystats.github.io/bayestestR/reference/rope_range.html) function. @@ -136,7 +136,7 @@ equivalence_test(model) ### Probability of Direction (*pd*) -[`p_direction()`](https://easystats.github.io/bayestestR/reference/p_direction.html) computes the **Probability of Direction** (*pd*, also known as the Maximum Probability of Effect - *MPE*). This index of effect existence varies between 50% and 100% and can be interpreted as the probability that a parameter (described by its posterior distribution) is strictly positive or negative (whichever is the most probable). It is mathematically defined as the proportion of the posterior distribution that is of the median's sign (see figure 3, panel B). +[`p_direction()`](https://easystats.github.io/bayestestR/reference/p_direction.html) computes the **Probability of Direction** (*pd*, also known as the Maximum Probability of Effect - *MPE*). This index of effect existence varies between 50% and 100% and can be interpreted as the probability that a parameter (described by its posterior distribution) is strictly positive or negative (whichever is the most probable). It is mathematically defined as the proportion of the posterior distribution that is of the median's sign (see **Figure 3**, panel B). ``` r p_direction(distribution_normal(100, 0.4, 0.2)) @@ -166,7 +166,7 @@ bayesfactor_parameters(posterior, prior, direction = "two-sided", null = 0) ### MAP-based *p*-value -[`p_map()`](https://easystats.github.io/bayestestR/reference/p_map.html) computes the odds that a parameter (described by its posterior distribution) has against the null hypothesis (*h0*) using Mills’ *Objective Bayesian Hypothesis Testing* framework [@mills2018objective; @mills2014bayesian]. It corresponds to the density value at 0 divided by the density at the MAP - the Maximum A Posteriori (see figure 3, panel D). +[`p_map()`](https://easystats.github.io/bayestestR/reference/p_map.html) computes the odds that a parameter (described by its posterior distribution) has against the null hypothesis (*h0*) using Mills’ *Objective Bayesian Hypothesis Testing* framework [@mills2018objective; @mills2014bayesian]. It corresponds to the density value at 0 divided by the density at the MAP - the Maximum A Posteriori (see **Figure 3**, panel D). ``` r p_map(distribution_normal(1000, mean = 1)) From 991486b150401c0a67edce23a63f6788068521f4 Mon Sep 17 00:00:00 2001 From: Dominique Makowski Date: Tue, 30 Jul 2019 10:14:56 +0800 Subject: [PATCH 08/21] ROPE-based p value dosc improvement --- R/p_map.R | 2 +- R/p_rope.R | 4 ++-- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/R/p_map.R b/R/p_map.R index 6edea97af..2ea5f8801 100644 --- a/R/p_map.R +++ b/R/p_map.R @@ -1,6 +1,6 @@ #' Bayesian p-value based on the density at the Maximum A Posteriori (MAP) #' -#' Compute a Bayesian equivalent of the p-value, related to the odds that a parameter (described by its posterior distribution) has against the null hypothesis (\emph{h0}) using Mills' (2014, 2017) \emph{Objective Bayesian Hypothesis Testing} framework. It corresponds to the density value at 0 divided by the density at the Maximum A Posteriori (MAP). +#' Compute a Bayesian equivalent of the \emph{p}-value, related to the odds that a parameter (described by its posterior distribution) has against the null hypothesis (\emph{h0}) using Mills' (2014, 2017) \emph{Objective Bayesian Hypothesis Testing} framework. It corresponds to the density value at 0 divided by the density at the Maximum A Posteriori (MAP). #' #' #' @param precision Number of points for density estimation. See the \code{n}-parameter in \link[=density]{density}. diff --git a/R/p_rope.R b/R/p_rope.R index 5806e4efd..1bf7393b3 100644 --- a/R/p_rope.R +++ b/R/p_rope.R @@ -1,9 +1,9 @@ #' ROPE-based p-value #' -#' Compute the ROPE-based p-value, an exploratory index representing the maximum percentage of \link[=hdi]{HDI} that does not contain (positive values) or is entirely contained (negative values) in the negligible values space defined by the \link[=rope]{ROPE}. It differs from the ROPE percentage, \emph{i.e.}, from the proportion of a given CI in the ROPE, as it represents the maximum CI to reach a ROPE proportion of 0\% (positive values) or 100\% (negative values). A ROPE-based \emph{p} of 97\% means that there is a probability of .97 that a parameter (described by its posterior distribution) is outside the ROPE. On the contrary, a ROPE-based p of -97\% means that there is a probability of .97 that the parameter is inside the ROPE. +#' The ROPE-based \emph{p}-value is an exploratory and non-validated index representing the maximum percentage of \link[=hdi]{HDI} that does not contain (or is entirely contained, in which case the value is prefixed with a negative sign), in the negligible values space defined by the \link[=rope]{ROPE}. It differs from the ROPE percentage, \emph{i.e.}, from the proportion of a given CI in the ROPE, as it represents the maximum CI values needed to reach a ROPE proportion of 0\% or 100\%. Whether the index reflects the ROPE reaching 0\% or 100\% is indicated through the sign: a negative sign is added to indicate that the probability corresponds to the probability of a not significant effect (a percentage in ROPE of 100\%). For instance, a ROPE-based \emph{p} of 97\% means that there is a probability of .97 that a parameter (described by its posterior distribution) is outside the ROPE. In other words, the 97\% HDI is the maximum HDI level for which the percentage in ROPE is 0\%. On the contrary, a ROPE-based p of -97\% indicates that there is a probability of .97 that the parameter is inside the ROPE (percentage in ROPE of 100\%). A value close to 0\% would indicate that the mode of the distribution falls perfectly at the edge of the ROPE, in which case the percentage of HDI needed to be on either side of the ROPE becomes infinitely small. Negative values do not refer to negative values \emph{per se}, simply indicating that the value corresponds to non-significance rather than significance. #' #' -#' @param range ROPE's lower and higher bounds. Should be a list of two values (e.g., \code{c(-0.1, 0.1)}) or \code{"default"}. If \code{"default"}, the range is set to \code{c(0.1, 0.1)} if input is a vector and \code{x +- 0.1*SD(response)} if a Bayesian model is provided. +#' @inheritParams rope #' @param precision The precision by which to explore the ROPE space (in percentage). Lower values increase the precision of the returned p value but can be quite computationaly costly. #' #' @inheritParams hdi From 169edc93a2cf36ca6397b222e82de9734a1f7e60 Mon Sep 17 00:00:00 2001 From: Dominique Makowski Date: Tue, 30 Jul 2019 10:20:25 +0800 Subject: [PATCH 09/21] added bayestestR mention in first paragraph --- paper/paper.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/paper/paper.md b/paper/paper.md index 22c24fe0a..0099e0146 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -35,7 +35,7 @@ affiliations: # Introduction -The Bayesian framework for statistics is quickly gaining in popularity among scientists, for reasons such as reliability and accuracy (particularly in noisy data and small samples), the possibility of incorporating prior knowledge into the analysis and the intuitive interpretation of results [@andrews2013prior; @etz2016bayesian; @kruschke2010believe; @kruschke2012time; @wagenmakers2018bayesian]. Adopting the Bayesian framework is more of a shift in the paradigm than a change in the methodology; All the common statistical procedures (*t*-tests, correlations, ANOVAs, regressions, etc.) can also be achieved within the Bayesian framework. One of the core difference is that in the *frequentist* view, the effects are fixed (but unknown) and data are random. On the other hand, instead of having single estimates of the "true effect", the Bayesian inference process computes the probability of different effects *given the observed data*, resulting in a distribution of possible values for the parameters, called the *posterior distribution*. +The Bayesian framework for statistics is quickly gaining in popularity among scientists, for reasons such as reliability and accuracy (particularly in noisy data and small samples), the possibility of incorporating prior knowledge into the analysis and the intuitive interpretation of results [@andrews2013prior; @etz2016bayesian; @kruschke2010believe; @kruschke2012time; @wagenmakers2018bayesian]. Adopting the Bayesian framework is more of a shift in the paradigm than a change in the methodology; All the common statistical procedures (*t*-tests, correlations, ANOVAs, regressions, etc.) can also be achieved within the Bayesian framework. One of the core difference is that in the *frequentist* view, the effects are fixed (but unknown) and data are random. On the other hand, instead of having single estimates of the "true effect", the Bayesian inference process computes the probability of different effects *given the observed data*, resulting in a distribution of possible values for the parameters, called the *posterior distribution*. The **bayestestR** package provides tools to describe these posterior distributions. Effects in the Bayesian framework can be described by [characterizing their posterior distribution](https://easystats.github.io/bayestestR/articles/guidelines.html). Commonly reported indices include measures of centrality (e.g., the median, mean or MAP estimate) and uncertainty (the [*credible* interval](https://easystats.github.io/bayestestR/articles/credible_interval.html) - CI). Cum grano salis, these are considered the counterparts to the coefficient point-estimates and confidence intervals of the frequentist framework. Additionally, **bayestestR** also focuses on implementing a Bayesian null-hypothesis testing framework (in a Bayesian sense, i.e., extended to general testing of "effect existence") by providing access to both established and exploratory indices of effect *existence* and *significance* [such as the Bayes factor, @morey2011bayes; the ROPE, @kruschke2018bayesian; the MAP-based *p*-value, @mills2018objective, or the Probability of Direction - *pd*]. From c2ee166b113a2c63571d98382d8cc4536bf00ecc Mon Sep 17 00:00:00 2001 From: Dominique Makowski Date: Tue, 30 Jul 2019 11:03:28 +0800 Subject: [PATCH 10/21] added visualisation example and that functions can be applied to models --- paper/Figure4.R | 33 ++++++++++++++++++++++++++++++++ paper/Figure4.png | Bin 0 -> 94572 bytes paper/paper.bib | 8 ++++++++ paper/paper.md | 47 +++++++++++++++++++++++++++++++++++++++++++++- 4 files changed, 87 insertions(+), 1 deletion(-) create mode 100644 paper/Figure4.R create mode 100644 paper/Figure4.png diff --git a/paper/Figure4.R b/paper/Figure4.R new file mode 100644 index 000000000..0dfb2f3a3 --- /dev/null +++ b/paper/Figure4.R @@ -0,0 +1,33 @@ +library(bayestestR) +library(tidyverse) + + +# Load the rstanarm and the see package +library(rstanarm) +library(see) + +# Fit a Bayesian linear regression +model <- stan_glm(Petal.Width ~ Petal.Length * Sepal.Width, data = iris) + +# Store results +result_pd <- p_direction(model) + +print(result_pd) +plot(result_pd) + +# Save -------------------------------------------------------------------- + +x <- data_plot(pd(model)) + +p <- x %>% + filter(y != "(Intercept)") %>% + as.data.frame() %>% + ggplot(aes(x = x, y = y, height = height, group = y, fill = fill)) + + ggridges::geom_ridgeline_gradient(color = "white") + + add_plot_attributes(x) + + geom_vline(aes(xintercept = 0), linetype = "dotted") + + theme_modern() + + scale_fill_manual(values = c("Negative" = "#E91E63", "Positive" = "#4CAF50")) + + theme(plot.title = element_text(hjust = 0.5)) +p +ggsave("Figure4.png", plot = p, width = 13, height = 8, units = "in", dpi = 450) diff --git a/paper/Figure4.png b/paper/Figure4.png new file mode 100644 index 0000000000000000000000000000000000000000..2329188810254475cbc83b442778052ed6bbb0a7 GIT binary patch literal 94572 zcmeFZXFyZS7BD)YBMNp9q$nUF)ppQ8Ac{%}f*nwrN)Zt(ARslzdK9G>3r$T#MFk^< zW*}CY0&Y|ck)j|F2|WZ6fj5bJpK$MeKi==}eL4FCGpt#&X7yQX$i;2;RZ`)SED`4x^*sTEpTLa*G?$+4Yt+DXE(i>vL!w1fU)8YkF 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z7^w!vj~9XPoTiDL3*1>fW2ZrVXAmfX+l^R_Q1@t#`aI1vU) MAP = 1.46 point_estimate(posterior) + #> Median = 2.31 point_estimate(posterior, centrality = "mean") + #> Mean = 2.96 point_estimate(posterior, centrality = "map") + #> MAP = 1.46 ``` @@ -80,12 +84,14 @@ By default, `hdi()` and `eti()` return the 89% intervals (`ci = 0.89`), deemed t ``` r hdi(posterior) + #> # Highest Density Interval #> #> 89% HDI #> [0.11, 6.05] eti(posterior) + #> # Equal-Tailed Interval #> #> 89% ETI @@ -107,6 +113,7 @@ Statistically, the probability of a posterior distribution of being different fr ``` r rope(distribution_normal(1000, mean = 1), range = c(-0.5, 0.5)) + #> # Proportion of samples inside the ROPE [-0.50, 0.50]: #> #> inside ROPE @@ -122,6 +129,7 @@ The proportion of HDI lying within this "null" region can be used as an decision library(rstanarm) model <- stan_glm(mpg ~ wt + gear, data = mtcars) equivalence_test(model) + #> # Test for Practical Equivalence #> #> ROPE: [-0.60 0.60] @@ -140,6 +148,7 @@ equivalence_test(model) ``` r p_direction(distribution_normal(100, 0.4, 0.2)) + #> # Probability of Direction (pd) #> #> pd = 98.00% @@ -156,6 +165,7 @@ prior <- distribution_normal(1000, mean = 0, sd = 1) posterior <- distribution_normal(1000, mean = 1, sd = 0.7) bayesfactor_parameters(posterior, prior, direction = "two-sided", null = 0) + #> # Bayes Factor (Savage-Dickey density ratio) #> #> Bayes Factor @@ -175,6 +185,41 @@ p_map(distribution_normal(1000, mean = 1)) #> p (MAP) = 0.629 ``` +## Visualisation and Compatibility with Models + + + +Most of bayestestR functions can be visualised (see **Figure 4**) by passing them in the `plot()` function (the [**see**](https://github.com/easystats/see) package needs to be installed). Moreover, these functions can be directly applied to statistical models (fitted for instance with **rstanarm** or **brms**), resulting in the description of the parameters of the model. + + +``` r +# Load the rstanarm and the see package +library(rstanarm) +library(see) + +# Fit a Bayesian linear regression +model <- stan_glm(Petal.Width ~ Petal.Length * Sepal.Width, data = iris) + +# Store results +result_pd <- p_direction(model) + +# Print and plot results +print(result_pd) + +# Probability of Direction (pd) + + Parameter pd + (Intercept) 72.47% + Petal.Length 99.88% + Sepal.Width 70.97% + Petal.Length:Sepal.Width 96.70% + +plot(result_pd) +``` + +![Visualisation of the pd for the parameters of a Bayesian regression model.](Figure4.png) + + # Licensing and Availability **bayestestR** is licensed under the GNU General Public License (v3.0), with all source code stored at GitHub (https://github.com/easystats/bayestestR), with a corresponding issue tracker for bug-reporting and feature enhancements. In the spirit of honest and open science, we encourage requests/tips for fixes, feature updates, as well as general questions and concerns via direct interaction with contributors and developers. From a52de8650ca3dc1c93374cf93e323c395bdffd7b Mon Sep 17 00:00:00 2001 From: Dominique Makowski Date: Tue, 30 Jul 2019 11:30:54 +0800 Subject: [PATCH 11/21] removed probability aliases and clarified docs --- .Rbuildignore | 1 + NAMESPACE | 2 -- R/estimate_density.R | 13 ++----------- man/density_at.Rd | 7 ++----- man/estimate_density.Rd | 4 ---- man/p_map.Rd | 2 +- man/p_rope.Rd | 7 +++---- paper/Figure4.R | 1 + 8 files changed, 10 insertions(+), 27 deletions(-) diff --git a/.Rbuildignore b/.Rbuildignore index 992c767ea..100d947c1 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -1,4 +1,5 @@ ^\.Rprofile$ +^\.github ^.*\.Rproj$ ^\.Rproj\.user$ ^\.travis.yml diff --git a/NAMESPACE b/NAMESPACE index 7b4c6118c..b4767cf86 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -165,7 +165,6 @@ export(distribution_uniform) export(effective_sample) export(equivalence_test) export(estimate_density) -export(estimate_probability) export(eti) export(hdi) export(map_estimate) @@ -177,7 +176,6 @@ export(p_to_pd) export(pd) export(pd_to_p) export(point_estimate) -export(probability_at) export(reshape_ci) export(rnorm_perfect) export(rope) diff --git a/R/estimate_density.R b/R/estimate_density.R index af75d66f0..a80044137 100644 --- a/R/estimate_density.R +++ b/R/estimate_density.R @@ -60,10 +60,6 @@ estimate_density <- function(x, method = "kernel", precision = 2^10, extend = FA UseMethod("estimate_density") } -#' @rdname estimate_density -#' @export -estimate_probability <- estimate_density - #' @keywords internal @@ -200,9 +196,9 @@ as.data.frame.density <- function(x, ...) { -#' Probability of a Given Point +#' Density Probability at a Given Value #' -#' Compute the density of a given point of a distribution. +#' Compute the density value at a given point of a distribution (i.e., the value of the \code{y} axis of a value \code{x} of a distribution). #' #' @param posterior Vector representing a posterior distribution. #' @param x The value of which to get the approximate probability. @@ -220,8 +216,3 @@ density_at <- function(posterior, x, precision = 2^10, ...) { stats::approx(density$x, density$y, xout = x)$y } - - -#' @rdname density_at -#' @export -probability_at <- density_at diff --git a/man/density_at.Rd b/man/density_at.Rd index b6573c013..b9719e15b 100644 --- a/man/density_at.Rd +++ b/man/density_at.Rd @@ -2,12 +2,9 @@ % Please edit documentation in R/estimate_density.R \name{density_at} \alias{density_at} -\alias{probability_at} -\title{Probability of a Given Point} +\title{Density Probability at a Given Value} \usage{ density_at(posterior, x, precision = 2^10, ...) - -probability_at(posterior, x, precision = 2^10, ...) } \arguments{ \item{posterior}{Vector representing a posterior distribution.} @@ -19,7 +16,7 @@ probability_at(posterior, x, precision = 2^10, ...) \item{...}{Currently not used.} } \description{ -Compute the density of a given point of a distribution. +Compute the density value at a given point of a distribution (i.e., the value of the \code{y} axis of a value \code{x} of a distribution). } \examples{ library(bayestestR) diff --git a/man/estimate_density.Rd b/man/estimate_density.Rd index 216a08cbb..0057c015b 100644 --- a/man/estimate_density.Rd +++ b/man/estimate_density.Rd @@ -2,14 +2,10 @@ % Please edit documentation in R/estimate_density.R \name{estimate_density} \alias{estimate_density} -\alias{estimate_probability} \title{Density Estimation} \usage{ estimate_density(x, method = "kernel", precision = 2^10, extend = FALSE, extend_scale = 0.1, bw = "SJ", ...) - -estimate_probability(x, method = "kernel", precision = 2^10, - extend = FALSE, extend_scale = 0.1, bw = "SJ", ...) } \arguments{ \item{x}{Vector representing a posterior distribution. Can also be a diff --git a/man/p_map.Rd b/man/p_map.Rd index 46a9c4c7e..4f995172a 100644 --- a/man/p_map.Rd +++ b/man/p_map.Rd @@ -43,7 +43,7 @@ or the zero-inflated part of the model be returned? May be abbreviated. Only applies to \pkg{brms}-models.} } \description{ -Compute a Bayesian equivalent of the p-value, related to the odds that a parameter (described by its posterior distribution) has against the null hypothesis (\emph{h0}) using Mills' (2014, 2017) \emph{Objective Bayesian Hypothesis Testing} framework. It corresponds to the density value at 0 divided by the density at the Maximum A Posteriori (MAP). +Compute a Bayesian equivalent of the \emph{p}-value, related to the odds that a parameter (described by its posterior distribution) has against the null hypothesis (\emph{h0}) using Mills' (2014, 2017) \emph{Objective Bayesian Hypothesis Testing} framework. It corresponds to the density value at 0 divided by the density at the Maximum A Posteriori (MAP). } \examples{ library(bayestestR) diff --git a/man/p_rope.Rd b/man/p_rope.Rd index d432ad27a..ab02ee102 100644 --- a/man/p_rope.Rd +++ b/man/p_rope.Rd @@ -29,12 +29,11 @@ p_rope(x, ...) "zi", "zero_inflated", "all"), parameters = NULL, ...) } \arguments{ -\item{x}{Vector representing a posterior distribution. Can also be a -\code{stanreg}, \code{brmsfit} or a \code{BayesFactor} model.} +\item{x}{Vector representing a posterior distribution. Can also be a \code{stanreg} or \code{brmsfit} model.} \item{...}{Currently not used.} -\item{range}{ROPE's lower and higher bounds. Should be a list of two values (e.g., \code{c(-0.1, 0.1)}) or \code{"default"}. If \code{"default"}, the range is set to \code{c(0.1, 0.1)} if input is a vector and \code{x +- 0.1*SD(response)} if a Bayesian model is provided.} +\item{range}{ROPE's lower and higher bounds. Should be a vector of length two (e.g., \code{c(-0.1, 0.1)}) or \code{"default"}. If \code{"default"}, the range is set to \code{c(-0.1, 0.1)} if input is a vector, and based on \code{\link[=rope_range]{rope_range()}} if a Bayesian model is provided.} \item{precision}{The precision by which to explore the ROPE space (in percentage). Lower values increase the precision of the returned p value but can be quite computationaly costly.} @@ -52,7 +51,7 @@ or the zero-inflated part of the model be returned? May be abbreviated. Only applies to \pkg{brms}-models.} } \description{ -Compute the ROPE-based p-value, an exploratory index representing the maximum percentage of \link[=hdi]{HDI} that does not contain (positive values) or is entirely contained (negative values) in the negligible values space defined by the \link[=rope]{ROPE}. It differs from the ROPE percentage, \emph{i.e.}, from the proportion of a given CI in the ROPE, as it represents the maximum CI to reach a ROPE proportion of 0\% (positive values) or 100\% (negative values). A ROPE-based \emph{p} of 97\% means that there is a probability of .97 that a parameter (described by its posterior distribution) is outside the ROPE. On the contrary, a ROPE-based p of -97\% means that there is a probability of .97 that the parameter is inside the ROPE. +The ROPE-based \emph{p}-value is an exploratory and non-validated index representing the maximum percentage of \link[=hdi]{HDI} that does not contain (or is entirely contained, in which case the value is prefixed with a negative sign), in the negligible values space defined by the \link[=rope]{ROPE}. It differs from the ROPE percentage, \emph{i.e.}, from the proportion of a given CI in the ROPE, as it represents the maximum CI values needed to reach a ROPE proportion of 0\% or 100\%. Whether the index reflects the ROPE reaching 0\% or 100\% is indicated through the sign: a negative sign is added to indicate that the probability corresponds to the probability of a not significant effect (a percentage in ROPE of 100\%). For instance, a ROPE-based \emph{p} of 97\% means that there is a probability of .97 that a parameter (described by its posterior distribution) is outside the ROPE. In other words, the 97\% HDI is the maximum HDI level for which the percentage in ROPE is 0\%. On the contrary, a ROPE-based p of -97\% indicates that there is a probability of .97 that the parameter is inside the ROPE (percentage in ROPE of 100\%). A value close to 0\% would indicate that the mode of the distribution falls perfectly at the edge of the ROPE, in which case the percentage of HDI needed to be on either side of the ROPE becomes infinitely small. Negative values do not refer to negative values \emph{per se}, simply indicating that the value corresponds to non-significance rather than significance. } \examples{ library(bayestestR) diff --git a/paper/Figure4.R b/paper/Figure4.R index 0dfb2f3a3..ba9082f75 100644 --- a/paper/Figure4.R +++ b/paper/Figure4.R @@ -12,6 +12,7 @@ model <- stan_glm(Petal.Width ~ Petal.Length * Sepal.Width, data = iris) # Store results result_pd <- p_direction(model) +# Print and plot results print(result_pd) plot(result_pd) From 158e45a320d969041ab7e27f779842d6cd28f743 Mon Sep 17 00:00:00 2001 From: mattansb <35330040+mattansb@users.noreply.github.com> Date: Tue, 30 Jul 2019 09:45:00 +0300 Subject: [PATCH 12/21] explain BF fig --- README.Rmd | 1 + 1 file changed, 1 insertion(+) diff --git a/README.Rmd b/README.Rmd index f7ef8c638..198bef972 100644 --- a/README.Rmd +++ b/README.Rmd @@ -259,6 +259,7 @@ posterior %>% xlab("\nParameter Value") + ylab("Probability Density\n") ``` +
*The lollipops represent the density of a point-null on the prior distribution (the blue lollipop on the dotted distribution) and on the posterior distribution (the red lollipop on the yellow distribution). The ratio between the two - the Svage-Dickey ratio - indicates the degree by which the mass of the parameter distribution has shifted away from or closer to the null.*
For more info, see [the Bayes factors vignette](https://easystats.github.io/bayestestR/articles/bayes_factors.html). From 57c9eaf5273af38ea06fd3c5e2d93470f4aedb1f Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Daniel=20L=C3=BCdecke?= Date: Tue, 30 Jul 2019 10:24:08 +0200 Subject: [PATCH 13/21] add textual output to readme --- README.Rmd | 39 ++++++++++-------- README.md | 62 ++++++++++++++++++++++++++--- man/figures/unnamed-chunk-10-1.png | Bin 103906 -> 62867 bytes man/figures/unnamed-chunk-13-1.png | Bin 100347 -> 57260 bytes man/figures/unnamed-chunk-15-1.png | Bin 103543 -> 62491 bytes man/figures/unnamed-chunk-17-1.png | Bin 109194 -> 62998 bytes man/figures/unnamed-chunk-6-1.png | Bin 107879 -> 62148 bytes man/figures/unnamed-chunk-8-1.png | Bin 119273 -> 67667 bytes 8 files changed, 79 insertions(+), 22 deletions(-) diff --git a/README.Rmd b/README.Rmd index 198bef972..abf9de9e6 100644 --- a/README.Rmd +++ b/README.Rmd @@ -81,7 +81,7 @@ Click on the buttons above to access the package [**documentation**](https://eas [**`describe_posterior()`**](https://easystats.github.io/bayestestR/reference/describe_posterior.html) is the master function with which you can compute all of the indices cited below *at once*. -```{r message=FALSE, warning=FALSE, results='hide'} +```{r message=FALSE, warning=FALSE} describe_posterior(rnorm(1000)) ``` @@ -93,8 +93,9 @@ describe_posterior(rnorm(1000)) [**`map_estimate()`**](https://easystats.github.io/bayestestR/reference/map_estimate.html) find the **Highest Maximum A Posteriori (MAP)** estimate of a posterior, *i.e.*, the value associated with the highest probability density (the "peak" of the posterior distribution). In other words, it is an estimation of the *mode* for continuous parameters. -```{r message=FALSE, warning=FALSE, results='hide'} -map_estimate(rnorm(1000, 1, 1)) +```{r message=FALSE, warning=FALSE} +posterior <- distribution_normal(100, 0.4, 0.2) +map_estimate(posterior) ``` ```{r message=FALSE, warning=FALSE, echo=FALSE} @@ -126,8 +127,9 @@ Unlike equal-tailed intervals (see [`ci()`](https://easystats.github.io/bayestes By default, `hdi()` returns the 89\% intervals (`ci = 0.89`), deemed to be more stable than, for instance, 95\% intervals (Kruschke, 2014). An effective sample size of at least 10.000 is recommended if 95\% intervals should be computed (Kruschke 2014, p. 183ff). Moreover, 89 is the highest prime number that does not exceed the already unstable 95\% threshold (McElreath, 2015). -```{r message=FALSE, warning=FALSE, results='hide'} -hdi(rnorm(1000), ci = .89) +```{r message=FALSE, warning=FALSE} +posterior <- distribution_normal(100, 0.4, 0.2) +hdi(posterior, ci = .89) ``` ```{r message=FALSE, warning=FALSE, echo=FALSE} @@ -162,8 +164,9 @@ Kruschke (2018) suggests that such null value could be set, by default, to the - Kruschke (2010, 2011, 2014) suggests using the proportion of the 95\% (or 90\%, considered more stable) HDI that falls within the ROPE as an index for "null-hypothesis" testing (as understood under the Bayesian framework, see [equivalence_test](https://easystats.github.io/bayestestR/reference/equivalence_test.html)). -```{r message=FALSE, warning=FALSE, results='hide'} -rope(rnorm(1000, 1, 1), range = c(-0.1, 0.1)) +```{r message=FALSE, warning=FALSE} +posterior <- distribution_normal(100, 0.4, 0.2) +rope(posterior, range = c(-0.1, 0.1)) ``` ```{r message=FALSE, warning=FALSE, echo=FALSE} @@ -192,8 +195,9 @@ posterior %>% **Test for Practical Equivalence** based on the *"HDI+ROPE decision rule"* (Kruschke, 2018) to check whether parameter values should be accepted or rejected against an explicitly formulated "null hypothesis" (*i.e.*, a [ROPE](https://easystats.github.io/bayestestR/reference/rope.html)). -```{r message=FALSE, warning=FALSE, results='hide'} -equivalence_test(rnorm(1000, 1, 1), range = c(-0.1, 0.1)) +```{r message=FALSE, warning=FALSE} +posterior <- distribution_normal(100, 0.4, 0.2) +equivalence_test(posterior, range = c(-0.1, 0.1)) ``` @@ -204,8 +208,9 @@ equivalence_test(rnorm(1000, 1, 1), range = c(-0.1, 0.1)) **Relationship with the p-value**: In most cases, it seems that the *pd* corresponds to the frequentist one-sided *p*-value through the formula `p-value = (1-pd/100)` and to the two-sided *p*-value (the most commonly reported) through the formula `p-value = 2*(1-pd/100)`. Thus, a `pd` of `95%`, `97.5%` `99.5%` and `99.95%` corresponds approximately to a two-sided *p*-value of respectively `.1`, `.05`, `.01` and `.001`. See the [*reporting guidelines*](https://easystats.github.io/bayestestR/articles/guidelines.html). -```{r message=FALSE, warning=FALSE, results='hide'} -p_direction(rnorm(1000, mean = 1, sd = 1)) +```{r message=FALSE, warning=FALSE} +posterior <- distribution_normal(100, 0.4, 0.2) +p_direction(posterior) ``` ```{r message=FALSE, warning=FALSE, echo=FALSE} @@ -230,7 +235,7 @@ posterior %>% When the null is an interval, the Bayes factor is computed by comparing the prior and posterior odds of the parameter falling within or outside the null; When the null is a point, a Savage-Dickey density ratio is computed, which is also an approximation of a Bayes factor comparing the marginal likelihoods of the model against a model in which the tested parameter has been restricted to the point null. -```{r message=FALSE, warning=FALSE, results='hide'} +```{r message=FALSE, warning=FALSE} prior <- rnorm(1000, mean = 0, sd = 1) posterior <- rnorm(1000, mean = 1, sd = 0.7) @@ -259,6 +264,7 @@ posterior %>% xlab("\nParameter Value") + ylab("Probability Density\n") ``` +
*The lollipops represent the density of a point-null on the prior distribution (the blue lollipop on the dotted distribution) and on the posterior distribution (the red lollipop on the yellow distribution). The ratio between the two - the Svage-Dickey ratio - indicates the degree by which the mass of the parameter distribution has shifted away from or closer to the null.*
For more info, see [the Bayes factors vignette](https://easystats.github.io/bayestestR/articles/bayes_factors.html). @@ -267,8 +273,9 @@ For more info, see [the Bayes factors vignette](https://easystats.github.io/baye [**`p_map()`**](https://easystats.github.io/bayestestR/reference/p_map.html) computes a Bayesian equivalent of the p-value, related to the odds that a parameter (described by its posterior distribution) has against the null hypothesis (*h0*) using Mills' (2014, 2017) *Objective Bayesian Hypothesis Testing* framework. It corresponds to the density value at 0 divided by the density at the Maximum A Posteriori (MAP). -```{r message=FALSE, warning=FALSE, results='hide'} -p_map(rnorm(1000, 1, 1)) +```{r message=FALSE, warning=FALSE} +posterior <- distribution_normal(100, 0.4, 0.2) +p_map(posterior) ``` ```{r message=FALSE, warning=FALSE, echo=FALSE} @@ -313,7 +320,7 @@ rope_range(model) [**`distribution()`**](https://easystats.github.io/bayestestR/reference/distribution.html): Generate a sample of size n with near-perfect distributions. -```{r message=FALSE, warning=FALSE, results='hide', eval=FALSE} +```{r message=FALSE, warning=FALSE} distribution(n = 10) ``` @@ -321,7 +328,7 @@ distribution(n = 10) [**`density_at()`**](https://easystats.github.io/bayestestR/reference/density_at.html): Compute the density of a given point of a distribution. -```{r message=FALSE, warning=FALSE, results='hide', eval=FALSE} +```{r message=FALSE, warning=FALSE} density_at(rnorm(1000, 1, 1), 1) ``` diff --git a/README.md b/README.md index 64352e335..89dcc2527 100644 --- a/README.md +++ b/README.md @@ -78,6 +78,10 @@ cited below *at once*. ``` r describe_posterior(rnorm(1000)) +## Parameter Median CI CI_low CI_high pd ROPE_CI ROPE_low ROPE_high +## 1 Posterior -0.0013 89 -1.6 1.5 0.5 89 -0.1 0.1 +## ROPE_Percentage +## 1 0.1 ``` ## Point-estimates @@ -91,7 +95,9 @@ find the **Highest Maximum A Posteriori (MAP)** estimate of a posterior, estimation of the *mode* for continuous parameters. ``` r -map_estimate(rnorm(1000, 1, 1)) +posterior <- distribution_normal(100, 0.4, 0.2) +map_estimate(posterior) +## MAP = 0.40 ``` ![](man/figures/unnamed-chunk-6-1.png) @@ -121,7 +127,12 @@ highest prime number that does not exceed the already unstable 95% threshold (McElreath, 2015). ``` r -hdi(rnorm(1000), ci = .89) +posterior <- distribution_normal(100, 0.4, 0.2) +hdi(posterior, ci = .89) +## # Highest Density Interval +## +## 89% HDI +## [0.09, 0.71] ``` ![](man/figures/unnamed-chunk-8-1.png) @@ -157,7 +168,12 @@ framework, see [equivalence\_test](https://easystats.github.io/bayestestR/reference/equivalence_test.html)). ``` r -rope(rnorm(1000, 1, 1), range = c(-0.1, 0.1)) +posterior <- distribution_normal(100, 0.4, 0.2) +rope(posterior, range = c(-0.1, 0.1)) +## # Proportion of samples inside the ROPE [-0.10, 0.10]: +## +## inside ROPE +## 1.11 % ``` ![](man/figures/unnamed-chunk-10-1.png) @@ -172,7 +188,14 @@ accepted or rejected against an explicitly formulated “null hypothesis” [ROPE](https://easystats.github.io/bayestestR/reference/rope.html)). ``` r -equivalence_test(rnorm(1000, 1, 1), range = c(-0.1, 0.1)) +posterior <- distribution_normal(100, 0.4, 0.2) +equivalence_test(posterior, range = c(-0.1, 0.1)) +## # Test for Practical Equivalence +## +## ROPE: [-0.10 0.10] +## +## H0 inside ROPE 89% HDI +## Undecided 0.01 % [0.09 0.71] ``` ### Probability of Direction (*p*d) @@ -198,7 +221,11 @@ the [*reporting guidelines*](https://easystats.github.io/bayestestR/articles/guidelines.html). ``` r -p_direction(rnorm(1000, mean = 1, sd = 1)) +posterior <- distribution_normal(100, 0.4, 0.2) +p_direction(posterior) +## # Probability of Direction (pd) +## +## pd = 98.00% ``` ![](man/figures/unnamed-chunk-13-1.png) @@ -225,10 +252,27 @@ prior <- rnorm(1000, mean = 0, sd = 1) posterior <- rnorm(1000, mean = 1, sd = 0.7) bayesfactor_parameters(posterior, prior, direction = "two-sided", null = 0) +## # Bayes Factor (Savage-Dickey density ratio) +## +## Bayes Factor +## 1.69 +## +## * Evidence Against The Null: [0] ``` ![](man/figures/unnamed-chunk-15-1.png) +
+ +*The lollipops represent the density of a point-null on the prior +distribution (the blue lollipop on the dotted distribution) and on the +posterior distribution (the red lollipop on the yellow distribution). +The ratio between the two - the Svage-Dickey ratio - indicates the +degree by which the mass of the parameter distribution has shifted away +from or closer to the null.* + +
+ For more info, see [the Bayes factors vignette](https://easystats.github.io/bayestestR/articles/bayes_factors.html). @@ -242,7 +286,11 @@ Hypothesis Testing* framework. It corresponds to the density value at 0 divided by the density at the Maximum A Posteriori (MAP). ``` r -p_map(rnorm(1000, 1, 1)) +posterior <- distribution_normal(100, 0.4, 0.2) +p_map(posterior) +## # MAP-based p-value +## +## p (MAP) = 0.193 ``` ![](man/figures/unnamed-chunk-17-1.png) @@ -283,6 +331,7 @@ Generate a sample of size n with near-perfect distributions. ``` r distribution(n = 10) +## [1] -1.28 -0.88 -0.59 -0.34 -0.11 0.11 0.34 0.59 0.88 1.28 ``` ### Probability of a Value @@ -292,6 +341,7 @@ Compute the density of a given point of a distribution. ``` r density_at(rnorm(1000, 1, 1), 1) +## [1] 0.39 ``` ## Credits diff --git a/man/figures/unnamed-chunk-10-1.png b/man/figures/unnamed-chunk-10-1.png index aa3d715d0a8a1f497a33bd5a1dc09a88b0b0a8c3..6b36fc01cce699ca7946f6ec9d920b305786539b 100644 GIT binary patch literal 62867 zcmc$`d0bOh*D$(I0z^cD78L~)6lIXn5sWe@RYD?zsDL6NPG}tfB`SvLP^xIHG7}UT ztcj?gq;&v+KrAX+2JLY|0Rgq(Q7R~5iVSz3l1WAH8b8HJ09rNqzakkjx}5OVrKNCEu3I}P!Mzz-ZQI9>4I 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zR@hQ7l__mAFymyLW{eOS|lQvM~5tUnu6ybJ!5_m6zTlIrfv z;2&&}F0T)4aUPCg8G5no`WaJI?3*xOGSJ^2qIXV3fBYdfFsbjY^1Ro<_KIbp9O0Pf zPDiIxK4dhEuYef;3+UBcO(hyBj@O6Im7-L}@UOE7SurMrNUzmfx48J+j^jXBh+%~! z+1^+E*XZiEvfpY9#YjFqHtl%t*&pov?AV(9>zKa67J+XY0bluYxG>DofwnTW+EJ(! zC(vMK7#fh2x$)09Nvv|_yT8h6U1og#{KN!)_|JU5*W!cI4EE!kQx>jeLoWrZ%4WV~ zuGC}kUNr-KJ~g?!gOUdSEqaeOVnscYZ?3NRPE~?T39Hjt{Pt9jR+TCHo`-?o3$DoFMEwWw5fcRmBQs+pafELJK>yvyDqUzfdiWcTz3h%j+?;h zQIlovzI5GP=VRH2o3t1<6?t%8=IfGpN_l2v=o=O9Tu6770S&@r(z_SS7r&793m!iN zG#^xYB%C|f+Iqh9fgmXG>tKN|bt)uzjSlwd<7I<%UhN8Y))69c{;&_FP+CfUCt)9eODSVdSN6Ln zedKLJ$8=Boa`}vJ;?EpRLk0b>dHqzmGu!xrs=M) Date: Tue, 30 Jul 2019 12:47:33 +0300 Subject: [PATCH 16/21] add sdBF ref --- README.Rmd | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/README.Rmd b/README.Rmd index 9b22e107c..c9ac9ea47 100644 --- a/README.Rmd +++ b/README.Rmd @@ -255,7 +255,8 @@ posterior %>% [**`bayesfactor_parameters()`**](https://easystats.github.io/bayestestR/reference/bayesfactor_parameters.html) computes Bayes factors against the null (either a point or an interval), bases on prior and posterior samples of a single parameter. This Bayes factor indicates the degree by which the mass of the posterior distribution has shifted further away from or closer to the null value(s) (relative to the prior distribution), thus indicating if the null value has become less or more likely given the observed data. -When the null is an interval, the Bayes factor is computed by comparing the prior and posterior odds of the parameter falling within or outside the null; When the null is a point, a Savage-Dickey density ratio is computed, which is also an approximation of a Bayes factor comparing the marginal likelihoods of the model against a model in which the tested parameter has been restricted to the point null. +When the null is an interval, the Bayes factor is computed by comparing the prior and posterior odds of the parameter falling within or outside the null; When the null is a point, a Savage-Dickey density ratio is computed, which is also an approximation of a Bayes factor comparing the marginal likelihoods of the model against a model in which the tested parameter has been restricted to the point null (Wagenmakers, Lodewyckx, Kuriyal, & Grasman, +2010). ```{r message=FALSE, warning=FALSE} prior <- rnorm(1000, mean = 0, sd = 1) From 185e633b915bac6230b52d191dc0d9c49d556f1b Mon Sep 17 00:00:00 2001 From: mattansb <35330040+mattansb@users.noreply.github.com> Date: Tue, 30 Jul 2019 12:49:28 +0300 Subject: [PATCH 17/21] minor verb --- README.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.Rmd b/README.Rmd index c9ac9ea47..f07bc545f 100644 --- a/README.Rmd +++ b/README.Rmd @@ -213,7 +213,7 @@ posterior %>% ### Equivalence test -[**`equivalence_test()`**](https://easystats.github.io/bayestestR/reference/equivalence_test.html) a +[**`equivalence_test()`**](https://easystats.github.io/bayestestR/reference/equivalence_test.html) is a **Test for Practical Equivalence** based on the *"HDI+ROPE decision rule"* (Kruschke, 2018) to check whether parameter values should be accepted or rejected against an explicitly formulated "null hypothesis" (*i.e.*, a [ROPE](https://easystats.github.io/bayestestR/reference/rope.html)). From 0824b23cbf098304f66fbb1fb8e197217875d6a1 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Daniel=20L=C3=BCdecke?= Date: Tue, 30 Jul 2019 11:55:18 +0200 Subject: [PATCH 18/21] add refs to readme --- README.Rmd | 21 +++++------ README.md | 95 ++++++++++++++++++++++++++++++++++++------------- paper/paper.bib | 16 +++++---- 3 files changed, 91 insertions(+), 41 deletions(-) diff --git a/README.Rmd b/README.Rmd index 9b22e107c..ba0ae9926 100644 --- a/README.Rmd +++ b/README.Rmd @@ -9,6 +9,7 @@ vignette: > %\VignetteIndexEntry{README} \usepackage[utf8]{inputenc} %\VignetteEngine{knitr::rmarkdown} +bibliography: paper/paper.bib editor_options: chunk_output_type: console --- @@ -128,7 +129,7 @@ posterior %>% Unlike equal-tailed intervals (see [`eti()`](https://easystats.github.io/bayestestR/reference/eti.html)) that typically exclude 2.5\% from each tail of the distribution, the HDI is *not* equal-tailed and therefore always includes the mode(s) of posterior distributions. -By default, `hdi()` returns the 89\% intervals (`ci = 0.89`), deemed to be more stable than, for instance, 95\% intervals (Kruschke, 2014). An effective sample size of at least 10.000 is recommended if 95\% intervals should be computed (Kruschke 2014, p. 183ff). Moreover, 89 indicates the arbitrariness of interval limits - its only remarkable property is being the highest prime number that does not exceed the already unstable 95\% threshold (McElreath, 2015). +By default, `hdi()` returns the 89\% intervals (`ci = 0.89`), deemed to be more stable than, for instance, 95\% intervals. An effective sample size of at least 10.000 is recommended if 95\% intervals should be computed [@kruschke2015doing]. Moreover, 89 indicates the arbitrariness of interval limits - its only remarkable property is being the highest prime number that does not exceed the already unstable 95\% threshold [@mcelreath2018statistical]. ```{r message=FALSE, warning=FALSE} posterior <- distribution_chisquared(100, 3) @@ -180,11 +181,11 @@ p <- see::plots(p1, p2, tags = TRUE) [**`rope()`**](https://easystats.github.io/bayestestR/reference/rope.html) computes the proportion (in percentage) of the HDI (default to the 89\% HDI) of a posterior distribution that lies within a region of practical equivalence. -Statistically, the probability of a posterior distribution of being different from 0 does not make much sense (the probability of it being different from a single point being infinite). Therefore, the idea underlining ROPE is to let the user define an area around the null value enclosing values that are *equivalent to the null* value for practical purposes (Kruschke 2010, 2011, 2014). +Statistically, the probability of a posterior distribution of being different from 0 does not make much sense (the probability of it being different from a single point being infinite). Therefore, the idea underlining ROPE is to let the user define an area around the null value enclosing values that are *equivalent to the null* value for practical purposes [@kruschke2018bayesian, @kruschke2018rejecting]. -Kruschke (2018) suggests that such null value could be set, by default, to the -0.1 to 0.1 range of a standardized parameter (negligible effect size according to Cohen, 1988). This could be generalized: For instance, for linear models, the ROPE could be set as `0 +/- .1 * sd(y)`. This ROPE range can be automatically computed for models using the [rope_range](https://easystats.github.io/bayestestR/reference/rope_range.html) function. +Kruschke suggests that such null value could be set, by default, to the -0.1 to 0.1 range of a standardized parameter (negligible effect size according to Cohen, 1988). This could be generalized: For instance, for linear models, the ROPE could be set as `0 +/- .1 * sd(y)`. This ROPE range can be automatically computed for models using the [rope_range](https://easystats.github.io/bayestestR/reference/rope_range.html) function. -Kruschke (2010, 2011, 2014) suggests using the proportion of the 95\% (or 90\%, considered more stable) HDI that falls within the ROPE as an index for "null-hypothesis" testing (as understood under the Bayesian framework, see [equivalence_test](https://easystats.github.io/bayestestR/reference/equivalence_test.html)). +Kruschke suggests using the proportion of the 95\% (or 90\%, considered more stable) HDI that falls within the ROPE as an index for "null-hypothesis" testing (as understood under the Bayesian framework, see [equivalence_test](https://easystats.github.io/bayestestR/reference/equivalence_test.html)). ```{r message=FALSE, warning=FALSE} posterior <- distribution_normal(100, 0.4, 0.2) @@ -214,7 +215,7 @@ posterior %>% ### Equivalence test [**`equivalence_test()`**](https://easystats.github.io/bayestestR/reference/equivalence_test.html) a -**Test for Practical Equivalence** based on the *"HDI+ROPE decision rule"* (Kruschke, 2018) to check whether parameter values should be accepted or rejected against an explicitly formulated "null hypothesis" (*i.e.*, a [ROPE](https://easystats.github.io/bayestestR/reference/rope.html)). +**Test for Practical Equivalence** based on the *"HDI+ROPE decision rule"* [@kruschke2018rejecting] to check whether parameter values should be accepted or rejected against an explicitly formulated "null hypothesis" (*i.e.*, a [ROPE](https://easystats.github.io/bayestestR/reference/rope.html)). ```{r message=FALSE, warning=FALSE} @@ -255,7 +256,7 @@ posterior %>% [**`bayesfactor_parameters()`**](https://easystats.github.io/bayestestR/reference/bayesfactor_parameters.html) computes Bayes factors against the null (either a point or an interval), bases on prior and posterior samples of a single parameter. This Bayes factor indicates the degree by which the mass of the posterior distribution has shifted further away from or closer to the null value(s) (relative to the prior distribution), thus indicating if the null value has become less or more likely given the observed data. -When the null is an interval, the Bayes factor is computed by comparing the prior and posterior odds of the parameter falling within or outside the null; When the null is a point, a Savage-Dickey density ratio is computed, which is also an approximation of a Bayes factor comparing the marginal likelihoods of the model against a model in which the tested parameter has been restricted to the point null. +When the null is an interval, the Bayes factor is computed by comparing the prior and posterior odds of the parameter falling within or outside the null; When the null is a point, a Savage-Dickey density ratio is computed, which is also an approximation of a Bayes factor comparing the marginal likelihoods of the model against a model in which the tested parameter has been restricted to the point null [@wagenmakers2010bayesian]. ```{r message=FALSE, warning=FALSE} prior <- rnorm(1000, mean = 0, sd = 1) @@ -325,7 +326,7 @@ posterior %>% ### Find ROPE's appropriate range -[**`rope_range()`**](https://easystats.github.io/bayestestR/reference/rope_range.html): This function attempts at automatically finding suitable "default" values for the Region Of Practical Equivalence (ROPE). Kruschke (2018) suggests that such null value could be set, by default, to a range from `-0.1` to `0.1` of a standardized parameter (negligible effect size according to Cohen, 1988), which can be generalised for linear models to `-0.1 * sd(y), 0.1 * sd(y)`. For logistic models, the parameters expressed in log odds ratio can be converted to standardized difference through the formula `sqrt(3)/pi`, resulting in a range of `-0.05` to `-0.05`. +[**`rope_range()`**](https://easystats.github.io/bayestestR/reference/rope_range.html): This function attempts at automatically finding suitable "default" values for the Region Of Practical Equivalence (ROPE). Kruschke (2018) suggests that such null value could be set, by default, to a range from `-0.1` to `0.1` of a standardized parameter (negligible effect size according to Cohen, 1988), which can be generalised for linear models to `-0.1 * sd(y), 0.1 * sd(y)`. For logistic models, the parameters expressed in log odds ratio can be converted to standardized difference through the formula `sqrt(3)/pi`, resulting in a range of `-0.05` to `0.05`. ```{r message=FALSE, warning=FALSE, results='hide', eval=FALSE} rope_range(model) @@ -355,10 +356,10 @@ density_at(rnorm(1000, 1, 1), 1) ``` - - ## Credits You can cite the package as following: -- Makowski, D., Ben-Shachar M. S., \& Lüdecke, D. (2019). *Understand and Describe Bayesian Models and Posterior Distributions using bayestestR*. Available from https://github.com/easystats/bayestestR. [DOI:10.5281/zenodo.2556486](https://zenodo.org/badge/latestdoi/165641861). \ No newline at end of file +- Makowski, D., Ben-Shachar M. S., \& Lüdecke, D. (2019). *Understand and Describe Bayesian Models and Posterior Distributions using bayestestR*. Available from https://github.com/easystats/bayestestR. [DOI:10.5281/zenodo.2556486](https://zenodo.org/badge/latestdoi/165641861). + +# References diff --git a/README.md b/README.md index f8b76b45e..db6da13d6 100644 --- a/README.md +++ b/README.md @@ -84,10 +84,10 @@ cited below at once. ``` r describe_posterior(rnorm(1000)) -## Parameter Median CI CI_low CI_high pd ROPE_CI ROPE_low ROPE_high -## 1 Posterior 0.053 89 -1.5 1.7 0.52 89 -0.1 0.1 +## Parameter Median CI CI_low CI_high pd ROPE_CI ROPE_low ROPE_high +## 1 Posterior -0.0011 89 -1.6 1.4 0.5 89 -0.1 0.1 ## ROPE_Percentage -## 1 0.084 +## 1 0.095 ``` ## Point-estimates @@ -126,12 +126,12 @@ is *not* equal-tailed and therefore always includes the mode(s) of posterior distributions. By default, `hdi()` returns the 89% intervals (`ci = 0.89`), deemed to -be more stable than, for instance, 95% intervals (Kruschke, 2014). An -effective sample size of at least 10.000 is recommended if 95% intervals -should be computed (Kruschke 2014, p. 183ff). Moreover, 89 indicates the -arbitrariness of interval limits - its only remarkable property is being -the highest prime number that does not exceed the already unstable 95% -threshold (McElreath, 2015). +be more stable than, for instance, 95% intervals. An effective sample +size of at least 10.000 is recommended if 95% intervals should be +computed (Kruschke 2015). Moreover, 89 indicates the arbitrariness of +interval limits - its only remarkable property is being the highest +prime number that does not exceed the already unstable 95% threshold +(McElreath 2018). ``` r posterior <- distribution_chisquared(100, 3) @@ -165,20 +165,20 @@ different from 0 does not make much sense (the probability of it being different from a single point being infinite). Therefore, the idea underlining ROPE is to let the user define an area around the null value enclosing values that are *equivalent to the null* value for practical -purposes (Kruschke 2010, 2011, 2014). +purposes (Kruschke and Liddell 2018, @kruschke2018rejecting). -Kruschke (2018) suggests that such null value could be set, by default, -to the -0.1 to 0.1 range of a standardized parameter (negligible effect -size according to Cohen, 1988). This could be generalized: For instance, -for linear models, the ROPE could be set as `0 +/- .1 * sd(y)`. This -ROPE range can be automatically computed for models using the +Kruschke suggests that such null value could be set, by default, to the +-0.1 to 0.1 range of a standardized parameter (negligible effect size +according to Cohen, 1988). This could be generalized: For instance, for +linear models, the ROPE could be set as `0 +/- .1 * sd(y)`. This ROPE +range can be automatically computed for models using the [rope\_range](https://easystats.github.io/bayestestR/reference/rope_range.html) function. -Kruschke (2010, 2011, 2014) suggests using the proportion of the 95% (or -90%, considered more stable) HDI that falls within the ROPE as an index -for “null-hypothesis” testing (as understood under the Bayesian -framework, see +Kruschke suggests using the proportion of the 95% (or 90%, considered +more stable) HDI that falls within the ROPE as an index for +“null-hypothesis” testing (as understood under the Bayesian framework, +see [equivalence\_test](https://easystats.github.io/bayestestR/reference/equivalence_test.html)). ``` r @@ -196,7 +196,7 @@ rope(posterior, range = c(-0.1, 0.1)) [**`equivalence_test()`**](https://easystats.github.io/bayestestR/reference/equivalence_test.html) a **Test for Practical Equivalence** based on the *“HDI+ROPE decision -rule”* (Kruschke, 2018) to check whether parameter values should be +rule”* (Kruschke 2018) to check whether parameter values should be accepted or rejected against an explicitly formulated “null hypothesis” (*i.e.*, a [ROPE](https://easystats.github.io/bayestestR/reference/rope.html)). @@ -259,7 +259,8 @@ the prior and posterior odds of the parameter falling within or outside the null; When the null is a point, a Savage-Dickey density ratio is computed, which is also an approximation of a Bayes factor comparing the marginal likelihoods of the model against a model in which the tested -parameter has been restricted to the point null. +parameter has been restricted to the point null (Wagenmakers et al. +2010). ``` r prior <- rnorm(1000, mean = 0, sd = 1) @@ -269,7 +270,7 @@ bayesfactor_parameters(posterior, prior, direction = "two-sided", null = 0) ## # Bayes Factor (Savage-Dickey density ratio) ## ## Bayes Factor -## 2.15 +## 1.63 ## ## * Evidence Against The Null: [0] ``` @@ -322,7 +323,7 @@ according to Cohen, 1988), which can be generalised for linear models to `-0.1 * sd(y), 0.1 * sd(y)`. For logistic models, the parameters expressed in log odds ratio can be converted to standardized difference through the formula `sqrt(3)/pi`, resulting in a range of `-0.05` to -`-0.05`. +`0.05`. ``` r rope_range(model) @@ -355,7 +356,7 @@ Compute the density of a given point of a distribution. ``` r density_at(rnorm(1000, 1, 1), 1) -## [1] 0.37 +## [1] 0.39 ``` ## Credits @@ -367,3 +368,49 @@ You can cite the package as following: bayestestR*. Available from . [DOI:10.5281/zenodo.2556486](https://zenodo.org/badge/latestdoi/165641861). + +# References + +
      + +
      + +Kruschke, John K. 2015. *Doing Bayesian Data Analysis: A Tutorial with +R, JAGS, and Stan*. 2. ed. Amsterdam: Elsevier, Academic Press. + +
      + +
      + +———. 2018. “Rejecting or Accepting Parameter Values in Bayesian +Estimation.” *Advances in Methods and Practices in Psychological +Science* 1 (2): 270–80. . + +
      + +
      + +Kruschke, John K, and Torrin M Liddell. 2018. “The Bayesian New +Statistics: Hypothesis Testing, Estimation, Meta-Analysis, and Power +Analysis from a Bayesian Perspective.” *Psychonomic Bulletin & Review* +25 (1): 178–206. . + +
      + +
      + +McElreath, Richard. 2018. *Statistical Rethinking*. Chapman; Hall/CRC. +. + +
      + +
      + +Wagenmakers, Eric-Jan, Tom Lodewyckx, Himanshu Kuriyal, and Raoul +Grasman. 2010. “Bayesian Hypothesis Testing for Psychologists: A +Tutorial on the SavageDickey Method.” *Cognitive Psychology* 60 (3): +158–89. . + +
      + +
      diff --git a/paper/paper.bib b/paper/paper.bib index 0b4b217a0..d32a114ec 100644 --- a/paper/paper.bib +++ b/paper/paper.bib @@ -366,17 +366,19 @@ @article{maxwell2015psychology @book{kruschke2015doing, - doi = {10.1016/b978-0-12-405888-0.00014-3}, - url = {https://doi.org/10.1016%2Fb978-0-12-405888-0.00014-3}, - year = 2015, - publisher = {Elsevier}, - pages = {399--416}, + address = {Amsterdam}, + edition = {2. ed}, + title = {Doing {Bayesian} data analysis: a tutorial with {R}, {JAGS}, and {Stan}}, + isbn = {978-0-12-405888-0}, + shorttitle = {Doing {Bayesian} data analysis}, + language = {eng}, + publisher = {Elsevier, Academic Press}, author = {Kruschke, John K}, - title = {Stan}, - booktitle = {Doing Bayesian Data Analysis} + year = {2015}, } + @misc{morey_2015_blog, title={Multiple Comparisons with BayesFactor, Part 2 – order restrictions}, url={https://richarddmorey.org/category/order-restrictions/}, From 1bb59f1b33008a35bd3154a471545b8e5dfa1c0d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Daniel=20L=C3=BCdecke?= Date: Tue, 30 Jul 2019 11:58:00 +0200 Subject: [PATCH 19/21] knit readme.md --- README.md | 12 ++++++------ 1 file changed, 6 insertions(+), 6 deletions(-) diff --git a/README.md b/README.md index db6da13d6..cb3d09b6e 100644 --- a/README.md +++ b/README.md @@ -84,10 +84,10 @@ cited below at once. ``` r describe_posterior(rnorm(1000)) -## Parameter Median CI CI_low CI_high pd ROPE_CI ROPE_low ROPE_high -## 1 Posterior -0.0011 89 -1.6 1.4 0.5 89 -0.1 0.1 +## Parameter Median CI CI_low CI_high pd ROPE_CI ROPE_low ROPE_high +## 1 Posterior 0.0082 89 -1.5 1.6 0.51 89 -0.1 0.1 ## ROPE_Percentage -## 1 0.095 +## 1 0.11 ``` ## Point-estimates @@ -195,7 +195,7 @@ rope(posterior, range = c(-0.1, 0.1)) ### Equivalence test [**`equivalence_test()`**](https://easystats.github.io/bayestestR/reference/equivalence_test.html) -a **Test for Practical Equivalence** based on the *“HDI+ROPE decision +is a **Test for Practical Equivalence** based on the *“HDI+ROPE decision rule”* (Kruschke 2018) to check whether parameter values should be accepted or rejected against an explicitly formulated “null hypothesis” (*i.e.*, a @@ -270,7 +270,7 @@ bayesfactor_parameters(posterior, prior, direction = "two-sided", null = 0) ## # Bayes Factor (Savage-Dickey density ratio) ## ## Bayes Factor -## 1.63 +## 1.71 ## ## * Evidence Against The Null: [0] ``` @@ -356,7 +356,7 @@ Compute the density of a given point of a distribution. ``` r density_at(rnorm(1000, 1, 1), 1) -## [1] 0.39 +## [1] 0.35 ``` ## Credits From 006b13d75289983c3cf2f51f892a04a15e95f739 Mon Sep 17 00:00:00 2001 From: Dominique Makowski Date: Tue, 30 Jul 2019 19:35:01 +0800 Subject: [PATCH 20/21] ci_method for ROPE --- R/rope.R | 26 ++++++++++++++------------ man/rope.Rd | 16 +++++++++------- 2 files changed, 23 insertions(+), 19 deletions(-) diff --git a/R/rope.R b/R/rope.R index 76cbff503..54b5a09be 100644 --- a/R/rope.R +++ b/R/rope.R @@ -5,6 +5,7 @@ #' @param x Vector representing a posterior distribution. Can also be a \code{stanreg} or \code{brmsfit} model. #' @param range ROPE's lower and higher bounds. Should be a vector of length two (e.g., \code{c(-0.1, 0.1)}) or \code{"default"}. If \code{"default"}, the range is set to \code{c(-0.1, 0.1)} if input is a vector, and based on \code{\link[=rope_range]{rope_range()}} if a Bayesian model is provided. #' @param ci The Credible Interval (CI) probability, corresponding to the proportion of HDI, to use for the percentage in ROPE. +#' @param ci_method The type of interval to use to quantify the percentage in ROPE. Can be 'HDI' (default) or 'ETI'. See \code{\link{ci}}. #' #' @inheritParams hdi #' @@ -116,7 +117,7 @@ rope.default <- function(x, ...) { #' @rdname rope #' @export -rope.numeric <- function(x, range = "default", ci = .89, verbose = TRUE, ...) { +rope.numeric <- function(x, range = "default", ci = .89, ci_method = "HDI", verbose = TRUE, ...) { if (all(range == "default")) { range <- c(-0.1, 0.1) } else if (!all(is.numeric(range)) || length(range) != 2) { @@ -124,7 +125,7 @@ rope.numeric <- function(x, range = "default", ci = .89, verbose = TRUE, ...) { } rope_values <- lapply(ci, function(i) { - .rope(x, range = range, ci = i, verbose = verbose) + .rope(x, range = range, ci = i, ci_method = ci_method, verbose = verbose) }) # "do.call(rbind)" does not bind attribute values together @@ -153,8 +154,8 @@ rope.numeric <- function(x, range = "default", ci = .89, verbose = TRUE, ...) { #' @rdname rope #' @export -rope.data.frame <- function(x, range = "default", ci = .89, verbose = TRUE, ...) { - out <- .prepare_rope_df(x, range, ci, verbose) +rope.data.frame <- function(x, range = "default", ci = .89, ci_method = "HDI", verbose = TRUE, ...) { + out <- .prepare_rope_df(x, range, ci, ci_method, verbose) HDI_area_attributes <- .compact_list(out$HDI_area) dat <- data.frame( Parameter = rep(names(HDI_area_attributes), each = length(ci)), @@ -193,9 +194,9 @@ rope.BFBayesFactor <- function(x, range = "default", ci = .89, verbose = TRUE, . } - -.rope <- function(x, range = c(-0.1, 0.1), ci = .89, verbose = TRUE) { - HDI_area <- .hdi_area <- hdi(x, ci, verbose) +#' @keywords internal +.rope <- function(x, range = c(-0.1, 0.1), ci = .89, ci_method = "HDI", verbose = TRUE) { + HDI_area <- .hdi_area <- ci(x, ci = ci, method = ci_method, verbose = verbose) if (anyNA(HDI_area)) { rope_percentage <- NA @@ -222,7 +223,7 @@ rope.BFBayesFactor <- function(x, range = "default", ci = .89, verbose = TRUE, . #' @rdname rope #' @export -rope.stanreg <- function(x, range = "default", ci = .89, effects = c("fixed", "random", "all"), parameters = NULL, verbose = TRUE, ...) { +rope.stanreg <- function(x, range = "default", ci = .89, ci_method = "HDI", effects = c("fixed", "random", "all"), parameters = NULL, verbose = TRUE, ...) { effects <- match.arg(effects) if (all(range == "default")) { @@ -237,7 +238,7 @@ rope.stanreg <- function(x, range = "default", ci = .89, effects = c("fixed", "r list <- lapply(c("fixed", "random"), function(.x) { parms <- insight::get_parameters(x, effects = .x, parameters = parameters) - getropedata <- .prepare_rope_df(parms, range, ci, verbose) + getropedata <- .prepare_rope_df(parms, range, ci, ci_method, verbose) tmp <- getropedata$tmp HDI_area <- getropedata$HDI_area @@ -290,7 +291,7 @@ rope.stanreg <- function(x, range = "default", ci = .89, effects = c("fixed", "r #' @rdname rope #' @export -rope.brmsfit <- function(x, range = "default", ci = .89, effects = c("fixed", "random", "all"), component = c("conditional", "zi", "zero_inflated", "all"), parameters = NULL, verbose = TRUE, ...) { +rope.brmsfit <- function(x, range = "default", ci = .89, ci_method = "HDI", effects = c("fixed", "random", "all"), component = c("conditional", "zi", "zero_inflated", "all"), parameters = NULL, verbose = TRUE, ...) { effects <- match.arg(effects) component <- match.arg(component) @@ -313,7 +314,7 @@ rope.brmsfit <- function(x, range = "default", ci = .89, effects = c("fixed", "r .get_rope <- function(.x, .y) { parms <- insight::get_parameters(x, effects = .x, component = .y, parameters = parameters) - getropedata <- .prepare_rope_df(parms, range, ci, verbose) + getropedata <- .prepare_rope_df(parms, range, ci, ci_method, verbose) tmp <- getropedata$tmp HDI_area <- getropedata$HDI_area @@ -379,12 +380,13 @@ rope.brmsfit <- function(x, range = "default", ci = .89, effects = c("fixed", "r #' @keywords internal -.prepare_rope_df <- function(parms, range, ci, verbose) { +.prepare_rope_df <- function(parms, range, ci, ci_method, verbose) { tmp <- sapply( parms, rope, range = range, ci = ci, + ci_method = ci_method, verbose = verbose, simplify = FALSE ) diff --git a/man/rope.Rd b/man/rope.Rd index 8bed5e8c9..3c0c4ed71 100644 --- a/man/rope.Rd +++ b/man/rope.Rd @@ -16,10 +16,10 @@ rope(x, ...) \method{rope}{default}(x, ...) \method{rope}{numeric}(x, range = "default", ci = 0.89, - verbose = TRUE, ...) + ci_method = "HDI", verbose = TRUE, ...) \method{rope}{data.frame}(x, range = "default", ci = 0.89, - verbose = TRUE, ...) + ci_method = "HDI", verbose = TRUE, ...) \method{rope}{emmGrid}(x, range = "default", ci = 0.89, verbose = TRUE, ...) @@ -28,13 +28,13 @@ rope(x, ...) verbose = TRUE, ...) \method{rope}{stanreg}(x, range = "default", ci = 0.89, - effects = c("fixed", "random", "all"), parameters = NULL, - verbose = TRUE, ...) + ci_method = "HDI", effects = c("fixed", "random", "all"), + parameters = NULL, verbose = TRUE, ...) \method{rope}{brmsfit}(x, range = "default", ci = 0.89, - effects = c("fixed", "random", "all"), component = c("conditional", - "zi", "zero_inflated", "all"), parameters = NULL, verbose = TRUE, - ...) + ci_method = "HDI", effects = c("fixed", "random", "all"), + component = c("conditional", "zi", "zero_inflated", "all"), + parameters = NULL, verbose = TRUE, ...) } \arguments{ \item{x}{Vector representing a posterior distribution. Can also be a \code{stanreg} or \code{brmsfit} model.} @@ -45,6 +45,8 @@ rope(x, ...) \item{ci}{The Credible Interval (CI) probability, corresponding to the proportion of HDI, to use for the percentage in ROPE.} +\item{ci_method}{The type of interval to use to quantify the percentage in ROPE. Can be 'HDI' (default) or 'ETI'. See \code{\link{ci}}.} + \item{verbose}{Toggle off warnings.} \item{effects}{Should results for fixed effects, random effects or both be returned? From a40e63036c873b687489a30f7e4729239032a2bd Mon Sep 17 00:00:00 2001 From: Dominique Makowski Date: Tue, 30 Jul 2019 19:43:18 +0800 Subject: [PATCH 21/21] added Tristan as reviewer in DESCRIPTION (and version bump) --- DESCRIPTION | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/DESCRIPTION b/DESCRIPTION index f39e69a10..d8bb8bd98 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -1,7 +1,7 @@ Package: bayestestR Type: Package Title: Understand and Describe Bayesian Models and Posterior Distributions -Version: 0.2.4 +Version: 0.2.5 Authors@R: c( person("Dominique", "Makowski", @@ -26,7 +26,11 @@ Authors@R: c( person("Paul-Christian", "Bürkner", role = c("rev"), - email = "paul.buerkner@gmail.com") + email = "paul.buerkner@gmail.com"), + person("Tristan", + "Mahr", + role = c("rev"), + email = "tristan.mahr@gmail.com") ) Maintainer: Dominique Makowski URL: https://github.com/easystats/bayestestR

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zMmb5NXeHHu5=6nZTz*MXzU&z0+q(4S_+MSMXL|d@1#>u!6}k<6eX?7se(lXzT&JtN z`E%dfSDxL^dk6=oek)@_d5v4kC>_bvsWj`FiWMqo7t?CW;}QK2{O^5 zsB$pY)Eb$hmqK}bsOa*N) zB!%VGj{-9hfTm8eTawJA7wX53i!YdccTb*LoQ zySAh^Ovc1}Di`?XJ4RpS1v~Hu0JuNG!&4xbhDBd}_`>b0UGsu2-Pw$M9QV+feVKdE z<^}b<<4obLU$MjC*?}b~v|4oD{-m1(wSKxqjc@|Emha4r@(dWaP9oM=p{duFWT&jT zyheJ{ZMJW+6(WfdWpF1DC?l9sCh-Hfb;3m6MYl~=!6+x+%KrR>&s z$d(m=aW{IDjjSh4)~Qi+DR&)3@zv6NyluC#865B2;8-%TFksfY^}#RUM_+3@(>6z4 zR)2>536MwtG}~#cheYJJl9p>USH9wRkqH+tfdmaJej~v&R0xQ;m`A<$EITx-yyX{q97SCf>;W=fj0-$P@>lD=*0L|JdF}d)tw9)#@}0tq4%So2!8xng9G5G@X*F@YEnS|!1(*0{|_5Q-qolFypOIk P$ko?1(J44-f9L-I+in61 From 3796c930b0c72350f79e07e368b2727f39fef05d Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Daniel=20L=C3=BCdecke?= Date: Tue, 30 Jul 2019 11:07:11 +0200 Subject: [PATCH 14/21] plot-method for map_estimate() --- NAMESPACE | 1 + R/map_estimate.R | 9 ++++++++- R/plot.R | 9 +++++++++ 3 files changed, 18 insertions(+), 1 deletion(-) diff --git a/NAMESPACE b/NAMESPACE index b4767cf86..8734d519f 100644 --- a/NAMESPACE +++ b/NAMESPACE @@ -101,6 +101,7 @@ S3method(plot,equivalence_test) S3method(plot,estimate_density) S3method(plot,eti) S3method(plot,hdi) +S3method(plot,map_estimate) S3method(plot,p_direction) S3method(plot,point_estimate) S3method(plot,rope) diff --git a/R/map_estimate.R b/R/map_estimate.R index 964fb8662..782903080 100644 --- a/R/map_estimate.R +++ b/R/map_estimate.R @@ -63,7 +63,10 @@ map_estimate.numeric <- function(x, precision = 2^10, ...) { out <- hdp_x attr(out, "MAP_density") <- hdp_y - class(out) <- unique(c("map_estimate", class(out))) + attr(out, "data") <- x + attr(out, "centrality") <- "map" + class(out) <- unique(c("map_estimate", "see_point_estimate", class(out))) + out } @@ -86,6 +89,10 @@ map_estimate.numeric <- function(x, precision = 2^10, ...) { ) attr(out, "MAP_density") <- sapply(l, attr, "MAP_density") + attr(out, "object_name") <- deparse(substitute(x), width.cutoff = 500) + attr(out, "centrality") <- "map" + class(out) <- unique(c("map_estimate", "see_point_estimate", class(out))) + class(out) <- unique(c("map_estimate", class(out))) out } diff --git a/R/plot.R b/R/plot.R index e1d8851a2..bad0ce4b7 100644 --- a/R/plot.R +++ b/R/plot.R @@ -25,6 +25,15 @@ plot.point_estimate <- function(x, ...) { } +#' @export +plot.map_estimate <- function(x, ...) { + if (!requireNamespace("see", quietly = TRUE)) { + stop("Package 'see' needed to plot point-estimates. Please install it by running `install.packages('see')`.") + } + NextMethod() +} + + #' @export plot.rope <- function(x, ...) { if (!requireNamespace("see", quietly = TRUE)) { From 34782cf6ca75a43a5738b5579b7e3462ee3b381a Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Daniel=20L=C3=BCdecke?= Date: Tue, 30 Jul 2019 11:34:22 +0200 Subject: [PATCH 15/21] address various reviewer comments --- README.Rmd | 64 +++++++++++++++++++---------- README.md | 44 +++++++++++++------- man/figures/unnamed-chunk-10-1.png | Bin 62867 -> 63338 bytes man/figures/unnamed-chunk-13-1.png | Bin 57260 -> 57724 bytes man/figures/unnamed-chunk-15-1.png | Bin 62491 -> 59888 bytes man/figures/unnamed-chunk-17-1.png | Bin 62998 -> 63353 bytes man/figures/unnamed-chunk-6-1.png | Bin 62148 -> 62517 bytes man/figures/unnamed-chunk-8-1.png | Bin 67667 -> 75741 bytes paper/paper.md | 2 +- 9 files changed, 73 insertions(+), 37 deletions(-) diff --git a/README.Rmd b/README.Rmd index abf9de9e6..9b22e107c 100644 --- a/README.Rmd +++ b/README.Rmd @@ -79,7 +79,11 @@ Click on the buttons above to access the package [**documentation**](https://eas # Features -[**`describe_posterior()`**](https://easystats.github.io/bayestestR/reference/describe_posterior.html) is the master function with which you can compute all of the indices cited below *at once*. +The following figures are meant to illustrate the (statistical) concepts behind the functions. However, for most functions, `plot()`-methods are available from the [see-package](http://easystats.github.io/see). + +## Describing the Posterior Distribution + +[**`describe_posterior()`**](https://easystats.github.io/bayestestR/reference/describe_posterior.html) is the master function with which you can compute all of the indices cited below at once. ```{r message=FALSE, warning=FALSE} describe_posterior(rnorm(1000)) @@ -88,7 +92,6 @@ describe_posterior(rnorm(1000)) ## Point-estimates - ### MAP Estimate [**`map_estimate()`**](https://easystats.github.io/bayestestR/reference/map_estimate.html) find the **Highest Maximum A Posteriori (MAP)** estimate of a posterior, *i.e.*, the value associated with the highest probability density (the "peak" of the posterior distribution). In other words, it is an estimation of the *mode* for continuous parameters. @@ -110,7 +113,7 @@ posterior %>% geom_segment(x=0.4, xend=0.4, y=0, yend=attributes(map_result)$MAP_density, color="#E91E63", size=1) + geom_point(x=map_result, y=attributes(map_result)$MAP_density, color="#E91E63", size=5) + geom_vline(xintercept=0, linetype="dotted") + - theme_classic() + + theme_classic(base_size = 12) + scale_y_continuous(expand = c(0, 0), limits = c(0, 2)) + xlab("\nParameter Value") + ylab("Probability Density\n") @@ -119,36 +122,55 @@ posterior %>% ## Uncertainty -### Highest Density Interval (HDI) - *Credible* Interval (CI) +### Highest Density Interval (HDI) and Equal-Tailed Interval (ETI) -[**`hdi()`**](https://easystats.github.io/bayestestR/reference/hdi.html) computes the **Highest Density Interval (HDI)** of a posterior distribution, *i.e.*, the interval which contains all points within the interval have a higher probability density than points outside the interval. The HDI can be used in the context of Bayesian posterior characterisation as **Credible Interval (CI)**. +[**`hdi()`**](https://easystats.github.io/bayestestR/reference/hdi.html) computes the **Highest Density Interval (HDI)** of a posterior distribution, i.e., the interval which contains all points within the interval have a higher probability density than points outside the interval. The HDI can be used in the context of Bayesian posterior characterisation as **Credible Interval (CI)**. -Unlike equal-tailed intervals (see [`ci()`](https://easystats.github.io/bayestestR/reference/ci.html)) that typically exclude 2.5\% from each tail of the distribution, the HDI is *not* equal-tailed and therefore always includes the mode(s) of posterior distributions. +Unlike equal-tailed intervals (see [`eti()`](https://easystats.github.io/bayestestR/reference/eti.html)) that typically exclude 2.5\% from each tail of the distribution, the HDI is *not* equal-tailed and therefore always includes the mode(s) of posterior distributions. -By default, `hdi()` returns the 89\% intervals (`ci = 0.89`), deemed to be more stable than, for instance, 95\% intervals (Kruschke, 2014). An effective sample size of at least 10.000 is recommended if 95\% intervals should be computed (Kruschke 2014, p. 183ff). Moreover, 89 is the highest prime number that does not exceed the already unstable 95\% threshold (McElreath, 2015). +By default, `hdi()` returns the 89\% intervals (`ci = 0.89`), deemed to be more stable than, for instance, 95\% intervals (Kruschke, 2014). An effective sample size of at least 10.000 is recommended if 95\% intervals should be computed (Kruschke 2014, p. 183ff). Moreover, 89 indicates the arbitrariness of interval limits - its only remarkable property is being the highest prime number that does not exceed the already unstable 95\% threshold (McElreath, 2015). ```{r message=FALSE, warning=FALSE} -posterior <- distribution_normal(100, 0.4, 0.2) +posterior <- distribution_chisquared(100, 3) + hdi(posterior, ci = .89) + +eti(posterior, ci = .89) ``` ```{r message=FALSE, warning=FALSE, echo=FALSE} -posterior <- distribution_normal(100, 0.4, 0.2) +posterior <- distribution_chisquared(100, 3) -posterior %>% - density() %>% - as.data.frame() %>% - mutate(fill = ifelse(x < hdi(posterior)$CI_low, "low", - ifelse(x > hdi(posterior)$CI_high, "high", "middle"))) %>% +dat <- as.data.frame(density(posterior)) + +p1 <- dat %>% mutate(fill = ifelse(x < hdi(posterior)$CI_low, "low", + ifelse(x > hdi(posterior)$CI_high, "high", "middle"))) %>% ggplot(aes(x=x, y=y, fill=fill)) + geom_ribbon(aes(ymin=0, ymax=y)) + geom_vline(xintercept=0, linetype="dotted") + - theme_classic() + - scale_y_continuous(expand = c(0, 0), limits = c(0, 2)) + + theme_classic(base_size = 12) + + scale_y_continuous(expand = c(0, 0), limits = c(0, .25)) + scale_fill_manual(values=c("high"="#FFC107", "low"="#FFC107", "middle"="#E91E63"), guide=FALSE) + - annotate("text", x=0.4, y=1, label="The 89% HDI", color="white", size=8) + + annotate("text", x=2.5, y=.05, label="The 89% HDI", color="white", size=5) + + xlab(NULL) + + ylab("Probability Density\n") + +# ggsave("paper/Figure2.png", width = 13, height = 8, units = "in", dpi = 300) + + +p2 <- dat %>% mutate(fill = ifelse(x < ci(posterior)$CI_low, "low", + ifelse(x > ci(posterior)$CI_high, "high", "middle"))) %>% + ggplot(aes(x=x, y=y, fill=fill)) + + geom_ribbon(aes(ymin=0, ymax=y)) + + geom_vline(xintercept=0, linetype="dotted") + + theme_classic(base_size = 12) + + scale_y_continuous(expand = c(0, 0), limits = c(0, .25)) + + scale_fill_manual(values=c("high"="#FFC107", "low"="#FFC107", "middle"="#2196F3"), guide=FALSE) + + annotate("text", x=2.9, y=.05, label="The 89% ETI", color="white", size=5) + xlab("\nParameter Value") + ylab("Probability Density\n") + +p <- see::plots(p1, p2, tags = TRUE) ``` @@ -179,7 +201,7 @@ posterior %>% ggplot(aes(x=x, y=y, fill=fill)) + geom_ribbon(aes(ymin=0, ymax=y)) + geom_vline(xintercept=0, linetype="dotted") + - theme_classic() + + theme_classic(base_size = 12) + scale_y_continuous(expand = c(0, 0), limits = c(0, 2)) + scale_x_continuous(breaks = c(-0.1, 0.1, 0.4)) + scale_fill_manual(values=c("high"="#FFC107", "low"="#FFC107", "middle"="#E91E63"), guide=FALSE) + @@ -222,7 +244,7 @@ posterior %>% ggplot(aes(x=x, y=y, fill=fill)) + geom_ribbon(aes(ymin=0, ymax=y)) + geom_vline(xintercept=0, linetype="dotted") + - theme_classic() + + theme_classic(base_size = 12) + scale_y_continuous(expand = c(0, 0), limits = c(0, 2)) + scale_fill_manual(values=c("high"="#FFC107", "low"="#E91E63"), guide=FALSE) + xlab("\nParameter Value") + @@ -258,7 +280,7 @@ posterior %>% geom_point(x=0, y=max(prior$y), color="#2196F3", size=5) + geom_segment(x=0, xend=0, y=0, yend=density_at(posterior$x, 0, bw="nrd0"), color="#E91E63", size=1) + geom_point(x=0, y=density_at(posterior$x, 0, bw="nrd0"), color="#E91E63", size=5) + - theme_classic() + + theme_classic(base_size = 12) + scale_y_continuous(expand = c(0, 0), limits = c(0, 0.65)) + scale_fill_manual(values=c("high"="#FFC107", "low"="#E91E63"), guide=FALSE) + xlab("\nParameter Value") + @@ -292,7 +314,7 @@ posterior %>% geom_point(x=map_result, y=attributes(map_result)$MAP_density, color="#E91E63", size=5) + geom_point(x=0, y=density_at(posterior, 0, bw="nrd0"), color="#E91E63", size=5) + geom_vline(xintercept=0, linetype="dotted") + - theme_classic() + + theme_classic(base_size = 12) + scale_y_continuous(expand = c(0, 0), limits = c(0, 2)) + xlab("\nParameter Value") + ylab("Probability Density\n") diff --git a/README.md b/README.md index 89dcc2527..f8b76b45e 100644 --- a/README.md +++ b/README.md @@ -72,16 +72,22 @@ check-out these vignettes: # Features +The following figures are meant to illustrate the (statistical) concepts +behind the functions. However, for most functions, `plot()`-methods are +available from the [see-package](http://easystats.github.io/see). + +## Describing the Posterior Distribution + [**`describe_posterior()`**](https://easystats.github.io/bayestestR/reference/describe_posterior.html) is the master function with which you can compute all of the indices -cited below *at once*. +cited below at once. ``` r describe_posterior(rnorm(1000)) -## Parameter Median CI CI_low CI_high pd ROPE_CI ROPE_low ROPE_high -## 1 Posterior -0.0013 89 -1.6 1.5 0.5 89 -0.1 0.1 +## Parameter Median CI CI_low CI_high pd ROPE_CI ROPE_low ROPE_high +## 1 Posterior 0.053 89 -1.5 1.7 0.52 89 -0.1 0.1 ## ROPE_Percentage -## 1 0.1 +## 1 0.084 ``` ## Point-estimates @@ -104,35 +110,43 @@ map_estimate(posterior) ## Uncertainty -### Highest Density Interval (HDI) - *Credible* Interval (CI) +### Highest Density Interval (HDI) and Equal-Tailed Interval (ETI) [**`hdi()`**](https://easystats.github.io/bayestestR/reference/hdi.html) computes the **Highest Density Interval (HDI)** of a posterior -distribution, *i.e.*, the interval which contains all points within the +distribution, i.e., the interval which contains all points within the interval have a higher probability density than points outside the interval. The HDI can be used in the context of Bayesian posterior characterisation as **Credible Interval (CI)**. Unlike equal-tailed intervals (see -[`ci()`](https://easystats.github.io/bayestestR/reference/ci.html)) that -typically exclude 2.5% from each tail of the distribution, the HDI is -*not* equal-tailed and therefore always includes the mode(s) of +[`eti()`](https://easystats.github.io/bayestestR/reference/eti.html)) +that typically exclude 2.5% from each tail of the distribution, the HDI +is *not* equal-tailed and therefore always includes the mode(s) of posterior distributions. By default, `hdi()` returns the 89% intervals (`ci = 0.89`), deemed to be more stable than, for instance, 95% intervals (Kruschke, 2014). An effective sample size of at least 10.000 is recommended if 95% intervals -should be computed (Kruschke 2014, p. 183ff). Moreover, 89 is the -highest prime number that does not exceed the already unstable 95% +should be computed (Kruschke 2014, p. 183ff). Moreover, 89 indicates the +arbitrariness of interval limits - its only remarkable property is being +the highest prime number that does not exceed the already unstable 95% threshold (McElreath, 2015). ``` r -posterior <- distribution_normal(100, 0.4, 0.2) +posterior <- distribution_chisquared(100, 3) + hdi(posterior, ci = .89) ## # Highest Density Interval ## ## 89% HDI -## [0.09, 0.71] +## [0.11, 6.05] + +eti(posterior, ci = .89) +## # Equal-Tailed Interval +## +## 89% ETI +## [0.42, 7.27] ``` ![](man/figures/unnamed-chunk-8-1.png) @@ -255,7 +269,7 @@ bayesfactor_parameters(posterior, prior, direction = "two-sided", null = 0) ## # Bayes Factor (Savage-Dickey density ratio) ## ## Bayes Factor -## 1.69 +## 2.15 ## ## * Evidence Against The Null: [0] ``` @@ -341,7 +355,7 @@ Compute the density of a given point of a distribution. ``` r density_at(rnorm(1000, 1, 1), 1) -## [1] 0.39 +## [1] 0.37 ``` ## Credits diff --git a/man/figures/unnamed-chunk-10-1.png 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