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+
+
+
+ 20240715180932-466f4c859b3754b8ec00d71722f7d17b5a10d3af
+ 20240715180932
+
+ JOSS Admin
+ admin@theoj.org
+
+ The Open Journal
+
+
+
+
+ Journal of Open Source Software
+ JOSS
+ 2475-9066
+
+ 10.21105/joss
+ https://joss.theoj.org
+
+
+
+
+ 07
+ 2024
+
+
+ 9
+
+ 99
+
+
+
+ ddtlcm: An R package for overcoming weak separation in
+Bayesian latent class analysis via tree-regularization
+
+
+
+ Mengbing
+ Li
+ https://orcid.org/0000-0002-2264-8006
+
+
+ Bolin
+ Wu
+
+
+ Briana
+ Stephenson
+
+
+ Zhenke
+ Wu
+ https://orcid.org/0000-0001-7582-669X
+
+
+
+ 07
+ 15
+ 2024
+
+
+ 6220
+
+
+ 10.21105/joss.06220
+
+
+ http://creativecommons.org/licenses/by/4.0/
+ http://creativecommons.org/licenses/by/4.0/
+ http://creativecommons.org/licenses/by/4.0/
+
+
+
+ Software archive
+ 10.5281/zenodo.12711232
+
+
+ GitHub review issue
+ https://github.com/openjournals/joss-reviews/issues/6220
+
+
+
+ 10.21105/joss.06220
+ https://joss.theoj.org/papers/10.21105/joss.06220
+
+
+ https://joss.theoj.org/papers/10.21105/joss.06220.pdf
+
+
+
+
+
+ BayesLCA: An R package for Bayesian latent
+class analysis
+ White
+ Journal of Statistical
+Software
+ 61
+ 10.18637/jss.v061.i13
+ 1548-7660
+ 2014
+ White, A., & Murphy, T. B.
+(2014). BayesLCA: An R package for Bayesian latent class analysis.
+Journal of Statistical Software, 61, 1–28.
+https://doi.org/10.18637/jss.v061.i13
+
+
+ poLCA: An R package for polytomous variable
+latent class analysis
+ Linzer
+ Journal of Statistical
+Software
+ 42
+ 10.18637/jss.v042.i10
+ 1548-7660
+ 2011
+ Linzer, D. A., & Lewis, J. B.
+(2011). poLCA: An R package for polytomous variable latent class
+analysis. Journal of Statistical Software, 42, 1–29.
+https://doi.org/10.18637/jss.v042.i10
+
+
+ randomLCA: An R package for latent class with
+random effects analysis
+ Beath
+ Journal of Statistical
+Software
+ 81
+ 10.18637/jss.v081.i13
+ 2017
+ Beath, K. J. (2017). randomLCA: An R
+package for latent class with random effects analysis. Journal of
+Statistical Software, 81, 1–25.
+https://doi.org/10.18637/jss.v081.i13
+
+
+ Tree-regularized Bayesian latent class
+analysis for improving weakly separated dietary pattern subtyping in
+small-sized subpopulations
+ Li
+ arXiv preprint
+arXiv:2306.04700
+ 2023
+ Li, M., Stephenson, B., & Wu, Z.
+(2023). Tree-regularized Bayesian latent class analysis for improving
+weakly separated dietary pattern subtyping in small-sized
+subpopulations. arXiv Preprint arXiv:2306.04700.
+
+
+ Density Modeling and Clustering Using
+Dirichlet Diffusion Trees
+ Neal
+ Bayesian Statistics 7: Proceedings of the
+Seventh Valencia International Meeting
+ 10.1093/oso/9780198526155.003.0042
+ 9780198526155
+ 2003
+ Neal, R. M. (2003). Density Modeling
+and Clustering Using Dirichlet Diffusion Trees. In Bayesian Statistics
+7: Proceedings of the Seventh Valencia International Meeting. Oxford
+University Press.
+https://doi.org/10.1093/oso/9780198526155.003.0042
+
+
+ Handling the label switching problem in
+latent class models via the ECR algorithm
+ Papastamoulis
+ Communications in Statistics - Simulation and
+Computation
+ 4
+ 43
+ 10.1080/03610918.2012.718840
+ 0361-0918
+ 2014
+ Papastamoulis, P. (2014). Handling
+the label switching problem in latent class models via the ECR
+algorithm. Communications in Statistics - Simulation and Computation,
+43(4), 913–927.
+https://doi.org/10.1080/03610918.2012.718840
+
+
+
+
+
+
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+
+
+
+
+
+
+
+Journal of Open Source Software
+JOSS
+
+2475-9066
+
+Open Journals
+
+
+
+6220
+10.21105/joss.06220
+
+ddtlcm: An R package for overcoming weak separation in
+Bayesian latent class analysis via tree-regularization
+
+
+
+https://orcid.org/0000-0002-2264-8006
+
+Li
+Mengbing
+
+
+*
+
+
+
+Wu
+Bolin
+
+
+
+
+
+Stephenson
+Briana
+
+
+
+
+https://orcid.org/0000-0001-7582-669X
+
+Wu
+Zhenke
+
+
+*
+
+
+
+Department of Biostatistics, University of
+Michigan
+
+
+
+
+Department of Computer Science, University of
+Michigan
+
+
+
+
+Department of Biostatistics, Harvard
+University
+
+
+
+
+* E-mail:
+* E-mail:
+
+
+17
+9
+2023
+
+9
+99
+6220
+
+Authors of papers retain copyright and release the
+work under a Creative Commons Attribution 4.0 International License (CC
+BY 4.0)
+2022
+The article authors
+
+Authors of papers retain copyright and release the work under
+a Creative Commons Attribution 4.0 International License (CC BY
+4.0)
+
+
+
+Dirichlet diffusion tree
+latent class model
+ddtlcm
+nutrition epidemiology
+R
+
+
+
+
+
+ Summary
+
Latent class model (LCM) is a model-based clustering tool
+ frequently used by social, behavioral, and medical researchers to
+ cluster sampled individuals based on categorical responses.
+ Traditional applications of LCMs often focus on scenarios where a set
+ of unobserved classes are well-defined and easily distinguishable.
+ However, in numerous real-world applications, these classes are weakly
+ separated and difficult to distinguish. For example, nutritional
+ epidemiologists often encounter weak class separation when deriving
+ dietary patterns from dietary intake assessment
+ (Li
+ et al., 2023). Based on the number of diet components queried
+ and the heterogeneity of the study population, LCM-derived dietary
+ patterns can exhibit strong similarities, or weak separation,
+ resulting in numerical and inferential instabilities that challenge
+ scientific interpretation. This issue is exacerbated in small-sized
+ study populations.
+
To address these issues, we have developed an R package
+ ddtlcm that empowers LCMs to account for weak
+ class separation. This package implements a tree-regularized Bayesian
+ LCM that leverages statistical strength between latent classes to make
+ better estimates using limited data. With a tree-structured prior
+ distribution over class profiles, classes that are closer to one
+ another in the binary tree are encouraged to share more similar
+ profiles, and their profiles are shrunk towards their common ancestral
+ classes a priori, with the degree of shrinkage
+ varying across pre-specified item groups defined thematically with
+ clinical significance. The ddtlcm package takes
+ data on multivariate binary responses over items in pre-specified
+ major groups, and generates statistics and visualizations based on the
+ inferred tree structures and LCM parameters. Overall,
+ ddtlcm provides tools designed to enhance the
+ robustness and interpretability of LCMs in the presence of weak class
+ separation, particularly useful for small sample sizes.
+
+
+ Statement of Need
+
A number of packages are capable of fitting LCMs in R. For example,
+ poLCA
+ (Linzer
+ & Lewis, 2011) is a fully featured package that fits LCMs
+ and latent class regression on polytomous outcomes.
+ BayesLCA
+ (White
+ & Murphy, 2014) is designed for Bayesian LCMs for binary
+ outcomes. randomLCA
+ (Beath,
+ 2017) provides tools to perform LCMs with individual-specific
+ random effects. These packages focus on LCMs where the class profiles
+ are well-separated. Directly applying these packages to data that
+ suffer from weak separation may result in large standard deviations of
+ the class profiles, tendency to merge similar classes, and inaccurate
+ individual class membership assignments, phenomena highly prevalent in
+ small-sized study populations. These phenomena have been demonstrated
+ using poLCA and
+ BayesLCA, which are more relevant to our stated
+ problem of weak class separation, in Figures 2 and 3 of Li et al.
+ (2023).
+
The package ddtlcm implements the
+ tree-regularized LCM proposed in Li et al.
+ (2023), a
+ general framework to facilitate the sharing of information between
+ classes to make better estimates of parameters using limited data. The
+ model addresses weak separation for small sample sizes by (1) sharing
+ statistical strength between classes guided by an unknown tree, and
+ (2) accounting for varying degrees of shrinkage across major item
+ groups. The proposed model uses a Dirichlet diffusion tree (DDT)
+ process
+ (Neal,
+ 2003) as a fully probabilistic device to specify a prior
+ distribution for the class profiles on the leaves of an unknown tree
+ (hence termed “DDT-LCM”). Classes positioned closer on the tree
+ exhibit more profile similarities. The degrees of separation by major
+ item groups are modeled by item-group-specific diffusion
+ variances.
+
+
+ Usage
+
In the following, we use an example list of model parameters, named
+ “parameter_diet”, that comes with the package to demonstrate the
+ utility of ddtlcm in deriving weakly separated
+ latent class profiles. We start with demonstrating how a simulated
+ dataset is generated. We next apply the primary model fitting function
+ to the simulated dataset. Finally we summarize the fitted model and
+ visualize the result.
+
+ Data Loading
+
The “parameter_diet” contains model parameters obtained from
+ applying DDT-LCM to dietary assessment data described in Li et al.
+ (2023).
+ We use it as a semi-synthetic data-generating mechanism to mimic the
+ weak separation issue in the real world. Specifically, the data set
+ includes a tree named “tree_phylo” (class “phylo”), a list of
+
+
+ J=78
+ food item labels, and a list of
+
+ G=7
+ pre-defined major food groups to which the food items belong. The
+ food groups are dairy, fat, fruit, grain, meat, sugar, and
+ vegetables.
+ install.packages("ddtlcm")
+library(ddtlcm)
+# load the data
+data(parameter_diet)
+# unlist the elements into variables in the global environment
+list2env(setNames(parameter_diet, names(parameter_diet)), envir = globalenv())
+# look at items in group 1
+g <- 1
+# indices of the items in group 1
+item_membership_list[g]
+ [[1]]
+ [1] 1 2 3 4 5 6 7 8 9 10 11
+
Below we look at the short labels of the items in group 1. For
+ the sake of space, see Supplementary Table S6.1 in Li et al.
+ (2023)
+ for full description of the items.
+ # The name of the list element is the major food group label
+item_name_list[g]
+ $Dairy
+ [1] "dairy_1" "dairy_2" "dairy_3" "dairy_4" "dairy_5"
+ "dairy_6" "dairy_7" "dairy_8" "dairy_9" "dairy_10" "dairy_11"
+
+
+ Data Simulation
+
Data simulation given the true parameter values in
+ parameter_diet is handled by the
+ simulate_lcm_given_tree()
+ function. Following the dietary assessment example, we simulate a
+ multivariate binary data matrix of
+
+ N=496
+ subjects over the
+
+ J=78
+ food items, from
+
+ K=6
+ latent classes along “tree_phylo”. The resulting class profiles are
+ weakly separated. Note that the number of latent classes equals the
+ number of leaves in “tree_phylo”.
+ # number of individuals
+N <- 496
+# random seed to generate node parameters given the tree
+seed_parameter = 1
+# random seed to generate multivariate binary observations from LCM
+seed_response = 1
+# simulate data given the parameters
+sim_data <- simulate_lcm_given_tree(tree_phylo, N,
+ class_probability, item_membership_list, Sigma_by_group,
+ root_node_location = 0, seed_parameter = seed_parameter,
+ seed_response = seed_response)
+
+
+ Model Fitting
+
The primary model fitting function,
+ ddtlcm_fit(), implements a hybrid
+ Metropolis-Hastings-within-Gibbs algorithm to sample from the
+ posterior distribution of model parameters. We assume that the
+ number of latent classes
+
+ K=6
+ is known. To use ddtlcm_fit(), we need to
+ specify the number of classes (K), a matrix
+ of multivariate binary observations (data), a
+ list of item group memberships
+ (item_membership_list), and the number of
+ posterior samples to collect (total_iters).
+ For a quick illustration, here we specify a small number
+ total_iters = 100.
+ set.seed(999)
+# number of latent classes, same as number of leaves on the tree
+K <- 6
+result <- ddtlcm_fit(K = K, data = sim_data$response_matrix,
+ item_membership_list = item_membership_list, total_iters = 100)
+print(result)
+ ---------------------------------------------
+DDT-LCM with K = 6 latent classes run on 496 observations and 78
+items in 7 major groups. 100 iterations of posterior samples drawn.
+---------------------------------------------
+
To have a more comprehensive view of the results obtained from
+ 1000 posterior draws, we can load data named
+ result_diet_1000iters to perform posterior
+ summaries as described by the steps in the following sections.
+ data(result_diet_1000iters)
+# let the variable names be consistent for posterior summaries in the subsequent sections
+result <- result_diet_1000iters
+
+
+ Model Summary
+
We next summarize the posterior samples using the generic
+ function summary(). We discard the first 50
+ iterations as burn-ins (burnin = 50). To deal
+ with identifiability of finite mixture models, we perform post-hoc
+ label switching using the Equivalence Classes Representatives (ECR,
+ Papastamoulis
+ (2014))
+ method by specifying relabel = TRUE. To save
+ space in the document, we do not print the summary result
+ (be_quiet = TRUE).
A generic plot() function is available in
+ the package to visualize the summarized result. By specifying
+ plot_option = "all", we plot both
+ the maximum a posterior (MAP) tree and the class
+ profiles. Plotting only the tree or the class profiles is also
+ available through
+ plot_option = "profile" or
+ plot_option = "tree".
+
Figure 1 displays the result obtained from the above model
+ summary. On the left shows the MAP tree structure over the latent
+ classes. The numbers on the branches indicate the branch lengths. On
+ the right shows class profiles, where major item groups are
+ distinguished by different colors. The description of items is
+ provided in Table S6.1 in the supplement of
+ (Li
+ et al., 2023). The numbers after the class labels indicate
+ class prevalences along with 95% credible intervals. Error bars show
+ the 95% credible intervals of item response probabilities.
We also provide an accompanying Shiny app with point-and-click
+ interactivity to allow visualization and exploration of model results.
+ The app, accessible at (https://bolinw.shinyapps.io/ddtlcm_app/), is
+ designed with three modes, allowing users to 1) simulate data using
+ user-specified parameters or exemplar parameters mimicking a real data
+ set, 2) upload raw multivariate binary observed data, or 3) upload
+ posterior samples collected from a completed fit of the DDT-LCM. Users
+ can explore the app to fully understand the properties of the model,
+ analyze their own data, save the fitted results, and produce
+ visualizations.
+
+
+ Conclusions
+
We developed an R package ddtlcm that
+ addresses a long-standing weak class separation issue in latent class
+ analysis, greatly enhancing numerical and inferential stability
+ relative to existing popular packages. This paper offers a
+ step-by-step example that contextualizes the workflow in a
+ semi-synthetic diet data. Details about usage and more elaborate
+ examples can be found at (https://github.com/limengbinggz/ddtlcm).
+
+
+ Acknowledgements
+
This work is partially supported by a Michigan Institute for Data
+ Science seed grant. The authors declare no conflicts of interest.
+
+
+
+
+
+
+
+
+ WhiteArthur
+ MurphyThomas Brendan
+
+ BayesLCA: An R package for Bayesian latent class analysis
+ Journal of Statistical Software
+ 201411
+ 61
+ 1548-7660
+ 10.18637/jss.v061.i13
+ 1
+ 28
+
+
+
+
+
+ LinzerDrew A.
+ LewisJeffrey B.
+
+ poLCA: An R package for polytomous variable latent class analysis
+ Journal of Statistical Software
+ 201106
+ 42
+ 1548-7660
+ 10.18637/jss.v042.i10
+ 1
+ 29
+
+
+
+
+
+ BeathKen J
+
+ randomLCA: An R package for latent class with random effects analysis
+ Journal of Statistical Software
+ 2017
+ 81
+ 10.18637/jss.v081.i13
+ 1
+ 25
+
+
+
+
+
+ LiMengbing
+ StephensonBriana
+ WuZhenke
+
+ Tree-regularized Bayesian latent class analysis for improving weakly separated dietary pattern subtyping in small-sized subpopulations
+ arXiv preprint arXiv:2306.04700
+ 2023
+
+
+
+
+
+ NealRadford M
+
+ Density Modeling and Clustering Using Dirichlet Diffusion Trees
+ Bayesian Statistics 7: Proceedings of the Seventh Valencia International Meeting
+ Oxford University Press
+ 200307
+ 9780198526155
+ https://doi.org/10.1093/oso/9780198526155.003.0042
+ 10.1093/oso/9780198526155.003.0042
+
+
+
+
+
+ PapastamoulisPanagiotis
+
+ Handling the label switching problem in latent class models via the ECR algorithm
+ Communications in Statistics - Simulation and Computation
+ Taylor & Francis
+ 201401
+ 43
+ 4
+ 0361-0918
+ 10.1080/03610918.2012.718840
+ 913
+ 927
+
+
+
+
+
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