TY - JOUR
T1 - Exploratory Restricted Latent Class Models with Monotonicity Requirements under PÒLYA–GAMMA Data Augmentation
AU - Balamuta, James Joseph
AU - Culpepper, Steven Andrew
N1 - Funding Information:
This research was partially supported by National Science Foundation, Division of Methodology, Measurement, and Statistics program grants #1758631 and #1951057. This work made use of the Illinois Campus Cluster, a computing resource that is operated by the Illinois Campus Cluster Program (ICCP) in conjunction with the National Center for Supercomputing Applications (NCSA) and which is supported by funds from the University of Illinois at Urbana-Champaign.
Publisher Copyright:
© 2021, The Psychometric Society.
PY - 2022
Y1 - 2022
N2 - Restricted latent class models (RLCMs) provide an important framework for supporting diagnostic research in education and psychology. Recent research proposed fully exploratory methods for inferring the latent structure. However, prior research is limited by the use of restrictive monotonicity condition or prior formulations that are unable to incorporate prior information about the latent structure to validate expert knowledge. We develop new methods that relax existing monotonicity restrictions and provide greater insight about the latent structure. Furthermore, existing Bayesian methods only use a probit link function and we provide a new formulation for using the exploratory RLCM with a logit link function that has an additional advantage of being computationally more efficient for larger sample sizes. We present four new Bayesian formulations that employ different link functions (i.e., the logit using the Pòlya–gamma data augmentation versus the probit) and priors for inducing sparsity in the latent structure. We report Monte Carlo simulation studies to demonstrate accurate parameter recovery. Furthermore, we report results from an application to the Last Series of the Standard Progressive Matrices to illustrate our new methods.
AB - Restricted latent class models (RLCMs) provide an important framework for supporting diagnostic research in education and psychology. Recent research proposed fully exploratory methods for inferring the latent structure. However, prior research is limited by the use of restrictive monotonicity condition or prior formulations that are unable to incorporate prior information about the latent structure to validate expert knowledge. We develop new methods that relax existing monotonicity restrictions and provide greater insight about the latent structure. Furthermore, existing Bayesian methods only use a probit link function and we provide a new formulation for using the exploratory RLCM with a logit link function that has an additional advantage of being computationally more efficient for larger sample sizes. We present four new Bayesian formulations that employ different link functions (i.e., the logit using the Pòlya–gamma data augmentation versus the probit) and priors for inducing sparsity in the latent structure. We report Monte Carlo simulation studies to demonstrate accurate parameter recovery. Furthermore, we report results from an application to the Last Series of the Standard Progressive Matrices to illustrate our new methods.
KW - Bayesian
KW - Pòlya–gamma data augmentation
KW - restricted latent class models
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U2 - 10.1007/s11336-021-09815-9
DO - 10.1007/s11336-021-09815-9
M3 - Article
C2 - 35023017
AN - SCOPUS:85122725876
JO - Psychometrika
JF - Psychometrika
SN - 0033-3123
ER -