Bayesian Estimation of Multivariate Latent Regression Models: Gauss Versus Laplace

Steven Andrew Culpepper and Trevor Park

Journal of Educational and Behavioral Statistics, 2017, vol. 42, issue 5, 591-616

Abstract: A latent multivariate regression model is developed that employs a generalized asymmetric Laplace (GAL) prior distribution for regression coefficients. The model is designed for high-dimensional applications where an approximate sparsity condition is satisfied, such that many regression coefficients are near zero after accounting for all the model predictors. The model is applicable to large-scale assessments such as the National Assessment of Educational Progress (NAEP), which includes hundreds of student, teacher, and school predictors of latent achievement. Monte Carlo evidence suggests that employing the GAL prior provides more precise estimation of coefficients that equal zero in comparison to a multivariate normal (MVN) prior, which translates to more accurate model selection. Furthermore, the GAL yielded less biased estimates of regression coefficients in smaller samples. The developed model is applied to mathematics achievement data from the 2011 NAEP for 175,200 eighth graders. The GAL and MVN NAEP estimates were similar, but the GAL was more parsimonious by selecting 12 fewer (i.e., 83 of the 148) variable groups. There were noticeable differences between estimates computed with a GAL prior and plausible value regressions with the AM software (beta version 0.06.00). Implications of the results are discussed for test developers and applied researchers.

Keywords: multivariate regression; Bayesian Lasso; National Assessment of Educational Progress; multivariate generalized asymmetric Laplace distribution; probit model (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://journals.sagepub.com/doi/10.3102/1076998617700598 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:sae:jedbes:v:42:y:2017:i:5:p:591-616

DOI: 10.3102/1076998617700598

Access Statistics for this article

More articles in Journal of Educational and Behavioral Statistics
Bibliographic data for series maintained by SAGE Publications ().