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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 591-616 |
| Number of pages | 26 |
| Journal | Journal of Educational and Behavioral Statistics |
| Volume | 42 |
| Issue number | 5 |
| DOIs | |
| State | Published - Oct 1 2017 |
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Keywords
- Bayesian Lasso
- National Assessment of Educational Progress
- multivariate generalized asymmetric Laplace distribution
- multivariate regression
- probit model
ASJC Scopus subject areas
- Education
- Social Sciences (miscellaneous)
Cite this
Bayesian Estimation of Multivariate Latent Regression Models : Gauss Versus Laplace. / Culpepper, Steven Andrew; Park, Trevor H.
In: Journal of Educational and Behavioral Statistics, Vol. 42, No. 5, 01.10.2017, p. 591-616.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Bayesian Estimation of Multivariate Latent Regression Models
T2 - Gauss Versus Laplace
AU - Culpepper, Steven Andrew
AU - Park, Trevor H
PY - 2017/10/1
Y1 - 2017/10/1
N2 - 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.
AB - 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.
KW - Bayesian Lasso
KW - National Assessment of Educational Progress
KW - multivariate generalized asymmetric Laplace distribution
KW - multivariate regression
KW - probit model
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UR - http://www.scopus.com/inward/citedby.url?scp=85029076772&partnerID=8YFLogxK
U2 - 10.3102/1076998617700598
DO - 10.3102/1076998617700598
M3 - Article
VL - 42
SP - 591
EP - 616
JO - Journal of Educational and Behavioral Statistics
JF - Journal of Educational and Behavioral Statistics
SN - 1076-9986
IS - 5
ER -