ERIC Number: ED414311
Record Type: Non-Journal
Publication Date: 1997-Aug
Empirical Bayes Estimates of Parameters from the Logistic Regression Model. ACT Research Report Series 97-6.
Houston, Walter M.; Woodruff, David J.
Maximum likelihood and least-squares estimates of parameters from the logistic regression model are derived from an iteratively reweighted linear regression algorithm. Empirical Bayes estimates are derived using an m-group regression model to regress the within-group estimates toward common values. The m-group regression model assumes that the parameter vectors from "m" groups are independent, and identically distributed, observations from a multivariate normal "prior" distribution. Based on asymptotic normality of maximum likelihood estimates, the posterior distributions are multivariate normal. Under the assumption that the parameter vectors from the "m" groups are interchangeable, the hyperparameters of the common prior distribution are estimated using the EM algorithm. Results from an empirical study of the relative stability of the empirical Bayes and maximum likelihood estimates are consistent with those reported previously for the m-group regression model. Estimates that use collateral information from exchangeable groups to regress within-group parameter estimates toward a common value are more stable than estimators calculated exclusively from within-group data. An appendix discusses parameter and hyperparameter estimates for an ACT Assessment English examination. (Contains 14 tables and 14 references.) (Author/SLD)
Descriptors: Bayesian Statistics, Estimation (Mathematics), Least Squares Statistics, Maximum Likelihood Statistics, Regression (Statistics)
ACT Research Report Series, P.O. Box 168, Iowa City, IA 52243-0168.
Publication Type: Reports - Evaluative
Education Level: N/A
Authoring Institution: American Coll. Testing Program, Iowa City, IA.