Bayesian Analysis of Binary Probit Models: The Case of Measurement Error and Sequential Regression Modeling for Missing Explaining Factors

• Activity Number: 115
• Type: Topic Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Survey Research Methods
• Author(s): Christian Aßmann and Benno Schonberger*+
• Companies: University of Bamberg
• Keywords: MICE ; MCMC ; Bayesian Analysis ; Probit ; Measurement Error ; Panel Data

Abstract

The structure of multiple imputation algorithms is well suited for incorporation in MCMC estimation algorithms providing the analysis of primary interest. This paper implements two approaches to approximate the full conditional distribution of missing values within a sequential regression setup. In the context of a panel data set of bone ages with missing data, simple parametric models are chosen to provide an approximation of the full conditional distribution. Robustness checks are provided documenting the adequacy of the proposed approach. The resulting imputation algorithm is adapted within a MCMC algorithm allowing inference incorporating the uncertainty of missing explaining factors. Alternatively, a non parametric approach is chosen to mimic the full conditional distribution for missing values within variables with nominal and ordinal scale. This approach is applied within a Binary Probit Model incorportating a measurement error for the dependent variable aiming at an analysis of unit non response. Out-of-sample forecast criteria are used to gauge adequacy of non nested model spefications.