A Composite Conditional Likelihood Approach to Estimation in a Logistic Regression Model with Crossed Random Effects

• Activity Number: 498
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Jorgen Petersen*+
• Companies: University of Copenhagen
• Keywords: logistic regression ; random effects model ; estimation ; composite likelihood ; Rater agreement.

Abstract

In an example that will serve to motivate and illustrate the proposed approach, raters have supplied dichotomous ratings of the same cases in a sample. The model includes two sets of parameters: one set for the individuals (representing the severity of the 139 cases) being rated, and another set of parameters that allow the 32 raters to have different propensities to score a given set of individuals positively or negatively.

Estimating the rater variation would in a traditional approach involve distributional assumptions about the two sets of parameters and lead to high dimensional integrals for which no analytical solutions exist. Instead a composite likelihood is studied (involving all pairs of raters). For each pair, a conditional likelihood is used which eliminates the influence of the individual-specific parameters which results in a composite conditional likelihood consisting of only one-dimensional integral that are solved numerically. Properties of the resulting estimator are described.