An Equivalence of Conditional and Unconditional Maximum Likelihood Estimators via Infinite Replication of Observations for Matched Pairs Designs

• Activity Number: 582
• Type: Contributed
• Date/Time: Wednesday, August 1, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Survey Research Methods
• Author(s): Zhulin He*+ and Babette A Brumback
• Companies: University of Florida and University of Florida
• Keywords: conditional logistic regression ; complex survey data ; pseudosample ; matched pairs ; Legendre polynomials ; ordinary differential equations

Abstract

With complex survey data, one might try to implement conditional logistic regression by applying it to a pseudosample constructed by replicating the observations according to integer-scaled versions of the sampling weights. However, this method has been found to produce inconsistent results. To understand why, we investigate the performance of conditional logistic regression applied to replicated data from a matched pairs design with general covariates. We show both theoretically and empirically that as the number of replications approaches infinity, the resulting estimator converges identically to the one from an unconditional logistic regression with a fixed effect for each pair as applied to the original matched pairs sample. This latter estimator is well-known to be inconsistent, which at least partly explains why conditional logistic regression applied to a pseudosample tends to fail.