Comparing Samples of Partially Paired Categorical Data

• Activity Number: 75 - Contributed Poster Presentations: Biometrics Section
• Type: Contributed
• Date/Time: Monday, August 3, 2020 : 10:00 AM to 2:00 PM
• Sponsor: Biometrics Section
• Author(s): PHILIP DIXON*
• Companies: Iowa State University
• Keywords: partially paired data; GLMM; probability of invasiveness

Abstract

There are standard statistical methods for comparing the probability of an event in two samples. Commonly used frequentist methods are a Chi-square test for two independent samples and McNemar’s test for paired data. What can be done when the data are partially paired, i.e. some observations are paired and others are not? A Generalized Linear Mixed Effects Model (GLMM) with a random effect to account for pairing is known to be difficult to fit when data are sparse. I show that the GLMM can be fit to data with as few as 20% paired observations using either high-quality numerical approximations or Bayesian methods. A more important issue is the choice of conditional (on the random effects) or marginal (to population averages) inference. Marginal probabilities can be estimated from posterior samples from a Bayesian GLMM and I derive a maximum likelihood estimate that does not require fitting a GLMM. These methods are illustrated using data on the invasiveness of trees and shrubs introduced to two areas around Chicago. For these data, marginal probabilities are more appropriate.