EXTENDING THE INTERPRETATION AND UTILITY OF MIXED EFFECTS LOGISTIC-REGRESSION MODELS

The veterinary research community has begun to use mixed effects logis tic regression (MELR) for analyzing disease data obtained from groups of animals. In this article we discuss the issues of how to analyze th ese models and how to interpret MELR risk estimates and random effect variances (single and nested). We provide empirical evidence for their use and present equations for interpreting the results and comparing ordinary logistic regression (OLR) and MELR. These equations allow for a deeper interpretation of what random effects signify within the MEL R model and help reveal the relationship between marginal (OLR) coeffi cients and conditional (MELR) coefficients. We used three veterinary d ata sets to illustrate our aims. The data sets contained data on vesic ular stomatitis virus infection in cattle, Mycoplasma gallisepticum in fection in chicken hocks, and three infectious conditions in puppies ( respiratory, intestinal illness, and internal parasites). The chicken data had nested random effects such that 357 flocks were housed on 104 different farms operated by 45 different owners. Significant random e ffects were detected for all but intestinal illness in puppies and the nested farm random effect in the chicken data. The intra-group correl ation coefficients on the legit scale, calculated from the random effe ct variances, were 0.47 and 0.55 for the cow and chicken data, respect ively. This indicated that about 50% of the total variance on the legi t scale for the probability of disease was attributable to unmeasured or unmeasurable group-level factors. Since the farm random effect was not significant once the owner random effect was controlled for in the chicken data, the unknown factor(s) inducing the intra-group correlat ion was operating at the owner level or higher. These data sets were a lso used to illustrate why predicted probabilities from the MELR model should not be presented as point estimates. For example, the predicte d OLR probability of testing seropositive to vesicular stomatitis viru s New Jersey serotype (VSV-NJ) for 5-year-old Bos taurus cattle living at an elevation of 0-500 m with a mean annual rainfall of 0-2 m was 7 4%. Given that significant herd random effects were present, however, the true probability of testing seropositive to VSV-NJ for such a cow should be formulated as a range of herd-specific probabilities: the pr obability varied from 48 to 97% for the central 65% of the herds and f rom 14 to 99% for the central 95% of the herds. We have also shown why marginal OLR coefficients are biased downward as estimates of conditi onal MELR coefficients owing to the intra-group correlation and non-li nearity of the logistic regression model.