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- Title
On estimating and testing associations between random coefficients from multivariate generalized linear mixed models of longitudinal outcomes.
- Authors
Mikulich-Gilbertson, Susan K.; Wagner, Brandie D.; Riggs, Paula D.; Zerbe, Gary O.
- Abstract
Different types of outcomes (e.g. binary, count, continuous) can be simultaneously modeled with multivariate generalized linear mixed models by assuming: (1) same or different link functions, (2) same or different conditional distributions, and (3) conditional independence given random subject effects. Others have used this approach for determining simple associations between subject-specific parameters (e.g. correlations between slopes). We demonstrate how more complex associations (e.g. partial regression coefficients between slopes adjusting for intercepts, time lags of maximum correlation) can be estimated. Reparameterizing the model to directly estimate coefficients allows us to compare standard errors based on the inverse of the Hessian matrix with more usual standard errors approximated by the delta method; a mathematical proof demonstrates their equivalence when the gradient vector approaches zero. Reparameterization also allows us to evaluate significance of coefficients with likelihood ratio tests and to compare this approach with more usual Wald-type t-tests and Fisher's z transformations. Simulations indicate that the delta method and inverse Hessian standard errors are nearly equivalent and consistently overestimate the true standard error. Only the likelihood ratio test based on the reparameterized model has an acceptable type I error rate and is therefore recommended for testing associations between stochastic parameters. Online supplementary materials include our medical data example, annotated code, and simulation details.
- Subjects
MULTILEVEL models; HESSIAN matrices; REGRESSION analysis; MATHEMATICAL proofs; ERRORS; SMOKING prevention; SMOKING &; psychology; ATTENTION-deficit hyperactivity disorder; COGNITIVE therapy; ALCOHOL drinking; EXPERIMENTAL design; LONGITUDINAL method; SMOKING; STATISTICS; DISEASE complications
- Publication
Statistical Methods in Medical Research, 2017, Vol 26, Issue 3, p1130
- ISSN
0962-2802
- Publication type
journal article
- DOI
10.1177/0962280214568522