On estimating and testing associations between random coefficients from multivariate generalized linear mixed models...

Area of Science:

• Biostatistics
• Statistical Modeling

Background:

• Multivariate generalized linear mixed models (MGLMMs) can simultaneously model diverse outcome types (binary, count, continuous).
• Existing MGLMM applications focus on simple associations between subject-specific parameters, like correlations between slopes.
• Complex associations, such as partial regression coefficients and time lags, remain less explored.

Purpose of the Study:

• To demonstrate the estimation of complex associations between subject-specific parameters within MGLMMs.
• To compare different methods for estimating standard errors and testing significance of these associations.
• To identify the most reliable statistical approach for analyzing complex parameter relationships in MGLMMs.

Main Methods:

• Utilizing multivariate generalized linear mixed models (MGLMMs) with flexible assumptions for link functions and conditional distributions.
• Reparameterizing the MGLMM to directly estimate coefficients for complex associations.
• Comparing standard errors derived from the inverse Hessian matrix and the delta method.
• Evaluating significance using likelihood ratio tests, Wald-type t-tests, and Fisher's z transformations.

Main Results:

• Reparameterization enables the estimation of complex associations, including partial regression coefficients and time lags.
• Delta method and inverse Hessian standard errors are nearly equivalent but tend to overestimate the true standard error.
• Likelihood ratio tests on the reparameterized model demonstrate an acceptable Type I error rate, unlike other methods.

Conclusions:

• The reparameterized MGLMM approach effectively estimates complex associations between stochastic parameters.
• The likelihood ratio test is the recommended method for assessing the significance of these associations due to its superior Type I error control.
• This work provides a robust framework for advanced statistical analysis in biostatistics and related fields.