• Corpus ID: 248987510

Multivariate generalized linear mixed models for underdispersed count data

@inproceedings{Silva2022MultivariateGL,
  title={Multivariate generalized linear mixed models for underdispersed count data},
  author={Guilherme Parreira da Silva and Henrique Aparecido Laureano and Ricardo Rasmussen Petterle and Paulo Justiniano Ribeiro J'unior and Wagner Hugo Bonat},
  year={2022}
}

• Guilherme Parreira da Silva, H. A. Laureano, +2 authors W. H. Bonat
• Published 21 May 2022
• Mathematics

Researchers are often interested in understanding the relationship between a set of covariates and a set of response variables. To achieve this goal, the use of regression analysis, either linear or generalized linear models, is largely applied. However, such models only allow users to model one response variable at a time. Moreover, it is not possible to directly calculate from the regression model a correlation measure between the response variables. In this article, we employed the Multivariate Gen- eralized Linear Mixed Models framework, which allows the specification of a set of response variables and calculates the correlation between them through a random ef- fect structure that follows a multivariate normal distribution. We used the maximum likelihood estimation framework to estimate all model parameters using Laplace ap- proximation to integrate out the random effects. The derivatives are provided by automatic differentiation. The outer maximization was made using a general-purpose algorithm such as PORT and BFGS . We delimited this problem by studying only count response variables with the following distributions: Poisson, negative binomial (NB) and COM-Poisson. While the first distribution can model only equidispersed data, the second models equi and overdispersed, and the third models all types of dis- persion. The models were implemented on software R with package TMB , based on C++ templates. Besides the full specification, models with simpler structures in the covariance matrix were considered (fixed and common variance, fixed dispersion, ρ set to 0). These models were applied to a dataset from the National Health and Nutrition Examination Survey, where three underdispersed response variables were measured at 1281 subjects. The COM-Poisson model full specified overcome the other two competitors considering three goodness-of-fit indexes: AIC, BIC and likelihood. As a consequence, it estimated parameters with smaller standard error and a greater number of significant correlation coefficients. Therefore, the proposed model can deal with multivariate count responses and measures the correlation between them taking into account the effects of the covariates.