Multivariate Generalized Linear Mixed Models for Count Data
Univariate regression models have rich literature for counting data. However, this is not the case for multivariate count data. Therefore, we present the Multivariate Generalized Linear Mixed Models framework that deals with a multivariate set of responses, measuring the correlation between them th...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Austrian Statistical Society
2024-01-01
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| Series: | Austrian Journal of Statistics |
| Online Access: | https://www.ajs.or.at/index.php/ajs/article/view/1574 |
| _version_ | 1827379039531171840 |
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| author | Guilherme Parreira da Silva Henrique Aparecido Laureano Ricardo Rasmussen Petterle Paulo Justiniano Ribeiro Júnior Wagner Hugo Bonat |
| author_facet | Guilherme Parreira da Silva Henrique Aparecido Laureano Ricardo Rasmussen Petterle Paulo Justiniano Ribeiro Júnior Wagner Hugo Bonat |
| author_sort | Guilherme Parreira da Silva |
| collection | DOAJ |
| description |
Univariate regression models have rich literature for counting data. However, this is not the case for multivariate count data. Therefore, we present the Multivariate Generalized Linear Mixed Models framework that deals with a multivariate set of responses, measuring the correlation between them through random effects that follows a multivariate normal distribution. This model is based on a GLMM with a random intercept and the estimation process remains the same as a standard GLMM with random effects integrated out via Laplace approximation. We efficiently implemented this model through the TMB package available in R. We used Poisson, negative binomial (NB), and COM-Poisson distributions. To assess the estimator properties, we conducted a simulation study considering four different sample sizes and three different correlation values for each distribution. We achieved unbiased and consistent estimators for Poisson and NB distributions; for COM-Poisson estimators were consistent, but biased, especially for dispersion, variance, and correlation parameter estimators. These models were applied to two datasets.
The first concerns a sample from 30 different sites collected in Australia where the number of times each one of the 41 different ant species was registered; which results in an impressive 820 variance-covariance and 41 dispersion parameters are estimated simultaneously, let alone the regression parameters. The second is from the Australia Health Survey with 5 response variables and 5190 respondents. These datasets can be considered overdispersed by the generalized dispersion index. The COM-Poisson model overcame the other two competitors considering three goodness-of-fit indexes, AIC, BIC, and maximized log-likelihood values. As a result, it estimated parameters with smaller standard errors and a greater number of significant correlation coefficients. Therefore, the proposed model is capable of dealing with multivariate count data, either under- equi- or overdispersed responses, and measuring any kind of correlation between them taking into account the effects of the covariates.
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| first_indexed | 2024-03-08T13:05:24Z |
| format | Article |
| id | doaj.art-967f2bbcb5564896a2e8677f84387e4e |
| institution | Directory Open Access Journal |
| issn | 1026-597X |
| language | English |
| last_indexed | 2024-03-08T13:05:24Z |
| publishDate | 2024-01-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| spelling | doaj.art-967f2bbcb5564896a2e8677f84387e4e2024-01-18T20:26:44ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2024-01-0153110.17713/ajs.v53i1.1574Multivariate Generalized Linear Mixed Models for Count DataGuilherme Parreira da Silva0Henrique Aparecido Laureano1Ricardo Rasmussen Petterle2Paulo Justiniano Ribeiro Júnior3Wagner Hugo Bonat4Federal University of ParanáInstituto de Pesquisa Pelé Pequeno PríncipeFederal University of ParanáFederal University of ParanáFederal University of Paraná Univariate regression models have rich literature for counting data. However, this is not the case for multivariate count data. Therefore, we present the Multivariate Generalized Linear Mixed Models framework that deals with a multivariate set of responses, measuring the correlation between them through random effects that follows a multivariate normal distribution. This model is based on a GLMM with a random intercept and the estimation process remains the same as a standard GLMM with random effects integrated out via Laplace approximation. We efficiently implemented this model through the TMB package available in R. We used Poisson, negative binomial (NB), and COM-Poisson distributions. To assess the estimator properties, we conducted a simulation study considering four different sample sizes and three different correlation values for each distribution. We achieved unbiased and consistent estimators for Poisson and NB distributions; for COM-Poisson estimators were consistent, but biased, especially for dispersion, variance, and correlation parameter estimators. These models were applied to two datasets. The first concerns a sample from 30 different sites collected in Australia where the number of times each one of the 41 different ant species was registered; which results in an impressive 820 variance-covariance and 41 dispersion parameters are estimated simultaneously, let alone the regression parameters. The second is from the Australia Health Survey with 5 response variables and 5190 respondents. These datasets can be considered overdispersed by the generalized dispersion index. The COM-Poisson model overcame the other two competitors considering three goodness-of-fit indexes, AIC, BIC, and maximized log-likelihood values. As a result, it estimated parameters with smaller standard errors and a greater number of significant correlation coefficients. Therefore, the proposed model is capable of dealing with multivariate count data, either under- equi- or overdispersed responses, and measuring any kind of correlation between them taking into account the effects of the covariates. https://www.ajs.or.at/index.php/ajs/article/view/1574 |
| spellingShingle | Guilherme Parreira da Silva Henrique Aparecido Laureano Ricardo Rasmussen Petterle Paulo Justiniano Ribeiro Júnior Wagner Hugo Bonat Multivariate Generalized Linear Mixed Models for Count Data Austrian Journal of Statistics |
| title | Multivariate Generalized Linear Mixed Models for Count Data |
| title_full | Multivariate Generalized Linear Mixed Models for Count Data |
| title_fullStr | Multivariate Generalized Linear Mixed Models for Count Data |
| title_full_unstemmed | Multivariate Generalized Linear Mixed Models for Count Data |
| title_short | Multivariate Generalized Linear Mixed Models for Count Data |
| title_sort | multivariate generalized linear mixed models for count data |
| url | https://www.ajs.or.at/index.php/ajs/article/view/1574 |
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