Comparing estimation approaches for generalized additive mixed models with binary outcomes

Abstract

Generalized additive mixed models (GAMMs) extend generalized linear mixed models (GLMMs) to allow the covariates to be nonparametrically associated with the response. Estimation of such models for correlated binary data is challenging and estimation techniques often yield contrasting results. Via simulations, we compared the performance of the Bayesian and likelihood-based methods for estimating the components of GAMMs under a wide range of conditions. For the Bayesian method, we also assessed the sensitivity of the results to the choice of prior distributions of the variance components. In addition, we investigated the effect of multicollinearity among covariates on the estimation of the model components. We then applied the methods to the Bangladesh Demographic Health Survey data to identify the factors associated with the malnutrition of children in Bangladesh. While no method uniformly performed best in estimating all components of the model, the Bayesian method using half-Cauchy priors for variance components generally performed better, especially for small cluster size. The overall curve fitting performance was sensitive to the prior selection for the Bayesian methods and also to the extent of multicollinearity.

Keywords:

• Penalized splines
• generalized linear mixed models
• penalized quasi-likelihood
• Laplace approximation
• Markov chain Monte Carlo
• variance components

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data that support the findings of this study are openly available in ‘The Demographic and Health Surveys (DHS) Program -- Bangladesh: Standard DHS, 2014 Dataset’ at https://dhsprogram.com/data/dataset/Bangladesh_Standard-DHS_2014.cfm?flag=0.

Additional information

Funding

Dr. Benedetti is supported by the Fonds de recherche Santé Québec (FRQS).