In recent years, generalized linear latent variable models (GLLVMs) have gained popularity in community ecology, where they are used to model the environmental factors driving changes in species assemblages, while accounting for potential spatial and/or temporal as well as between species correlations. This paper is motivated by the Southern Ocean Continuous Plankton Recorder survey, an international longitudinal survey focused on studying marine assemblages in the Indian sector of the Southern Ocean.
When modeling spatial-temporal community ecology data, it is becoming common to include a spatial-temporal correlation function in the latent variable structure, as opposed to making the standard assumption of independence. Using the SO-CPR survey, we set out to study whether, given the computational benefits, there are aspects of inference for GLLVMs which are robust to deliberately assuming independence for the latent variable structure. Focused is placed on estimation and inference of the environmental covariates and prediction of the latent variables, as we explore the impact of misspecification (assuming independence) in the presence of spatial-temporal correlations.