Bayesian influence analysis of generalized partial linear mixed models for longitudinal data

Bayesian multilevel logistic regression models: a case study applied to the results of two questionnaires administered to university students

Bayesian multilevel models—also known as hierarchical or mixed models—are used in situations in which the aim is to model the random effect of groups or levels. In this paper, we conduct a simulation study to compare the predictive ability of 1-level Bayesian multilevel logistic regression models with that of 2-level Bayesian multilevel logistic regression models by using the prior Scaled Beta2 and inverse-gamma distributions to model the standard deviation in the 2-level. Then, these models are employed to estimate the correct answers in two questionnaires administered to university students throughout the first academic semester of 2018. The results show that 2-level models have a better predictive ability and provide more precise probability intervals than 1-level models, particularly when the prior Scaled Beta2 distribution is used to model the standard deviation in the second level. Moreover, the probability intervals of 1-level Bayesian multilevel logistic regression models proved to be more precise when Scaled Beta2 distributions, rather than an inverse-gamma distribution, are employed to model the standard deviation or when 1-level Bayesian multilevel logistic regression models, are used.

Bayesian Influence Analysis of the Skew-Normal Spatial Autoregression Models

In spatial data analysis, outliers or influential observations have a considerable influence on statistical inference. This paper develops Bayesian influence analysis, including the local influence approach and case influence measures in skew-normal spatial autoregression models (SSARMs). The Bayesian local influence method is proposed to evaluate the impact of small perturbations in data, the distribution of sampling and prior. To measure the extent of different perturbations in SSARMs, the Bayes factor, the ϕ-divergence and the posterior mean distance are established. A Bayesian case influence measure is presented to examine the influence points in SSARMs. The potential influence points in the models are identified by Cook’s posterior mean distance and Cook’s posterior mode distance ϕ-divergence. The Bayesian influence analysis formulation of spatial data is given. Simulation studies and examples verify the effectiveness of the presented methodologies.