Statistical Modelling

Compared to modelling observable data, it is more difficult to choose a suitable distribution to describe latent variables since no prior knowledge or observable information can be used and only normal or nonparametric distributions are mainly applied to random effects for generalized linear mixed models (GLMMs) in the literature. To enhance the modelling toolkit, this article investigates a class of parametric skew elliptical random effects in multilevel binomial regression models using a Bayesian approach; the class includes skew normal, skew Students’ t-distributions and others. Skewness mechanism is considered through multiplying skewness parameter Δ by standardized folded elliptical random variables, and the posterior sampling is realized by working on a binary skewness indicator (BSI) instead of continuous Δ for parameter identifiability. Simulation study shows that the original continuous skewness parameter Δ and the posterior mean of BSI may have dichotomous signs to describe the directional (right/left) skewness; thus we address the importance of assuming specific random effects distribution and interpreting the skewness carefully. The methodology is exemplified through reanalyzing a teratogenic activity study of two niacin analogs published in the biological literature, and sampling-based model comparison shows that the parametric skew normal random effects model works largely better than nonparametric Dirichlet process mixture models for this data set.

Models are developed to adjust for measurement errors in normally distributed predictor and response variables and categorical predictors with misclassification errors. The models allow for a hierarchical data structure and for correlations among the errors and misclassifications. Markov Chain Monte Carlo (MCMC) estimation is used and implemented in a set of MATLAB macros.

We propose a multivariate volatility model for the behaviour of eight international equity indices. We show that many volatility models with heavy tails in financial work can be viewed as the GLM class of models with random effects in the dispersion. Hence, the h-likelihood approach, which provides efficient and simpler algorithms for GLM class, can be used as an estimation method for models used in finance. A comparison of the h-likelihood estimators with the ML estimators is made and its relative merits are discussed.

In this paper we propose a semi-parametric Bayesian analysis of a spatio-temporal autoregressive model (STAR) with neighbourhood effects similar to those of Pace et al. (1998, 2000). This approach allows us to make inferences about the parameters of the model and, more particularly, about the number of neighbours, without having to appeal to asymptotic results. In addition, the procedure used to obtain the out-sample predictions takes into account the uncertainty associated to the estimation of the model parameters in a more realistic way. The methodology is illustrated by means of an application to the real estate market in the city of Zaragoza (Spain).