Statistical Modelling current issue

Multilevel models with multivariate mixed response types

Goldstein, H., Carpenter, J., Kenward, M. G, Levin, K. A — Wed, 21 Oct 2009 06:57:22 PDT

We build upon the existing literature to formulate a class of models for multivariate mixtures of Gaussian, ordered or unordered categorical responses and continuous distributions that are not Gaussian, each of which can be defined at any level of a multilevel data hierarchy. We describe a Markov chain Monte Carlo algorithm for fitting such models. We show how this unifies a number of disparate problems, including partially observed data and missing data in generalized linear modelling. The two-level model is considered in detail with worked examples of applications to a prediction problem and to multiple imputation for missing data. We conclude with a discussion outlining possible extensions and connections in the literature. Software for estimating the models is freely available.

Latent trajectory modelling of multivariate binary data

Beath, K. J, Heller, G. Z — Wed, 21 Oct 2009 06:57:22 PDT

Latent trajectory analysis is a form of latent class analysis, where the manifest variables are longitudinal measurements of a single outcome. The latent classes may correspond to either constant increasing or decreasing levels of the outcome over time and describe different severity or course of a disease. Extension to multiple outcomes at each time point allows more accurate determination of classes, with classes based on combination of the outcomes, however requiring models which account for both correlation between outcomes and periods. Three models are described for multiple binary outcomes, observed at each time point: a latent class model where all outcomes are considered independent at all time points, a model incorporating random effects for subject only and one incorporating random effects for subject and period. The methods are applied to data on asthma and allergy symptoms in infants, with symptoms recorded at four time points, and it is shown that the incorporation of subject and period heterogeneity results in lower estimates of the number of latent classes.

Multinomial-Poisson models subject to inequality constraints

Cazzaro, M., Colombi, R. — Wed, 21 Oct 2009 06:57:22 PDT

Lang’s Multinomial-Poisson Homogeneous (MPH) models and Homogeneous Linear Predictor (HLP) Multinomial-Poisson models include as special cases many models for contingency table analysis that have been introduced in the effort to overcome well-known limitations of the log-linear models. Here the definitions of MPH and HLP models are extended to include inequality constraints. It is shown that inequality constrained MPH and HLP models are very flexible and rich family of models for contingency table analysis. The inequality constrained hierarchical multinomial marginal models which are an important sub-class of MPH models are also examined.

Robustness for general design mixed models using the t-distribution

Staudenmayer, J, Lake, E E, Wand, M P — Wed, 21 Oct 2009 06:57:22 PDT

The t-distribution allows the incorporation of outlier robustness into statistical models while retaining the elegance of likelihood-based inference. In this paper, we develop and implement a linear mixed model for the general design of the linear mixed model using the univariate t-distribution. This general design allows a considerably richer class of models to be fit than is possible with existing methods. Included in this class are semi-parametric regression and smoothing and spatial models.