The paper considers confidence intervals based on sandwich variance estimates. The sandwich estimates have a larger variability compared to classical variance estimates. This has the effect that the coverage probability of confidence intervals based on sandwich variance estimates and t-distribution quantiles falls below the nominal value. We suggest a simple adjustment to compensate this defect.

The method of quasi-least squares has been introduced and developed recently in a series of three papers: Chaganty (1997), Shults and Chaganty (1998), and Chaganty and Shults (1999). These papers are concerned with estimating the parameters in longitudinal data analysis problems that occur in the framework of generalized linear models. In this presentation I will discuss the application of the method to analyze some multivariate discrete mixture models. Examples will be given to illustrate the method on real life data.

Longitudinal data with counted response have been an important problem in health sciences. This paper proposes a transition model to analyze the longitudinal data consisting of a counted response variable observed at unequal time intervals, time-dependent covariates and baseline covariates which are time-independent. A nonlinear optimization algorithm is used to estimate the parameters in this model. The model characteristics are investigated. An application of this method to the ophthalmologic data is provided and compared with GEE and generalized linear mixed effects model.

Biological Control of pests is an important branch of entomology, providing environmentally friendly forms of crop protection. Bioassays are used to find the optimal conditions for the production of parasites and strategies for application in the field. In some of these assays, proportions are measured and, often, these data have an inflated number of zeros. In this work, six models will be applied to datasets obtained from biological control assays for Diatraea saccharalis, a common pest in sugar cane production. A natural choice for modelling proportion data is the binomial model. The second model will be an overdispersed version of the binomial model, estimated by a quasi-likelihood method. This model was initially built to model overdispersion generated by individual variability in the probability of success. When interest is only in the positive proportion data, a model can be based on the truncated binomial distribution and in its overdispersed version. The last two models include the zero proportions and are based on a finite mixture model with the binomial distribution or its overdispersed version for the positive data. Here we will present the models, discuss their estimation and compare the results.

A project which originated with the aim of documenting the implications of dropouts for tests of significance based on general linear mixed model procedures resulted in recognition of problems in the use of SAS PROC MIXED for this purpose. In responding to suggestions and criticisms, we have reanalyzed realistically simulated clinical trials data using an alternative error model formulation, different approaches to inclusions of covariates to model dropout patterns, and different ways to include the critical time variable in the mixed model. Through simulation, We investigate the type I errors and powers of the PROC MIXED tests of significance for GROUP and TIMExGROUP hypotheses to less than optimal modeling of the error covariance structure.

This study determines whether spatial clusters are present in a given colon cancer and melanoma data set by applying test of spatial homogeneity under generalized Poisson distribution (GPD) instead of standard Poisson distribution. It determines whether spatial-temporal clusters are present for the data by applying Ederer et al. test of clustering. It investigates the effects of population size on colon cancer and melanoma cases using three nonlinear models: Poisson regression (PR), negative binomial regression (NBR), and generalized Poisson regression (GPR) models. Also, it measures the effects of: average time to diagnosis on colon cancer and melanoma cases; mean distance (in miles) between diagnosed melanoma cases; and mean time to diagnosis (in months) on melanoma cases.

Two types of random effects models for repeated measurements on two or more response variables are considered. The first model is an extension of the Generalized Linear Mixed Model (GLMM) and can accommodate any combination of outcome variables in the exponential family. A separate GLMM is formulated for each response variable and then the models are combined by imposing a joint multivariate normal distribution on the subject-specific random effects. The responses on the same subject are assumed to be conditionally independent given the random effects, which allows estimation procedures for GLMM to be directly modified for this more general model. The second model is a correlated probit model for repeated measurements on a bivariate response, consisting of a binary and a continuous outcome. This model does not assume conditional independence between the two variables, which makes it more general than the corresponding GLMM. Maximum likelihood estimates can be obtained using a Monte Carlo EM algorithm.

In many areas of research data is collected over time or in clusters. In such situations the responses for a given individual or within a given cluster are often correlated. For non-normal responses, generalized linear mixed models (GLMM's) provide a mechanism for modelling overdispersion or correlation by incorporating random effects. In this work we present random effects models for nominal and ordinal response data. The models are motivated as generalizations of a multivariate generalized linear model. We consider both parametric and nonparametric assumptions concerning the distribution of the random effects. In the parametric approach a normal distribution is assumed and maximum likelihood estimation is carried out by either adaptive Gauss-Hermite quadrature or Monte-Carlo techniques. In the nonparametric approach we assume that the random effects distribution is discrete with unknown masses, mass points, and support size. Nonparametric maximum likelihood estimates of the regression parameters and the discrete distribution are obtained by way of an accelerated EM algorithm. Application of the two approaches for the cumulative logit link, adjacent-category logit link, and baseline-category logit link is discussed.