Inferences in longitudinal multinomial fixed and mixed models

Analyzing categorical data collected over time is an important research topic. Even though there exists numerous studies on analysis of categorical data in cross sectional setup, the analysis of this type of data in the longitudinal setup is, however, not adequately addressed. In this thesis, we develop two correlation models for multinomial (> 2 categories) longitudinal data, namely, a conditional linear probability based model and a non-linear logistic probability based model; and provide likelihood inferences for category effects, fixed covariate effects and correlations or dynamic dependence parameters. The inferences are done for both complete history and contingency tables based data. For the history based data, the thesis also models the influences of individual random effects in addition to the fixed covariate effects. Furthermore, as in many practical situations the number of individuals involved in the study may be small, in the thesis, we have examined the finite sample performance of the likelihood estimates both in fixed and mixed model setups

Zero Truncated Bivariate Poisson Model: Marginal-Conditional Modeling Approach with an Application to Traffic Accident Data

Abstract A new covariate dependent zero-truncated bivariate Poisson model is proposed in this paper employing generalized linear model. A marginal-conditional approach is used to show the bivariate model. The proposed model with estimation procedure and tests for goodness-of-fit and under (or over) dispersion are shown and applied to road safety data. Two correlated outcome variables considered in this study are number of cars involved in an accident and number of casualties for given number of cars

Generalized quasi-likelihood versus hierarchical likelihood inferences in generalized linear mixed models for count data

Inferences in generalized linear mixed models (GLMMs) which includes count and binary data as special cases are extremely important. As it is proven to be difficult to obtain consistent and efficient estimates of the parameters (regression effects and variance of the random effects) of such models, there is a vast growing literature dealing with this important estimation problem. Among them, the method of moments (MM), Penalized quasilikelihood (PQL) and Hierarchical likelihood (HL) approaches are more familiar. It is however known that the MM approach always produces consistent estimates, whereas the PQL approach may not provide consistent estimates for all the parameters of the model. A recently proposed generalized quasilikelihood (GQL) approach has proven to be better in the sense of consistency and efficiency as compared to the MM and other improved MM (IMM) procedures. There does not, however, exist any comparative study between the GQL and the HL approaches. In this thesis, we have made a comparison between these two approaches mainly through an extensive simulation study involving the Poisson-normal mixed model. It is found that the HL approach may not produce consistent estimates for the regression effects specially when the variance of the random effects is large. In contrast, the GQL approach is found to always produce consistent estimates for all parameters of the model. These two estimation methodologies are also illustrated by analyzing a data set on the health care utilization in St. John's, Canada

A generalized right truncated bivariate Poisson regression model with applications to health data.

A generalized right truncated bivariate Poisson regression model is proposed in this paper. Estimation and tests for goodness of fit and over or under dispersion are illustrated for both untruncated and right truncated bivariate Poisson regression models using marginal-conditional approach. Estimation and test procedures are illustrated for bivariate Poisson regression models with applications to Health and Retirement Study data on number of health conditions and the number of health care services utilized. The proposed test statistics are easy to compute and it is evident from the results that the models fit the data very well. A comparison between the right truncated and untruncated bivariate Poisson regression models using the test for nonnested models clearly shows that the truncated model performs significantly better than the untruncated model

Analysis of repeated measures data

This book presents a broad range of statistical techniques to address emerging needs in the field of repeated measures. It also provides a comprehensive overview of extensions of generalized linear models for the bivariate exponential family of distributions, which represent a new development in analysing repeated measures data. The demand for statistical models for correlated outcomes has grown rapidly recently, mainly due to presence of two types of underlying associations: associations between outcomes, and associations between explanatory variables and outcomes. The book systematically addresses key problems arising in the modelling of repeated measures data, bearing in mind those factors that play a major role in estimating the underlying relationships between covariates and outcome variables for correlated outcome data. In addition, it presents new approaches to addressing current challenges in the field of repeated measures and models based on conditional and joint probabilities. Markov models of first and higher orders are used for conditional models in addition to conditional probabilities as a function of covariates. Similarly, joint models are developed using both marginal-conditional probabilities as well as joint probabilities as a function of covariates. In addition to generalized linear models for bivariate outcomes, it highlights extended semi-parametric models for continuous failure time data and their applications in order to include models for a broader range of outcome variables that researchers encounter in various fields. The book further discusses the problem of analysing repeated measures data for failure time in the competing risk framework, which is now taking on an increasingly important role in the field of survival analysis, reliability and actuarial science. Details on how to perform the analyses are included in each chapter and supplemented with newly developed R packages and functions along with SAS codes and macro/IML. It is a valuable resource for researchers, graduate students and other users of statistical techniques for analysing repeated measures data

Parameter estimates for the truncated bivariate poisson models using the data on number of conditions and utilization of healthcare services (HRS, 2010).

<p>Parameter estimates for the truncated bivariate poisson models using the data on number of conditions and utilization of healthcare services (HRS, 2010).</p

Descriptive measures of outcome variables.

<p>Descriptive measures of outcome variables.</p

A Markov Model for Analyzing Polytomous Outcome Data

This paper highlights the estimation and test procedures for multi-state Markov models with covariate dependences in higher orders. Logistic link functions are used to analyze the transition probabilities of three or more states of a Markov model emerging from a longitudinal study. For illustration purpose the models are used for analysis of panel data on Health and Retirement Study conducted in USA during 1992-2002. The applications use self reported data on perceived emotional health at each round of the nationwide survey conducted among the elderly people. Useful and detailed results on the change in the perceived emotional health status among the elderly people are obtained