Exploratory multivariate longitudinal data analysis and models for multivariate longitudinal binary data

Longitudinal data occurs when repeated measurements from the same subject are observed over time. In this thesis, exploratory data analysis and models are utilized jointly to analyze longitudinal data which leads to stronger and better justified conclusions. The complex structure of longitudinal data with covariates requires new visual methods that enable interactive exploration. Here we catalog the general principles of exploratory data analysis for multivariate longitudinal data, and illustrate the use of the linked brushing approach for studying the mean structure over time. It is possible to reveal the unexpected, to explore the interaction between responses and covariates, to observe the individual variations, understand structure in multiple dimensions, and diagnose and fix models by using these methods. We also propose models for multivariate longitudinal binary data that directly model marginal covariate effects while accounting for the dependence across time via a transition structure and across responses within a subject for a given time via random effects. Markov Chain Monte Carlo Methods, specifically Gibbs sampling with Hybrid steps, are used to sample from the posterior distribution of parameters. Graphical and quantitative checks are used to assess model fit. The methods are illustrated on several real datasets, primarily the Iowa Youth and Families Project.*;*This dissertation is a compound document (contains both a paper copy and a CD as part of the dissertation)

First-order marginalised transition random effects models with probit link function

Marginalised models, also known as marginally specified models, have recently become a popular tool for analysis of discrete longitudinal data. Despite being a novel statistical methodology, these models introduce complex constraint equations and model fitting algorithms. On the other hand, there is a lack of publicly available software to fit these models. In this paper, we propose a three-level marginalised model for analysis of multivariate longitudinal binary outcome. The implicit function theorem is introduced to approximately solve the marginal constraint equations explicitly. probit link enables direct solutions to the convolution equations. Parameters are estimated by maximum likelihood via a Fisher-Scoring algorithm. A simulation study is conducted to examine the finite-sample properties of the estimator. We illustrate the model with an application to the data set from the Iowa Youth and Families Project. The R package pnmtrem is prepared to fit the model

Exploratory multivariate longitudinal data analysis and models for multivariate longitudinal binary data

Longitudinal data occurs when repeated measurements from the same subject are observed over time. In this thesis, exploratory data analysis and models are utilized jointly to analyze longitudinal data which leads to stronger and better justified conclusions. The complex structure of longitudinal data with covariates requires new visual methods that enable interactive exploration. Here we catalog the general principles of exploratory data analysis for multivariate longitudinal data, and illustrate the use of the linked brushing approach for studying the mean structure over time. It is possible to reveal the unexpected, to explore the interaction between responses and covariates, to observe the individual variations, understand structure in multiple dimensions, and diagnose and fix models by using these methods. We also propose models for multivariate longitudinal binary data that directly model marginal covariate effects while accounting for the dependence across time via a transition structure and across responses within a subject for a given time via random effects. Markov Chain Monte Carlo Methods, specifically Gibbs sampling with Hybrid steps, are used to sample from the posterior distribution of parameters. Graphical and quantitative checks are used to assess model fit. The methods are illustrated on several real datasets, primarily the Iowa Youth and Families Project.*;*This dissertation is a compound document (contains both a paper copy and a CD as part of the dissertation).</p

Flexible multivariate marginal models for analyzing multivariate longitudinal data, with applications in R

Most of the available multivariate statistical models dictate on fitting different parameters for the covariate effects on each multiple responses. This might be unnecessary and inefficient for some cases. In this article, we propose a modelling framework for multivariate marginal models to analyze multivariate longitudinal data which provides flexible model building strategies. We show that the model handles several response families such as binomial, count and continuous. We illustrate the model on the Kenya Morbidity data set. A simulation study is conducted to examine the parameter estimates. An R package mmm2 is proposed to fit the model

mmm:an R package for analyzing multivariate longitudinal data with multivariate marginal models.

Modeling multivariate longitudinal data has many challenges in terms of both statistical and computational aspects. Statistical challenges occur due to complex dependence structures. Computational challenges are due to the complex algorithms, the use of numerical methods, and potential convergence problems. Therefore, there is a lack of software for such data. This paper introduces an R package mmm prepared for marginal modeling of multivariate longitudinal data. Parameter estimations are achieved by generalized estimating equations approach. A real life data set is applied to illustrate the core features of the package, and sample R code snippets are provided. It is shown that the multivariate marginal models considered in this paper and mmm are valid for binary, continuous and count multivariate longitudinal responses

Forecasting multivariate longitudinal binary data with marginal and marginally specified models

Forecasting with longitudinal data has been rarely studied. Most of the available studies are for continuous response and all of them are for univariate response. In this study, we consider forecasting multivariate longitudinal binary data. Five different models including simple ones, univariate and multivariate marginal models, and complex ones, marginally specified models, are studied to forecast such data. Model forecasting abilities are illustrated via a real-life data set and a simulation study. The simulation study includes a model independent data generation to provide a fair environment for model competitions. Independent variables are forecast as well as the dependent ones to mimic the real-life cases best. Several accuracy measures are considered to compare model forecasting abilities. Results show that complex models yield better forecasts