Novel Statistical Estimation Algorithms and Tools for Binomial and Multinomial Longitudinal Data

Not Available "Statistical modeling and analysis for longitudinal data are important in many applications ranging across behavioral and medical sciences. Statistical theory based on continuous variables and Gaussian distributional assumptions is well developed, andappropriate tools such as NLME (Nonlinear and Linear Mixed Effects: see Pinheiros and Bates (2001)) are available. Corresponding algorithms and software for discrete binomial and multinomial data are much less well developed, and pose nontrivial choicesand challenges. We propose to develop methods based on probit assumptions that essentially say that the data arises from discretizing hidden continuous variables, whence "missing value" methods such as EM algorithms and MCMC data augmentation Bayesianmethods can be devised that can build on the available software for the continuous case. We believe R software to accomplish this is a feasible project that will significantly extend what is currently available and will be found useful by many researchers.The proposed new statistical algorithms and tools can benefit many public and private organizations, including the federal government, and academic and other nongovernmenal research institutions such as pharmaceutical companies, where longitudinal andother forms of hierarchical data are common. The published theoretical results will benefit the statistics community in general. A software package written in R will reach many users, and, eventually, the algorithms can be implemented in other collectionssuch as MATLAB and SAS, thus multiplying the effect of the initiative and increasing the payoff from our small business enterprise resources to improve the effectiveness and validity of data analysis in many fields."