Bayesian analysis of hierarchical models for polychotomous data from a multi-stage cluster sample

In this thesis we present a hierarchical Bayesian methodology for analyzing polychotomous data from multi-stage cluster samples. We begin with a model for multinomial data drawn from a two-stage cluster sample of a finite population. This model is then extended to incorporate partially observed data assuming that the data are missing at random (MAR), in the terminology of Little and Rubin (1987). We next develop a model for polychotomous data collected via a three-stage cluster sample. As with the two-stage model, we describe the methodology for dealing with partially observed data assuming they are MAR. We apply these two methodologies to the 1990 Slovenian Public Opinion Survey and present the results of these analyses. Finally, we fashion a multivariate probit model for a special type of multinomial data, multivariate binary data. We then construct this model that incorporates covariate information for the case of a two-stage cluster sample. Specifically, we outline this methodology for a two-stage cluster sample. This approach also allows for the integration of missing data into the analysis if the data are MAR. For all of the above models we use Markov chain Monte Carlo techniques to simulate samples from the posterior distribution. These samples are then utilized in making inference from the models

Bayesian analysis of hierarchical models for polychotomous data from a multi-stage cluster sample

In this thesis we present a hierarchical Bayesian methodology for analyzing polychotomous data from multi-stage cluster samples. We begin with a model for multinomial data drawn from a two-stage cluster sample of a finite population. This model is then extended to incorporate partially observed data assuming that the data are missing at random (MAR), in the terminology of Little and Rubin (1987). We next develop a model for polychotomous data collected via a three-stage cluster sample. As with the two-stage model, we describe the methodology for dealing with partially observed data assuming they are MAR. We apply these two methodologies to the 1990 Slovenian Public Opinion Survey and present the results of these analyses. Finally, we fashion a multivariate probit model for a special type of multinomial data, multivariate binary data. We then construct this model that incorporates covariate information for the case of a two-stage cluster sample. Specifically, we outline this methodology for a two-stage cluster sample. This approach also allows for the integration of missing data into the analysis if the data are MAR. For all of the above models we use Markov chain Monte Carlo techniques to simulate samples from the posterior distribution. These samples are then utilized in making inference from the models.</p

An Alternative to the NFL Draft Pick Value Chart Based upon Player Performance

In this paper, we consider the National Football League Pick Value Chart and propose an alternative. The current Pick Value Chart was created approximately 20 years ago and has been used since to determine the value of draft selections for trading of draft selections. For this paper, we analyze the first 255 draft selections for the years 1991 to 2001. As part of our analysis, we consider four non-position dependent metrics to measure and model player performance at each of the first 255 draft selections. We perform a nonparametric regression of each performance metric onto player's selections. A comparison is then made between each fitted line and the Pick Value Chart. Having considered these comparisons, we propose an alternative Pick Value Chart.