# Research

## Tutorial on Bayesian Hierarchical Models in R - 2014

The purpose of this documentation is to present a practical understanding and implementation of a Bayesian Hierarchical model. Bayesian Hierarchical models allow analysts to account for endogeneity. A Bayesian Hierarchical model is a Bayesian network, a probabilistic graphical model that represents a set of random variables and their conditional dependencies via a directed acyclic graph . Bayesian Hierarchical models subset themselves by containing three or more levels of random variables or use latent variables. One level uses within-unit analysis and another level for across-unit analysis. Within-unit models describes individual respondents over time. The across-unit model is used to describe the diversity, or heterogeneity, of the units.

## Graphing, Mapping, and Coordinate scraping in R- 2014

The purpose of this paper is to be an introductory text for the R programming language’s graphing and mapping features. R is a free software programming language and software environment for statistical computing and graphics. While it performs similar functions to packages such as SAS and STATA, the systems have speciﬁc strengths and weaknesses. This paper uses ggplot2 and ggmap to show R’s graphing capabilities.

## Genetic Algorithm Construction for Tic-Tac-Toe in Excel - 2014

This excel file was developed in my Advanced Excel Analysis class. In this final product you play against an AI trained on a genetric algorithm. The program was developed by creating two AIs, each based on a genetric algorithm. After playing million of times against one another one of the AIs was chosen to play against humans. All code is left open for people to poke and prod as they like.

## Aggregation Bias in the US Personal Consumption Expenditure - 2014

The purpose of my analysis is to study whether there is aggregation bias in the United States Personal Consumption Expenditures Price Index. Using the National Income and Product Accounts that make up the PCE, I test whether there is con- vergence of inﬂation differentials in multiple levels of disaggregation. This paper explains inaccuracies that can occur and are exampled by basic ﬁrst generation panel unit root test and stationarity tests. Using the second generation panel unit root test developed by Bai and Ng (2004), this study ﬁnds aggregation bias from three tiers of PCE aggregation. These results are consistent with theoretical and empirical literature supporting that improper aggregation of indices can lead to erroneously concluding inﬂation differentials persistent.

## An Analysis of the Effects of Machinery in Labor Markets - 2013

The purpose of this analysis is to model how a ﬁrm interacts with union and non-union labor markets. The ﬁrm’s objective is to maximize proﬁt. Union workers threatening to go on strike have made the ﬁrm consider substituting union workers with machinery and non-union labor. The ﬁrm decides what proportion of union and non-union workers as well as machinery to use as inputs. The probability of the union workers going on strike is a negative function of the wage rate. A strike eliminates a portion of the proﬁts the ﬁrm could employ. The probability of non-union workers causing sabotage is a positive function of the amount of non-union workers. The amount of sabotage is proportionate to the amount of non-union workers and machinery minus the amount of union workers.

This model suggests that as the ﬁrm inputs more machinery, union labor’s ability to strike and cause sabotage will decrease until it is no longer considered a credible threat. Wages of non-union workers will always be slightly higher than wages of union workers. This creates a chiseling style of gameplay between each type of labor. If the workers choose to unionize and create a credible threat of striking, ﬁrms can agree to raise the wage of union workers, at the expense of ﬁring many workers in order to implement machinery.

## A Predictive Model for NFL Quarterback Fantasy Football Points - 2013

This analysis designs a model that predicts NFL rookie Quarterbacks’s fantasy football points. Theoretical models for judging the quality of football players are limited. We theorize that a player’s skill can be isolated by assessing their fantasy football points. This model will predict within a margin of error how well a Quarter back will perform his rookie year based oﬀ of their college career statistics. Data was gathered for Quarterbacks in the NFL drafts from 2009 to 2012. Our linear model will use college career statistics to predict fantasy football scores.

It is found that as the percentage of pass completions, average yards per game, and rushing touchdowns are signiﬁcant predictors of a rookie quarterbacks NFL fantasy points. The model used does not suﬀer from heteroskedasticity, but does have a large constant and standard error for the constant.