## Murray State Theses and Dissertations

#### Title

Evaluating an Ordinal Output using Data Modeling, Algorithmic Modeling, and Numerical Analysis

#### Abstract

Data and algorithmic modeling are two diﬀerent approaches used in predictive analytics. The models discussed from these two approaches include the proportional odds logit model (POLR), the vector generalized linear model (VGLM), the classiﬁcation and regression tree model (CART), and the random forests model (RF). Patterns in the data were analyzed using trigonometric polynomial approximations and Fast Fourier Transforms. Predictive modeling is used frequently in statistics and data science to ﬁnd the relationship between the explanatory (input) variables and a response (output) variable. Both approaches prove advantageous in diﬀerent cases depending on the data set. In our case, the data set contains an output variable that is ordinal. Using grade records from Murray State University, the goal is to ﬁnd the best predictive model that can implement an ordinal output by means of data modeling and algorithmic modeling. To train the models, k-fold cross validation is used to ﬁnd the optimal tuning parameters and performance for each of the models. The logarithmic loss (logLoss) performance metric is utilized to determine which method has the top predictive accuracy. A comparison of each statistical model and a look at alternative methods is discussed.

#### Year manuscript completed

2020

#### Year degree awarded

2020

#### Author's Keywords

machine learning, predictive modeling, student grades, ordinal output, ordinal, proportional odds logistic regression, POLR, vector generalized linear models, VGLM, CART, classification trees, classification and regression trees, random forests, random forest, RF, logLoss, logarithmic loss, multi-class, CV, cross validation, k-fold cross validation, training, testing, trigonometric interpolating polynomials, fast fourier transforms, FFT, fourier series

#### Thesis Advisor

Donald Adongo

#### Thesis Co-Advisor

Christopher Mecklin

#### Committee Chair

Edward Thome

#### Committee Member

Manoj Pathak

#### Document Type

Thesis

#### Recommended Citation

Brown, Martin Keagan Wynne, "Evaluating an Ordinal Output using Data Modeling, Algorithmic Modeling, and Numerical Analysis" (2020). *Murray State Theses and Dissertations*. 168.

https://digitalcommons.murraystate.edu/etd/168

#### Included in

Analysis Commons, Applied Statistics Commons, Numerical Analysis and Computation Commons, Other Applied Mathematics Commons, Other Mathematics Commons, Other Statistics and Probability Commons, Probability Commons, Statistical Models Commons