Correlated Ordinal Categorical Data Analysis

ISBN-10
ISBN-13
9798597009377
Category
Mathematical models
Pages
102
Language
English
Published
2020
Author
Yingzi Li

Description

This dissertation consists of two stand-alone but related studies about modeling correlated ordinal categorical variables. The first study evaluates the estimation performance of three models: Ordinal Logistic Regression (OLR), Generalized Estimating Equations (GEE), and Binary Dynamic Logit for Correlated Ordinal (BDLCO). OLR and GEE are well known models, and BDLCO is a newer model proposed by Sutradhar and Dasgupta (2016) which has three advantages: 1) it converts each ordinal response into a vector of binarized responses, i.e., 1 or greater than 1; 1 and 2 or greater than 2, etc., to preserve the ordering information; 2) it includes the binarized response of the previous period as dependence in the model and estimates the dependence parameters simultaneously with other parameters, which can improve estimation efficiency; 3) it does not require proportional-odds assumption.However, the dependence structure of the BDLCO model can increase the number of dependence parameters rapidly as the number of categories of the response increases, which causes convergence problem of the model. Therefore, the second study introduces the dependence using the latent variable instead of the binarized response of the previous period, i.e., a Latent Variable approach for Correlated Ordinal (LVCO).In both studies, the newer models are applied to an apple bloom data, and the results are compared to the estimation results from OLR. The parameter estimates from the two newer models are more accurate. To compare the model performance more generally, a set of simulation analyses are conducted to compare the average Biases and Mean Absolute Percentage Errors (MAPEs) of the estimates from OLR, GEE, BDLCO and LVCO models under scenarios when the proportional-odds assumption holds as well as it does not hold. Results show that BDLCO and LVCO models have much smaller average Biases under both scenarios, and even though the MAPEs are similar among all the models when proportional-odds assumption is satisfied, the newer models have smaller MAPEs when proportional-odds does not present. The LVCO model consistently has the smallest average Biases for all the parameters, and it generates more accurate dependence parameters compared to BDLCO.

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