Dissertation
A study on the comparison of treatments with a control for ordinal data using probit regression
Washington State University
Doctor of Philosophy (PhD), Washington State University
01/2021
DOI:
https://doi.org/10.7273/000002401
Handle:
https://hdl.handle.net/2376/119328
Abstract
In this dissertation we investigate the problem of inference based on ordinal regression models, with focus on the Probit model. Ordinal data, which is neither numerical or categorical in the real sense of the word, is often hard to analyse. The problem is exacerbated while comparing parameters of several treatments with an ordinal response. The common ways of dealing with ordinal data inference is using Likert type or CDF models. We discuss the existing literature on these and indicate how hard it is to extend these to situations of autocorrelation, multicollinearity and other practical problems arising in real data.
Here, we take a new look at the estimation problem of ordinal data by using a linear approximation of the underlying latent variable of the observed ordinal data. Our approach, a two-step Approximate Latent Linear Model (ALLM), is intuitive and allows for extension into situations where linear models and OLS can be used. The idea of ALLM is based on a weighted linear function and estimation is done using an iterative re-weighted least square approach. We use this approach for all the inference in this dissertation. We look at estimation and analyse a data problem using this method. Using Monte Carlo simulation, we look at bias and MSE of the ALLM and compare it to the CDF based method. We find that ALLM is computationally comparable and is better than the CDF method in terms of bias and MSE. We follow up with testing equality of the parameters of the ordinal regression model using ALLM. The approach is verified by looking at Type I error and power using Monte Carlo simulations. We follow up by proceeding to compare several treatments with a control. To conduct multiple testing, the test statistics are derived. We show that the ALLM based multiple comparison method maintains Type I error well and gives consistent power. Our impression is that as ALLM is a “linear approximation” and we are using weighted least squares, this will allow easier extensions when autocorrelation and multicollinearity issues arise in ordinal data. Future work in this direction is the next step.
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Details
- Title
- A study on the comparison of treatments with a control for ordinal data using probit regression
- Creators
- Debasmita Das
- Contributors
- Nairanjana Dasgupta (Advisor)Marc Evans (Committee Member)Abhishek Kaul (Committee Member)Xiongzhi Chen (Committee Member)
- Awarding Institution
- Washington State University
- Academic Unit
- Mathematics and Statistics, Department of
- Theses and Dissertations
- Doctor of Philosophy (PhD), Washington State University
- Publisher
- Washington State University
- Number of pages
- 106
- Identifiers
- 99900606653501842
- Language
- English
- Resource Type
- Dissertation