Author ORCID Identifier

Date Available


Year of Publication


Degree Name

Doctor of Philosophy (PhD)

Document Type

Doctoral Dissertation




Education Sciences

First Advisor

Dr. Kelly D. Bradley

Second Advisor

Dr. Michael Peabody


Ratio-type data plays an important role in real-world data analysis. Mass ratios have been created for different purposes, depending on time and people’s needs. Then, it is necessary to create a comprehensive score to extract information from those mass ratios when they measure the same concept from different perspectives. Therefore, this study adopts the same logic of psychometrics to systematically conduct scale development on ratio-type data under the Rasch model. However, it is first necessary to discretize the ratio-type data for use in the Rasch model. Therefore, this study also explores the effect of different data discretization methods on scale development by using financial profitability ratios as a demonstration. Results show that retaining more ratio categories can benefit Rasch modeling because it can better inform the model. The dynamic clustering algorithm, k-median is a better method for extracting characteristic patterns of the ratio-type data and preparing the data for the Rasch model. This study illustrates that there is no one-way good discretization method for ratio-type data under the Rasch model. It is more reasonable to use the traditional algorithm if each ratio has a target benchmark, whereas the k-median clustering algorithm achieves good modeling results when benchmark information is lacking.

Digital Object Identifier (DOI)