ThurCatD: a tool for analyzing ratings on an ordinal category scale

Area of Science:

• Psychometrics
• Statistical Modeling

Background:

• Ordinal scaling is frequently used in psychology to measure latent attributes.
• Existing methods may not fully capture the nuances of ordinal data.
• Thurstone's judgment scaling model provides a framework for analyzing such data.

Purpose of the Study:

• To present a novel algorithm for the analysis of ordinal scaling results.
• To model frequency data on ordinal categories for unidimensional psychological attributes.
• To implement parameter estimation and provide measures of statistical accuracy.

Main Methods:

• The algorithm models ordinal category frequencies using Thurstone's judgment scaling model.
• It employs maximum likelihood estimation for model parameters.
• Cramér-Rao bounds are calculated for standard error estimation.

Main Results:

• The algorithm provides estimated model parameters.
• Standard errors of these parameters are derived using Cramér-Rao bounds.
• A stress measure and a goodness-of-fit measure are supplied for model evaluation.

Conclusions:

• The developed algorithm offers a robust method for analyzing ordinal scaling data.
• It provides reliable parameter estimates and statistical accuracy measures.
• This facilitates a more rigorous evaluation of unidimensional psychological attributes.