Off-campus UMass Amherst users: To download dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users, please click the view more button below to purchase a copy of this dissertation from Proquest.
(Some titles may also be available free of charge in our Open Access Dissertation Collection, so please check there first.)
Evaluation of the weighted least squares method for the analysis of categorical data
Abstract
Hypotheses about the relationship among variables in a multiway contingency table may be tested by analysis of the probability distribution of observed frequencies or transformation of these frequencies. Two model-based approaches for the testing of structural hypotheses are the log-linear model, using iterative maximum-likelihood (ML) estimation procedures and the weighted least squares (WLS) linear model method of Grizzle, Starmer and Koch (GSK), a general noniterative procedure. Both methods asymptotically provide the same estimates and test statistics. This study compared the GSK and log-linear approaches for testing hypotheses in r x c contingency tables. Tables were simulated under various conditions of table, sample, row-, and column-effect sizes. Test statistics for row and column effects, and interaction were calculated using: (i) GSK linear model, untransformed proportion (p); (ii) GSK linear model, logarithm of the proportion (log p); (iii) GSK linear model, log-odds (log p/(1-p)); and (iv) log-linear model. Type I error rates were examined, and the relative power of the procedures was studied. The log-linear model yielded Type I error rates close to the expected values; all GSK models yielded error rates higher than expected, with smallest error rates associated with logarithmic transformations. Sample size and table size had no effect on Type I error rates. All GSK procedures were uniformly more powerful than the log-linear procedure. Differences were most noticeable with medium effect sizes and diminished as sample and effect sizes increased. There were no systematic differences due to table size. Findings from this study are pertinent to applied researchers who wish to test hypotheses other than those of independence with categorical data. Hypothesis testing and interpretation of results are straightforward with a model-based approach and are thus encouraged. The results indicate that GSK methods provide the most powerful tests. Since the GSK method is easily implemented and can be understood by researchers familiar with linear regression analysis, it is recommended that the GSK method be used to analyze categorical data.
Subject Area
Statistics
Recommended Citation
Reshetar, Rosemary Angela, "Evaluation of the weighted least squares method for the analysis of categorical data" (1991). Doctoral Dissertations Available from Proquest. AAI9207451.
https://scholarworks.umass.edu/dissertations/AAI9207451