ERIC Number: ED346118
Record Type: RIE
Publication Date: 1992-Apr
Reference Count: N/A
A Comparison of the Log-Linear and Weighted Least Squares Approaches for the Analysis of Categorical Data.
Reshetar, Rosemary A.; Swaminathan, Hariharan
This study compared the model of J. E. Grizzle, C. F. Starmer, and G. G. Koch (GSK, 1969) and log-linear model-based approaches for testing hypotheses in r x c contingency tables. Tables were simulated under various conditions of table, sample, row-effect size, and column-effect size. Test statistics for column (main) and interaction effects were calculated using: (1) the GSK linear model, untransformed proportion; (2) GSK linear model, logarithm of the proportion; (3) GSK linear model, log-odds [log (p/1-p)]; and (4) log-linear model. Type I error rates, distribution of the test statistics, and relative power of the procedures were studied. The log-linear method provided more accurate distributions of the chi square test statistics than did the GSK methods and yielded Type I error rates closer to the expected 5% and 1% levels. The GSK methods using linear and logarithmic response functions yielded less precise distributions of chi square test statistics and slightly inflated Type I error rates. This trend was most noticeable with the linear response function of untransformed proportions. Based on these findings, if the GSK method is used, a logarithmic transformation of the response function is recommended. It is also recommended that a more stringent Type I error rate be used with GSK methods since observed Type I error rates were higher than expected. Nine tables and six graphs present analysis results, and there is a five-item list of references. (SLD)
Publication Type: Reports - Evaluative; Speeches/Meeting Papers
Education Level: N/A
Authoring Institution: N/A
Identifiers: Categorical Data; Contingency Tables; Log Linear Models; Type I Errors; Weighted Data
Note: Paper presented at the Annual Meeting of the American Educational Research Association (San Francisco, CA, April 20-24, 1992).