Calculation of Adjusted Response Frequencies Using Least Squares Regression Methods

Abstract

The use of general linear regression methods for the analysis of categorical data is recommended. The general linear model analysis of a 0,1 coded re sponse variable produces estimates of the same re sponse probabilities that might otherwise be esti mated from frequencies in a multiway contingency table. When factors in the design are correlated, the regression analysis estimates the same response probabilities that would be estimated from the simple marginal frequencies in a balanced ortho gonal design. The independent effects that are es timated by the regression analysis are the un- weighted means of the response probabilities in various cells of a cross-classification design; how ever, it is not necessary that all cells in a complex design be filled in order for the estimates to have that interpretation. The advantages of the general linear model analysis include familiarity of most psychologists with the methods, availability of computer programs, and ease of application to problems that are too complex for development of complete multiway contingency tables.

Get full access to this article

View all access options for this article.

References

Barr, A.J. , Goodnight, J.H. , Sall, J.P. , & Helwig, J.T. A user's guide to the statistical analysis system '76. Raleigh, NC: SAS Institute, Inc., 1976.

Clyde, D.J. , Cramer, E.M. , & Shervin, R.J. Multivariate statistical programs. Coral Gables, FL: University of Miami, Biometric Laboratory, 1966. D'Agostino, R.B. Second look at analysis of variance on dichotomous data. Journal of Educational Measurement, 1971, 8, 327-330.

D'Agostino, R.B. Relation between the chi-squared and ANOVA tests for testing the equality of k independent dichotomous populations. American Statistician , 1972, 26, 30-32.

Dixon, W. J. (Ed.), BMD: Biomedical computer programs. Los Angeles: University of California Press, 1973.

Finn, J.D. MULTIVARIANCE: Univariate and multivariate analysis of variance. Ann Arbor, MI: National Educational Resources, 1978.

Grizzle, J.E. , Starmer, C.F. , & Koch, G.G. Analysis of categorical data by linear models. Biometrics , 1969, 25, 489-504.

Koch, G.G. , Johnson, W.D. , & Tolley, H.D. A linear models approach to the analysis of survival and extent of disease in multi-dimensional contingency tables. Journal of the American Statistical Association, 1972, 67, 783-796.

Lunney, G.H. Using analysis of variance with a dichotomous dependent variable: An empirical study. Journal of Educational Measurement, 1970, 7, 263-269.

Mantel, N. Chi-square tests with one degree of freedom ; extensions of the Mantel-Haenszel procedure. Journal of the American Statistical Society, 1963, 58, 690-700.

10.

Nie, N.H. , Hull, C.H. , Jenkins, J.G. , Steinbrenner, K. , & Bent, D.H. Statistical package for the social sciences (2nd ed.). New York: McGraw-Hill, 1975.

11.

Overall, J.E. , & Spiegel, D.K. Concerning least squares analysis of experimental data. Psychological Bulletin, 1969, 72, 311-322.

12.

Overall, J.E. , Spiegel, D.K. , & Cohen, J. Equivalence of orthogonal and non-orthogonal analysis of variance. Psychological Bulletin, 1975, 82, 182-186.

13.

Shaffer, J.P. Defining and testing hypothesis in multi-dimensional contingency tables. Psychological Bulletin, 1973, 79, 127-141.

14.

Woodward, J.A. , & Overall, J.E. A general multivariate analysis of variance computer program. Educational and Psychological Measurement, 1974, 34, 653-662.

15.

Woodward, J.A. , & Overall, J.E. The significance of treatment effects in ordered category data. Journal of Psyckiatric Research, 1977,13, 169-177.