GRM Introductory Overview - Building Models via Stepwise Regression
Stepwise model-building techniques for regression designs with a single dependent variable are described in numerous sources (e.g., see Darlington, 1990; Hocking, 1966, Lindeman, Merenda, and Gold, 1980; Morrison, 1967; Neter, Wasserman, and Kutner, 1985; Pedhazur, 1973; Stevens, 1986; Younger, 1985). The basic procedures involve 1) identifying an initial model, 2) iteratively "stepping," that is, repeatedly altering the model at the previous step by adding or removing a predictor variable in accordance with the "stepping criteria," and 3) terminating the search when stepping is no longer possible given the stepping criteria, or when a specified maximum number of steps has been reached.
The major changes in the stepwise model-building procedures implemented in GRM involve provisions for building models for designs with effects for categorical predictor variables, as well as designs with only single-degree-of-freedom effects for continuous predictor variables. This is done by 1) using the sigma-restricted parameterization, 2) treating the columns in the design matrix X for effects for categorical predictor variables as blocks of continuous predictor variables which are all entered or all removed in a single step, 3) using a g2 sweep operator (Dempster, 1969, p. 62; see also Jennrich, 1977) to enter and remove effects from the model and obtain the necessary stepwise statistics. The regression coefficients, degrees-of-freedom, error sums of squares, tolerances, etc., are all calculated as part of the sweeping operation (e.g., see Jennrich, 1977).
The following topics provide details on the use of stepwise model-building procedures as implemented in GRM.
Topics on building models via stepwise regression
Other GRM Introductory Overview Topics
A detailed discussion of univariate and multivariate ANOVA techniques can also be found in the Introductory Overview of the ANOVA/MANOVA module; a discussion of Multiple Regression methods is provided in the Overviews. Discussion of the ways in which the linear regression model is extended by the general linear model can be found in the Introductory Overview of the GLM module.