JSM 2004 - Toronto

Abstract #301004

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Activity Number: 230
Type: Contributed
Date/Time: Tuesday, August 10, 2004 : 10:30 AM to 12:20 PM
Sponsor: IMS
Abstract - #301004
Title: Fitting Main Effect Polynomials in Multifactor Experiments: Unequal Spacing and Unbalanced Data
Author(s): Charles J. Monlezun*+
Companies: Louisiana State University
Address: Dept of Experimental Statistics, Baton Rouge, LA, 70803,
Keywords: cell means ; orthogonal decomposition ; Gram-Schmidt ; weighted averages ; sequential sums ; regression
Abstract:

When the factor of interest arises from distinct levels of a quantitative variable, the main effects for that factor may be expressed as a polynomial function of the values of that quantitative variable. The main effect sums of squares for that factor may be partitioned into individual one-degree-of-freedom sums of squares for determining the actual degree of the main effect polynomial function. These one-degree-of-freedom sums of squares are shown to be the sequential sums of squares from the ordinary regression (with no intercept) of the observation vector on specially constructed independent variables. Main effects may be arbitrary weighted averages of cell means. Only the factor of interest need be associated with a bona fide quantitative variable. Construction of the independent variables and implementation of the no intercept regression require no special software, and may be performed using the regression procedure from any standard statistical computing package.

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