General Linear Model Essay

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In the social and behavioral sciences, traditionally, techniques involving categorical independent variables (e.g., t-test, ANOVA) and those involving continuous variables (e.g., correlation, regression) used to be treated as distinctly different data analysis systems intended for types of research that differed fundamentally in design, goals, and types of variables” (Cohen et al. 2003: xxv). Despite the superficial differences, these and many other statistical techniques share one thing in common: they are designed to analyze linear relationships among variables. Cohen (1968) demonstrated that ANOVA-type techniques and regression-type techniques were statistically equivalent. Because of this, many techniques can be conceptualized as belonging to a general statistical model called the general linear model (GLM).

The GLM underlies most of the statistical techniques used in social science research. In the conventional (and narrower) sense, GLM may be conceptualized as a regression-based model. In regression analysis, the independent variable is assumed to be a continuous variable. In ANOVA-type methods, the independent variable is a categorical variable representing group membership (either naturally occurring groups such as gender or ethnic groups, or groups based on manipulated variables such as treatment vs. control groups in an experimental design). However, it is easy to extend the regression technique to subsume ANOVA-type methods (e.g., t-test, ANOVA, ANCOVA, MANOVA) by converting the group membership categories to some form of pseudo” quantitative coding. Dummy coding” and effect coding” are the two most popular coding schemes for this purpose. This conceptualization of GLM is currently implemented in the major statistical software packages (e.g., SPSS, SAS).

Bibliography:

  • Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2003) Applied Multiple Regression Correlation Analysis for the Behavioral Sciences, 3rd edn. Lawrence Erlbaum, Mahwah, NJ.

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