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247 – Topics in Sample Design and Data Collection
Using the Inverse Transform to Specify Contrasts in Regression and Latent Curve Structural Equation Models
Thomas Templin
Wayne State University
A simple yet general method for specifying contrasts to test hypotheses in regression and latent curve structural equation models is presented. The traditional qualitative variable coding schemes used in multiple regression (e.g., dummy coding) have a more general formulation. Five matrices are involved: The coding scheme, A. The matrix which gives the distribution and ordering of cases, W; WA = X; X is the design matrix. The contrast coefficient matrix C; and C-1 = A. In practice, only C, C-1, and A are necessary because the statistical software generates the design matrix. This method has great generality because the same coding matrix, A, is used in multiple regression, multilevel modeling, and latent curve structural equal models. Starting with the contrasts allows one to compute the coding matrix, A, for a wide variety specific hypothesis.