The “ Handy - Dandy , Quick - n - Dirty ” Automated Contrast Generator - A SAS / IML R © Macro to Support the GLM , MIXED , and GENMOD Procedures

Contrasts are an important component of the armamentarium of the statistician. In the SAS/STAT R © GLM, ANOVA, MIXED, and GENMOD procedures, the contrasts are used to answer specific additional questions. In many cases, it is difficult to define contrasts which are estimable, or correctly formed. A macro which converts a question about differences between cells (defined in several ways) into estimable contrasts is described. This macro uses SAS/IML R © to convert the comparison into the various components of the comparison into SAS R © system contrasts. Using several macro components unique to the SAS/IML system, the macro generates contrasts which are invariably estimable. INTRODUCTION The SAS R © System offers a very complete set of procedures for the applied experimental statistician. From the basic tecniques offered in PROC ANOVA to the workhorse PROC GLM to the sophisticated and contemporarily interesting PROC MIXED and PROC GENMOD, the applied statistician can find useful tools for many experimental situations (note that, although PROC CATMOD is often considered to be one of this set of experimental design tools, it is excluded due to technical differences in the contrast construction methods employed by the CATMOD developers). When using these procedures, the experiment designer generally defines factors or categorical independent variables, and then considers specific hypotheses about the components of the experiment. Continuous variables can also be included as well. When the statistician considers the design, the factor-based differences between cells are usually of paramount importance. If we have an experiment involving two solutions (Factor S) and three concentrations of each (Factor C), we are usually interested in the differences between the levels of Factor S, the differences between the levels of Factor C, and the interaction between the two factors. These factors are tested using either a ratio of variance estimates or an estimated factor test (in PROC MIXED and PROC GENMOD). After examining tests for factors and interactions, further investigations are often needed to clarify matters. In the experiment involving the two solutions and three concentrations, further investigations may be needed to understand a significant interaction. These further questions are answered using contrasts. Here is an example of several contrasts. GA has 2 levels, GA has 3 levels, GA has 4 levels, so that the design has 24 cells (and all cells are represented). PROC GLM; CLASSES GA GB GC; MODEL DV=GA GB GC GA*GB; CONTRAST "GA Overall" GA 1 -1; CONTRAST "GB L1 V L2" GB 1 -1 0; CONTRAST "GC L2 V L3" GC 0 -1 1 0; CONTRAST "GB L1 V L3, GA:1" GC 1 0 -1 0 0 0; RUN; These contrasts are quite typical. In some cases, the contrasts are synonymous with other components of the design. In the example above, “GA Overall” is synonymous with the overall GA effect from the design as given. The other contrasts ask questions which cannot be addressed using standard design components. Thus, the applied statistician must understand contrasts to fully examine all relevant questions in most experimental design situations. 1 Statistics and Data Analysis SUGI 31