AMMI Macros for Multiplicative Interaction Models

When you are faced with analyzing two-way cross-classified experiments, you are almost always interested in whether the two factors interact or not, and if they do interact, combinations of the two factors are responsible for the interaction in the data. When there are no independent replications, there are no traditional tests for interaction. SAS® macros have been developed to provide user-friendly statistical software for the analysis and interpretation of interaction in two-way experiments. These newly developed macros are called the AMMI (Additive Main-effects and Multiplicative Interaction) macros. The AMMI models allow one to analyze two-way data with interaction even if there are no independent replications. In addition to fitting AMMI models and models such as Tukey’s single degree of freedom for nonadditivity Model, and Mandel’s bundle-of-straight-lines model, the macros provide many useful graphical displays including displays that help you determine the pattern of interaction when a pattern exists and that help you decide how many multiplicative interaction terms to include in the model. This paper describes how the AMMI macros can be installed, how they can be used, and the kinds of output they produce. INTRODUCTION A set of SAS macros called the AMMI macros has been developed to analyze two-way cross-classified experiments without independent replications under the SAS® software release 8.2 (TS2MO) in a windows environment. The AMMI macros consist of six independently executable main macros and 22 sub-macros that are called by the six main macros. The main AMMI macros are given in Figure 1. For information about the models that are fit: See Lee (2004) and/or Milliken and Johnson (1989). This paper shows: ● how to compile and store the AMMI macros on your SAS; ● how to prepare input data prior to calling a macro; ● how to assign parameter values in each macro; ● what may be expected as output from each macro; ● how to interpret the output generated by the AMMI macros. Analysis stage 1: Diagnosing interaction %PREVIEWAMMI(data,respon,factor1,factor2,ic=1,int=1,scree=1); : Explores interaction between two factors Analysis stage 2: Selecting a suitable model %FITAMMIMODEL(data,respon,factor1,factor2,additive=1,Tukey=1,Mandel=12,AMMI=1,dfm=1); : Fits the following models • Additive model without an interaction term • Tukey’s model • Mandel’s model regressed on factor1, factor2, or both • AMMI(#) model with specified # of interaction terms Analysis stage 3: Finding patterns of interaction %IC2BY2T(data,respon,factor1,factor2,sigma2=0,dferror=0); : Tests all 2x2 interaction contrasts %LSMTUKEY(data,respon,factor1,factor2,at=); : Fits Tukey’s model and gives least ssquares means %LSMANDEL(data,respon,factor1,factor2,Mandel=,at=0); : Fits Mandel’s model and gives least squares means %CONTRASTAMMI(data,respon,factor1,factor2,H=0,G=0,sim=1); : Fits AMMI(1) model and tests specified interaction contrasts Figure 1. Structure of the AMMI macros Coders’ Corner SUGI 31