Module 3: SAS. 3.1 Initial explorative analysis 02429/MIXED LINEAR MODELS PREPARED BY THE STATISTICS GROUPS AT IMM, DTU AND KU-LIFE

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1 /MIXED LINEAR MODELS PREPARED BY THE STATISTICS GROUPS AT IMM, DTU AND KU-LIFE Module 3: SAS 3.1 Initial explorative analysis SAS JMP Test of overall effects/model reduction Post hoc analysis and summarizing the results SAS JMP Initial explorative analysis Import the data set into SAS from planks described in Module 1. To produce the plots of figure 3.2 a data set with the appropriate means must be constructed in each case. For the top left plot means for each width and plank must be constructed. This is done by PROC MEANS in the following way: proc sort data=mixed.planks; /* SAS requires a sorting prior to the*/ by width plank; /* use of PROC MEANS */ proc means data=mixed.planks noprint; /* No printing! */ by width plank; /* This must match the by-statement of PROC SORT */ var humidity; /* The humidity is to be used */ output out=meandata mean=humidity; /* New data set is constructed:*/ /* the name humidity is chosen for the mean variable */ The plot is now produced by symbol1 i=join v=none; symbol2 i=join v=none; /* Asks for no plotting symbol and joining of the points */ /* Due to the high number of planks a 2nd statement is needed */ proc gplot data=meandata; plot humidity*width=plank/nolegend; 02429/Mixed Linear Models Last modified August 23, 2011

2 Module 3: SAS 2 title; The NOLEGEND option suppresses the 20 line symbol legends. Similarly, the top right plot is produced by proc sort data=mixed.planks; by depth plank; proc means data=mixed.planks noprint; by depth plank; var humidity; output out=meandata mean=humidity/nolegend; symbol1 i=join v=none; symbol2 i=join v=none; proc gplot data=meandata; plot humidity*depth=plank; title; And finally the bottom plots by: proc sort data=mixed.planks; by width depth; proc means data=mixed.planks noprint; by width depth; var humidity; output out=meandata mean=humidity; title The mean depth/width profile of the 20 planks ; symbol i=join v=none; proc gplot data=meandata; plot humidity*width=depth; plot humidity*depth=width; title; SAS JMP The profile plots of this section is probably easiest constructed in SAS JMP by specifying the various two-way ANOVA models and looking under the LSmeans results for

3 Module 3: SAS 3 the interaction ( LSMeans Plot ). It is not very flexible, though, in terms of being able to change the format of the plot. Another, maybe even easier approach is to use the Prediction Profiler of a large model, and then chose Interaction Profiler. 3.2 Test of overall effects/model reduction The analysis based on the basic model given is carried out by the following lines: proc mixed data=mixed.planks; class depth width plank; model humidity =depth width /ddfm=satterth; random plank; The interesting part of the output for now is the following: Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F depth <.0001 width <.0001 depth*width The analysis based on the reduced model given by is carried out by the following lines: proc mixed data=mixed.planks; class depth width plank; model humidity =depth width /ddfm=satterth; random plank; giving: Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F depth <.0001 width <.0001

4 Module 3: SAS Post hoc analysis and summarizing the results The final model is rerun with some additional requests regarding the significant effects: proc mixed data=mixed.planks; class depth width plank; model humidity =depth width /ddfm=satterth; random plank; lsmeans depth width/ pdiff CL adjust=tukey; The part of the output used for this section is: Covariance Parameter Estimates Cov Parm Estimate plank Residual Least Squares Means Standard Effect depth width Estimate Error DF t Value Pr > t depth <.0001 depth <.0001 depth <.0001 depth <.0001 depth <.0001 width <.0001 width <.0001 width <.0001 Least Squares Means Effect depth width Alpha Lower Upper depth depth depth depth depth width width width

5 Module 3: SAS 5 Standard Effect depth width _depth _width Estimate Error DF depth depth depth depth depth depth depth depth depth depth width width width Effect depth width _depth _width t Value Pr > t depth <.0001 depth <.0001 depth <.0001 depth depth depth depth <.0001 depth depth <.0001 depth <.0001 width width <.0001 width <.0001 Effect depth width _depth _width Adjustment Adj P Alpha depth 1 3 Tukey-Kramer < depth 1 5 Tukey-Kramer < depth 1 7 Tukey-Kramer < depth 1 9 Tukey-Kramer depth 3 5 Tukey-Kramer depth 3 7 Tukey-Kramer depth 3 9 Tukey-Kramer < depth 5 7 Tukey-Kramer depth 5 9 Tukey-Kramer < depth 7 9 Tukey-Kramer < width 1 2 Tukey-Kramer

6 Module 3: SAS 6 width 1 3 Tukey-Kramer < width 2 3 Tukey-Kramer < Effect depth width _depth _width Lower Upper depth depth depth depth depth depth depth depth depth depth width width width Adj Adj Effect depth width _depth _width Lower Upper depth depth depth depth depth depth depth depth depth depth width width width For the differences both the adjusted and un-adjusted P-values and confidence limits are given SAS JMP The mixed models are easily specified as described in Module 1: Use Fit Model and then click the corresponding fixed and random effects into model effects.