8.1 Example: Hormone treatment of steers Example with different slopes Example: Concentration of a hormone in cattle...

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1 /MIXED LINEAR MODELS PREPARED BY THE STATISTICS GROUPS AT IMM, DTU AND KU-LIFE Module 8: SAS 8.1 Example: Hormone treatment of steers Example with different slopes Example: Concentration of a hormone in cattle Example: Hormone treatment of steers. Import the data set into SAS from kidney as described in Module 1. The plot of the kidney fat weight versus the initial weight is constructed by the following lines: axis1 label=( Initial weight (kg) ); axis2 label=( Weight of kidney fat (g) ); proc gplot data=mixed.kidney gout=gout; plot Y*weight=treat/ haxis=axis1 vaxis=axis2; As already listed in the main part of this module the starting different slopes model is run in SAS by: model Y = weight treat weight*treat/ddfm=satterth; and the equal slopes model by: 02429/Mixed Linear Models Last modified August 23, 2011

2 Module 8: SAS 2 model Y = weight treat /ddfm=satterth; The model IGNORING the weight covariate is run by: model Y = treat /ddfm=satterth; The final equal slopes analysis with post hoc analysis is carried out by: model Y = weight treat /noint solution ddfm=satterth; lsmeans treat / CL pdiff; The NOINT option simplifies the SAS output such that α(1),..., α(4) are directly available in the output. The option merely changes the parametrization used by SAS: Instead of providing µ (the intercept ) being really the intercept value for treatment 4 and then three differences to this for treatments 1, 2 and 3, it provides the four treatment values directly. 8.2 Example with different slopes Import the data set into SAS from bib as described in Module 1. The lines to produce the basic plot of Y versus X are: axis1 label=( X ); axis2 label=(angle=90 X ); proc gplot data=mixed.bib; plot Y*X=trt/ haxis=axis1 vaxis=axis2; The lines to fit the different slopes model are:

3 Module 8: SAS 3 model y= trt x x*trt/ ddfm=satterth; And the same model with the relevant post hoc analysis: model y= trt x*trt/ noint solution ddfm=satterth CL outp=fit; lsmeans trt / AT X =17 pdiff CL; lsmeans trt / pdiff CL; lsmeans trt / AT X=37 pdiff CL; The NOINT option is used again for the sake of simplifying the outcome of the SOLU- TION option. For the same reason the main effect of x is omitted from the MODEL statement. This does NOT change the model, but has the same effect on the slopes information as the NOINT option has on the intercept values: The four slopes are given directly instead of indirectly. The OUTP=FIT option saves the predicted values of the model (including the BLUP estimates of the random block effects). These will be used for adding the expected lines to the scatter plot, see below. Note how the AT X=17 option for the LSMEANS statement easily provides the expected values (and differences when the PDIFF option is used) for this specific value of the covariate. Adding the four expected lines to the plot requires a little data handling. In the following a variable is constructed for each treatment that contains the observations for that specific treatment and missing values for the other three treatments (y1,y2,y3,y4) and similarly for the predicted values (p1,p2,p3,p4): data fit; set fit; if trt=1 then do; y1=y; p1=pred; end; if trt=2 then do; y2=y; p2=pred; end; if trt=3 then do; y3=y; p3=pred; end; if trt=4 then do; y4=y; p4=pred; end; Next the following plot lines will do the job: symbol5 v=none i=rl c=red; symbol6 v=none i=rl c=green; symbol7 v=none i=rl c=blue;

4 Module 8: SAS 4 symbol8 v=none i=rl c=orange; axis1 label=( X ); axis2 label=(angle=90 Y ); proc gplot data=fit; plot y1*x=1 y2*x=2 y3*x=3 y4*x=4 p1*x=5 p2*x=6 p3*x=7 p4*x=8 / overlay haxis=axis1 vaxis=axis2; Finally, the post hoc analysis focusing on the slopes is obtained by adding some ES- TIMATE statements: model y= trt x x*trt/ddfm=satterth; estimate b1-b2 x*trt ; estimate b1-b3 x*trt ; estimate b1-b4 x*trt ; estimate b2-b3 x*trt ; estimate b2-b4 x*trt ; estimate b3-b4 x*trt ; 8.3 Example: Concentration of a hormone in cattle Import the data set into SAS from hormbase as described in Module 1. The lines to produce the basic scatter plot are: axis1 label=( Inital concentration ); axis2 label=(angle=90 Final concentration ); proc gplot data=mixed.hormbase; plot final*initial=feed/ haxis=axis1 vaxis=axis2; The lines to do the simple one-way analysis of variance for the final concentration and the difference between the final and initial concentrations are given by: proc glm data=mixed.hormbase; class feed; model final D =feed ;

5 Module 8: SAS 5 The equal slopes analysis of covariance model (using the initial concentration as a baseline measurement) is carried out by: proc mixed data=mixed.hormbase; class feed; model final =initial feed /ddfm=satterth solution; lsmeans feed /pdiff CL;