How do we conduct linear mixed models with fixed factors, random factors and nested effects in R, SAS or SPSS? A mixed models with three fixed factors and a random factor, however, there is a nested relationship between a fixed factor and random factor. How do we do in R, SAS or SPSS.
For R, you will find examples and tutorials if you google your question.
You might find some good info on the UCLA "textbook examples" page for Singer & Willett's book.
http://www.ats.ucla.edu/stat/examples/alda/
A lot of Proc Mixed (SAS) and lme4 or nlme (R) examples out there on Google. You need to have a good grasp on mixed modelling in general or it may be very difficult to follow.
In SAS System the job should be:
PROC GLIMMIX DATA=name_file PLOTS=ALL;
CLASS x1 x2 x3 x4;
MODEL y= x1 x2 x3 x4 x1*x2 x1*x3 / DIST=NORMAL;
RANDOM x1 / SUBJECT=x2(x4) TYPE=CS GCORR;
COVTEST glm;
RUN;
QUIT;
For this JOB the dependent variable (y) should be a continuous variable due the NORMAL distribution specified at DIST=. If you have a discrete dependent variable you should change the DIST to POISSON or other.
x1=year (e.g. repeated measurements at the SUBJECT that is x2, for example trees that you had measured it diameter each year);
x3=some fixed effect measured at the trees;
x4=effect that created a nested situation. In the example of the trees, we may have a situation os different localization (e.g. 3 different municipalities);
x1*x2=interaction to evaluate the effect of x2 at some x1;
TYPE=CS is just the type of covariance matrix to account the dependence of the y between the repeated measurements. CS=Compound Symmetry.
I hope the help you
Best regards.
Thiago
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