If SUJET is coded as you indicate, your first comment could be right. But I can't tell how the OP codes this variable. SUJET may not be unique across all observations. But I think (?) that the first random statement may not be redundant with the radial smoother; the former is giving a constant covariance within SUJET, and the radial smoother is adding a time-dependent modification to that covariance. A bit like the AR(1)+RE structure on page 181 of Littell et al. (2006; SAS for Mixed Models, 2nd edition). This comes from combining CS and and AR(1) (see also page 177 in this book). I would have to play around with this, probably with an example, to really figure this out. As far as double splines, I would normally agree with you. However, Walt Stroup does the same thing in his 2013 book (see section 15.3, and 15.4.5.1). A bit like a random coefficient model. So, I see justification for this approach. However, the spline for the fixed effect is calculated differently from the radial spline in the random statement. The knots are at different places and the basis function is different. If I were doing it, I would try to line these up directly. But this would require some specialized coding. Example 40.6 is a different, and definitely a good, way to approach the problem. I have used this approach for other purposes. Basically, one then uses BLUPs to get Y_hat for the interaction terms. This would make the contrasts of interest trickier (but achievable with some work). ... View more

Glad you figured out why you get the result with the linear model for time.  The same process I showed with the linear model works with a spline. Define the estimate statements for each treatment at each relevant time. Then get the difference of the two treatments at each of two single times. Then get this difference of these two differences, which is what you want. You can skip the other estimates once you have the one you really want. It is worth starting with all the different estimate statements so that you can check your work by looking at your data. ... View more

I don't understand your question. There is no such thing as a covariance of a fixed effect with a random effect. A fixed effect is not a random variable, so there is no variance or covariance. That is, there is no Var_beta. Of course, there is a variance of the estimated betas, but this is a different concept. ASYCOV gives you the variance-covariance matrix of the estimated variance-covariance parameters only (var_alpha, and so on). ... View more

LSMESTIMATE is just for means, not continuous variables (i.e., with class variables). So, unfortunately, you cannot use it with the example (time is continuous). The way I understand the question, you want a contrast of fixed effects. It doesn't matter if you have a radial smooth random effect, a simple variance component, or other random-effect structure. You can certainly get the desired contrast with an ESTIMATE statement. It gets tricky.  Here is a different example I put together quickly with treat with two levels (factor) and time as continuous. I show how to get the expected value for each treatment at time 1 and at time 3. Then the difference of treatments at each time (just subtract one from the other, some things cancel). Then the difference of the difference to get the difference of the two treatments at time 1 and at time 3 (terms cancel again).  All of this can also be done using the newer nonpositional syntax in the estimate statement. proc glimmix data=b; class indiv treat; model y = treat time treat*time / s ; random int / sub=indiv; estimate 'trt1 time 1' int 1 treat 1 0 time 1 treat*time 1 0; estimate 'trt2 time 1' int 1 treat 0 1 time 1 treat*time 0 1; estimate 'trt1 time 3' int 1 treat 1 0 time 3 treat*time 3 0; estimate 'trt2 time 3' int 1 treat 0 1 time 3 treat*time 0 3; estimate 'diff @ time 1' treat 1 -1 treat*time 1 -1; *just do the subtractions; estimate 'diff @ time 3' treat 1 -1 treat*time 3 -3; *time main effect cancels out; estimate 'diff of differneces' treat*time -2 2; *just subtract the above two. some things cancel and coefficients change; run; Hope this gives you guidance. If you have more than two levels to your treatment factor, things will change. Always look at the solution table (option /s in model statement) to see the order the procedure is using for the parameters. ... View more

ASYCOV is giving you the var-cov matrix of the var-cov parameters. So, you ARE getting the desired terms in the output. Square the SE for one of the estimated variances (in the Cov Param table) and you will get the diagonal variance of the matrix in the ASYCOV table. The off diagonal elements of the latter are the covariances, such as Cov(var_alpha,var_gamma).   However, your random term is not correct. Based on what you wrote, it should be random indiv trtment*indiv / G; Also, you need multiple observations within the treatment*individual combination for this to work, otherwise your model is overparameterized. ... View more

This seems like an issue for Technical Support. ... View more

My view is that you should treat the spline as one term. ... View more

You will have to look at the ODS OUTPUT tables (there is a list in the User's Guide right before the examples). Each table in the output corresponds to a different file that can be saved with the ods output statement. You may need to merge two or more of these in a post-model fitting step in a data statement. I don't have a specific example here because I haven't used GLMSELECT a lot. With a BY statement, these output files will be stacked with the results for each group identified. But I have some serious concerns about the model you are fitting. It looks like you are trying to decide if one should use a linear model in X or a cubic spline, or both for each group (essentially trying to see if there is curvilinearity?). Your use of the SPLIT option will consider each term of the spline (knot) as separate terms. With splines, the individual terms don't mean too much (they are arbitrary in order to get predictions that do mean something). Ending up with the second of four (or whatever) terms in a spline is pretty meaningless. I would take out the SPLIT; that way, the spline will be considered as a single term in the model. I also don't see a point of treating X as a factor (CLASS statement). This can create very strange spline basis functions (with many many terms). I didn't even think this would work until I tried it now on some data. I think the results are meaningless. Plus, with X as a factor in your example, X itself will capture any nonlinearity, leaving nothing for the spline function to represent. ... View more

The following may help you to learn about CHOOSE, etc. http://www2.sas.com/proceedings/sugi31/207-31.pdf ... View more

I think the STORE statement was only added in9.3 for the GLMSELECT procedure. ... View more

What version of sas are you using? STORE was not available in the earliest versions of GLMSELECT. ... View more

Here is a good place to get started for more information: Nonparametric Regression And now with the EFFECT statement, you can get splines with several other procedures. But watch out, these splines would not necessarily be penalized smoothing. That is, if you put a spline effect in the model statement in GLIMMIX, it would fit a spline, but there would be no shrinkage of the parameters towards zero. You can get splines in GLIMMIX with random statements that are penalized/smoothing. Check out the radial smoothing example in the User's Guide. As far as variable selection involving splines, I suggest the GLMSELECT procedure. If you have four variables, x1, x2, x3, x4, with splines for the first two (as an example): ... effect splx1=spline(x1); effect splx2=spline(x2); model y = splx1 splx2 x3 x4 / selection = ___________; There are many, MANY, options here, both for EFFECT and for selection. ... View more

I think the comment was meant to be a joke. ... View more