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This output shows that the results for only 32 study subjects and only 855 out of 1,455 observations were used in the PROC MIXED analysis.  This loss seems somewhat excessive.  In previous abbreviated lists of data on this Internet site, a few variables had missing values.  Do you think that this is why so many observations were excluded from the analysis?  It may be worthwhile to check the pattern of missing dependent variables and independent variables to determine whether you can exclude some variables with large percentages of missing values from the analysis.  For example, you can display the pattern of missing values by using the procedure, PROC MI, as follows:    proc mi nimpute=0;        var y var task height weight exerc1-exerc20;    run;    quit; I followed the PROC MIXED documentation for the MODEL statement syntax including the VAR*TASK interaction as an independent variable (see the documentation for the REPEATED statement option, TYPE, for multivariate repeated measures.  However, if the model that includes this VAR*TASK interaction does NOT converge, and if the model that excludes this interaction DOES converge, then the latter model may be the way to go.  Another alternative model would be to use the MODEL statement that includes only the VAR*TASK interaction without including the main-effect terms, VAR or TASK, as independent variables (the "cell means" model):     model response=var*task height weight . . . .; I prefer to use the condition number rather than the VIF statistic in PROC REG to identify groups of highly correlated independent variables.  A condition number of 30 or more (10 or more in models without intercept terms) and independent variables with relatively large variance proportions will identify such group(s).   Then, from subject matter knowledge or from the use of PROC VARCLUS to group highly correlated variables, you can select one or a few variables within each group to represent all the highly correlated variables in the group for use as independent variables in subsequent modelling. Since only one of the 20 exercises (exerc7) remained statistically significantly associated with the response after adjusting for VAR and TASK, this specific exercise may or may not be substantively associated with the response (perhaps a multiple comparison problem); perhaps subject-matter knowledge about what this exercise represents will help you to decide whether to keep it in the model or not.  However, to decide whether or not to include it in your assessment of the value of these exercises in predicting the response by comparing the information criteria of different models, I would compare the model having only VAR, TASK, WEIGHT, and HEIGHT as independent variables with the model having VAR, TASK, WEIGHT, HEIGHT, and all 20 of the exercise variables (not just EXERC7) because you didn't have any a priori reason to select only EXERC7. ... View more

Your experiment does not really have 934 subjects, only 50. Back on August 22nd, I sent some code that might be modified (see below) and work without error messages about infinite likelihoods.  Although PROC MIXED does not print an R-squared statistic as PROC GLM does, the IC option on the PROC MIXED statement will have SAS print various information criteria that allow you to compare the two approximately nested models (without and with the various values for the twenty exercise variables).  I also include a PROC REG paragraph to check for collinearity among the exercise variables and a PROC VARCLUS paragraph to see if the exercise variables group into correlated variable clusters. Matthew Zack ========================================================================================================================= * The first two of these procedures assume that only one observation per study subject is selected; *  and that this observation contains the values for all 20 exercise variables.; *  If this is false, then select only one observation per study subject in prior code (see below).; * Sort the original, WIDE data set; *  by study subject; proc sort data=wide;    by subject; run; * Select only one of the study subjects into a new data set; *  for analysis of the collinearity statistics and variable clustering; *  of the exercise variables.; data wide2;    set wide;    by subject;    if (first.subject eq 1)      then output wide2; run; * Check the exercise variables for collinearity.; *  Because these collinearity diagnostics are relevant only to the independent variables,; *  the value of the dependent variable is not relevant.; proc reg data=wide2;    model comp=exerc1-exerc20 / collin;    title10 "Collinearity diagnostics for the 20 exercise variables"; run; quit; * Check if the exercise variables group into clusters of correlated variables; proc varclus data=wide2;    var exerc1-exerc20;    title10 "Check if the exercise variables group into clusters of correlated variables"; run; * For each dependent variable, use the original, WIDE data set to creata a separate dependent variable; *  with the same name, RESPONSE, but indexed by the variable, VAR.; data long(drop=j comp shear1 shear2);      length var $ 12;      set wide;      array dv{3} comp shear1 shear2;      array varlist{3} $ 12 _temporary_ ("comp" "shear1" "shear2");      do j=1 to 3;        response=dv{j};        var=varlist{j};        output long;      end; run; * Sort data; *  by subject, task, and distinct dependent variable; proc sort data=long;    by subject task var; run; * Model dependent variables as multivariate repeated measures; *  Determine the effects of the task on the response; *  May vary the REPEATED statement variance-covariance matrix from TYPE=UN@CS to TYPE=UN@UN; proc mixed data=long ic;    class subject task var;    model response = var task var*task      / solution ddfm=kenwardroger;    repeated var task / type=un@cs subject=subject rcorr; run; quit; * Model dependent variables as multivariate repeated measures; *  Determine the effects of the task and the exercise values on the response; *  May vary the REPEATED statement variance-covariance matrix from TYPE=UN@CS to TYPE=UN@UN; proc mixed data=long ic;    class subject task var;    model response = var task var*task exerc1-exerc20      / solution ddfm=kenwardroger;    repeated var task / type=un@cs subject=subject rcorr; run; quit; ... View more

Since the values for each of exercises and for each of the tasks are connected to the three dependent variables only through their occurring in the same study subject, the tasks are not really nested within the exercises or vice-versa.  If you return to the original "short-but-wide" (few observations but many variables) data set with each of the values of the 20 exercises as a separate variable, you could include these exercises as independent variables in your model:  * Simple MANOVA model for each task alone;    proc glm;      class task;      model comp shear1 shear2=task / solution;      manova h=_all_ / printh printe summary;    run;    quit;   * Add in the 20 exercise variables;    proc glm;      class task;       model comp shear1 shear2=task exerc1-exerc20 / solution;      manova h=_all_ / printh printe summary;    run;    quit; You can compare the r-squared statistic for each task alone on each of the three dependent variables or the statistic, 1 - Wilks' lambda, for the r-squared statistic for each task alone on all three of the dependent variables.  Then see how much these r-squared statistics change when the 20 exercise variables are added to the model. One problem with this approach is that you have very many independent variables (an intercetp term, seven indicator variables for the 8-category task variable, and 20 exercise variables) for relatively few study subjects (N=50); the regression coefficients for these independent variables may be very imprecise.  PROC GLM will also delete observations when any of the dependent or independent variables are missing so that these analyses may be based on even fewer observations. This approach also does not account for the fact that the observations for the tasks are correlated observations within each study subject; you'd have to use PROC MIXED again with the doubly multivariate approach to account for these within-subject correlations (see previous discussions). A final problem with this approach is that it does not account for possible collinearity among the twenty exercise values.  You could check this out by using the collinearity diagnostics available in PROC REG.  Select only one observation from each study subject, and include all the exercises as independent variables in a model with any one of the three dependent variables as the dependent variable:  proc reg;      model comp=exerc1-exerc20 / collin; run; quit; If any of the condition indexes in the collinearity diagnostics are 30 or more, then variables with "large" variance proportions are probably close to collinear.  Then, only one of these collinear values of exercise need to be in the model.  PROC VARCLUS also "clusters" correlated variables, of which you can select one to represent all variables in a given cluster. Message was edited by: Matthew Zack ... View more

Steve Denham's suggestion about using the "best-subset" selection algorithm for independent variables in PROC LOGISTIC would give you a good clue about "important" independent variables.  Also consider PROC GLMSELECT that selects "good" sets of independent variables for models that are less affected by the biases in the usual forward and backwards stepwise selection methods.  Given that you have more than 30 independent variables, this implies more than one billion possible models; thus, using exhaustive searches through macros that successively select sets of independent variables is probably less feasible than the above two alternatives.  You may consider reducing the number of independent variables by using a method like PROC VARCLUS to "cluster" the independent variables and by then selecting one or a few of these variables to represent a given variable cluster.  Finally, you have the problem of selecting an appropriate variance-covariance/correlation matrix among the repeated measures.  This compounds the selection problem you have. ... View more

I really don't understand your data.  Within a particular subject at the same degree of RESPONSE, every variable except EXERCISE has the same value (for example, in subject S02).  Because EXERCISE can vary by almost 100-fold (for example, from 8.73 to 831), although the value of the RESPONSE does not change (for example, COMP=6,641), EXERCISE should have no predictive power as an independent variable on this RESPONSE (and other responses as well). Perhaps you should model the RESPONSEs (COMP, SHEAR1, and SHEAR2) on the other independent variables that do NOT change--TASK, GROUP, TIME, HEIGHT, and WEIGHT.  I do not see how the values of EXERCISE affect RESPONSE.  I also don't understand what these values of EXERCISE represent since they appear to change while the values of the variables that do NOT change remain the same. ... View more

After all of this discussion, I did not realize that exercise was a continuous variable.  Your first message describing your question (August 14, 2013 at 4:41 pm) describes your 50 subjects as performing "20 different TYPES of exercise (vertical jump, . . .)", implying that exercise is a categorical/nominal variable with 20 different values.  Now, it appears that exercise is a continuous value that measures the performance (in some units) on these different types of exercise.  This distinction between a nominal and a continuous value is important because it would make a difference in the model.  Obviously, continuous variables should NOT be placed in a CLASS statement but should be placed as a covariate/independent variable in the MODEL statement. Since you have already excluded EXERCISE from the CLASS statemnte (yesterday afternoon's message), that appears to be the appropriate approach to take.  The error message/note that you received about an "infinite likelihood. . . because of a nonpositive definite estimated R matrix" is, according to the PROC MIXED documentation, "usually no cause for concern if the iterations continue".  It may indicate that "observations from the same subject are producing identical rows" in the R matrix; that is, the same subject has duplicate covariates (VAR and TASK) in the PROC MIXED REPEATED statement.  Check if and why this might be so.  You might also use the R and the RCORR options of the REPEATED statement to print/display the first two blocks of the repeated-measures variance-covariance matrix and its corresponding correlation matrix (see the PROC MIXED REPEATED statement documentation:  for example, R=1,2 and RCORR=1,2). To reduce memory requirements for PROC MIXED, you can also use the two other tips I suggested for reducing the time the procedure takes:  Change the multivariate variance-covariance TYPE in the REPEATED statement from TYPE=UN@UN to TYPE=UN@CS, or make the categorical version of EXERCISE into a BY-variable and analyze the effect on the DVs through different TASKs of each kind of EXERCISE separately. ... View more

Deleting EXERCISE from the CLASS statement means that SAS interprets the TASK|EXERCISE "independent variable" in the MODEL statement as consisting of a nominal variable, TASK; a continuous variable, EXERCISE; and an interaction term between a nominal variable, TASK, and a continuous variable, EXERCISE.  Since EXERCISE is not a continuous variable but a nominal variable, this model does not make any sense even if it runs much faster than the original model with EXERCISE as a nominal variable.  The PROC MIXED documentation describes several techniques to reduce the running time.  One possibility is to  include changing the variance-covariance matrix TYPE in the REPEATED statement from TYPE=UN@UN to TYPE=UN@CS, which will reduce the number of parameters to estimate for this matrix at the expense of assuming a single compound symmetry (CS) parameter to model the variability in the TASKs.  The second possibility is to analyze your data in pieces using a BY-variable (for example, BY EXERCISE), though this has its own problems. ... View more