To compute or compare LS-means for an effect that is related to a covariate, you can use the AT option in the LSMEANS statement, available in the GLM, MIXED, GENMOD, and many other modeling procedures. By default, all continuous covariates are set at their means when computing LSMEANS. For details, see "Construction of Least Squares Means" in the description of the LSMEANS statement. You can modify the values used for continuous covariates with the AT option. To avoid extrapolating outside the range of the data, the values specified in the AT option should generally be within the observed range.

Consider the following data set.

      data test;
        input trt $ x y;
        datalines;
      A  10.3928   20.469
      A  1.0304   2.242
      A  4.0038   10.384
      A  19.6831   38.936
      A  12.2837   25.062
      B  25.8380   80.616
      B  5.6191   20.881
      B  25.3164   77.252
      B  10.0879   31.314
      B  27.0792   85.066
      C  27.6587  113.275
      C  15.8211   67.454
      C  6.9228   31.015
      C  11.5046   49.103
      C  10.2614   44.924
      ;

The following LSMEANS statements compute LS-means for each level of TRT at x=10, the mean of X which is the default if AT is omitted, and x=20. Note that these values are within the observed range of X in the data. The PDIFF option produces multiple comparisons among the TRT levels at these covariate values.

      proc mixed data=test;
        class trt;
        model y = trt x*trt / noint;
        lsmeans trt / at x=10  pdiff; 
        lsmeans trt / at means pdiff;
        lsmeans trt / at x=20  pdiff; 
        run;

Following are the results of the LSMEANS statements.

Operating System and Release Information

data test;
  input trt $ x y;
  datalines;
 A   10.3928     20.469
 A    1.0304      2.242
 A    4.0038     10.384
 A   19.6831     38.936
 A   12.2837     25.062
 B   25.8380     80.616
 B    5.6191     20.881
 B   25.3164     77.252
 B   10.0879     31.314
 B   27.0792     85.066
 C   27.6587    113.275
 C   15.8211     67.454
 C   6.9228     31.015
 C   11.5046     49.103
 C   10.2614     44.924
;

proc mixed data=test;
   class trt;
   model y = trt x*trt / noint;
   lsmeans trt / at x=10 pdiff;   
   lsmeans trt / at means pdiff;  /* LSMEANS at mean, the default */
   lsmeans trt / at x=20 pdiff;  
run;

  Least Squares Means

                                       Standard
Effect    trt         x    Estimate       Error      DF    t Value    Pr > |t|

trt       A       10.00     20.4177      0.5323       9      38.36      <.0001
trt       B       10.00     32.6617      0.7394       9      44.18      <.0001
trt       C       10.00     43.5815      0.6232       9      69.94      <.0001
trt       A       14.23     28.5322      0.6559       9      43.50      <.0001
trt       B       14.23     45.3622      0.5939       9      76.37      <.0001
trt       C       14.23     60.3608      0.5308       9     113.71      <.0001
trt       A       20.00     39.5850      1.0046       9      39.40      <.0001
trt       B       20.00     62.6614      0.5354       9     117.05      <.0001
trt       C       20.00     83.2157      0.6707       9     124.07      <.0001


                          Differences of Least Squares Means

                                               Standard
Effect    trt    _trt         x    Estimate       Error      DF    t Value    Pr > |t|

trt       A      B        10.00    -12.2440      0.9110       9     -13.44      <.0001
trt       A      C        10.00    -23.1638      0.8196       9     -28.26      <.0001
trt       B      C        10.00    -10.9198      0.9669       9     -11.29      <.0001
trt       A      B        14.23    -16.8299      0.8848       9     -19.02      <.0001
trt       A      C        14.23    -31.8285      0.8438       9     -37.72      <.0001
trt       B      C        14.23    -14.9986      0.7966       9     -18.83      <.0001
trt       A      B        20.00    -23.0764      1.1383       9     -20.27      <.0001
trt       A      C        20.00    -43.6307      1.2079       9     -36.12      <.0001
trt       B      C        20.00    -20.5543      0.8582       9     -23.95      <.0001