Multilevel Analysis by Tom Snijders and Roel Bosker Chapter 8: Heteroscedasticity | SAS Textbook Examples

In this chapter we will be using the following centered variables: GndC_verb is iq_verb centered around the grand mean; GrpMC_verb contains the group means of GndC_verb; GndC_ses is ses centered around the grand mean.

We are using the schools3 data set from chapter 5 containing the centered variables mentioned in the first paragraph. The following is code is for creating schools3 from the mlbook1 dataset.

data schools;
  set 'c:sasmlbook1';
run;
*centering verb_iq around grand mean. ;
proc sql;
  create table schools1 as
  select *, iq_verb - mean(iq_verb) as GndC_verb
  from schools;
quit;
*Creating GrpMC_verb contains group means of GndC_iq. ;
proc sql;
  create table schools2 as
  select *, mean(GndC_verb) as GrpMC_verb
  from schools1
  group by schoolnr;
quit;
*Creating the variable GndC_ses equal to ses centered around its grand mean.;
proc sql;
  create table schools3 as
  select *, ses - mean(ses) as GndC_ses 
  from schools2;
quit;

Table 8.1, p. 111
The homoscedastic model.

proc mixed data=schools3 covtest noclprint noitprint method=ml dfbw;
  class schoolnr;
  model langpost = GndC_verb GndC_ses sex GrpMC_verb / solution;
  random intercept GndC_verb / subject=schoolnr type=un;
run;

<output omitted>

                  Covariance Parameter Estimates

                                     Standard         Z
Cov Parm     Subject     Estimate       Error     Value        Pr Z
UN(1,1)      schoolNR      8.2740      1.3422      6.16      <.0001
UN(2,1)      schoolNR     -0.7629      0.2767     -2.76      0.0058
UN(2,2)      schoolNR      0.1686     0.08534      1.98      0.0241
Residual                  37.5565      1.1677     32.16      <.0001

           Fit Statistics

-2 Log Likelihood             15005.5
AIC (smaller is better)       15023.5
AICC (smaller is better)      15023.6
BIC (smaller is better)       15049.4

                   Solution for Fixed Effects

                          Standard
Effect        Estimate       Error      DF    t Value    Pr > |t|
Intercept      39.5300      0.3132     129     126.20      <.0001
GndC_verb       2.2676     0.08080    2153      28.06      <.0001
GndC_ses        0.1518     0.01436    2153      10.57      <.0001
sex             2.6442      0.2637    2153      10.03      <.0001
GrpMC_verb      1.0226      0.3223     129       3.17      0.0019

Table 8.1, p. 111
The heteroscedastic model.

*we create a dummy variable for sex to include sex both as cont and categorical;
data schools3;
  set schools3;
  id = sex;
run;
proc mixed data=schools3 noitprint noclprint covtest method = ml dfbw;
  class id pupilnr;
  model langpost = gndc_verb GndC_ses sex GrpMC_verb / solution;
  random intercept GndC_verb / subject=schoolnr g type = un;
  repeated /subject = pupilnr group= id;
run;

<output omitted>

                       Covariance Parameter Estimates

                                              Standard         Z
Cov Parm     Subject     Group    Estimate       Error     Value        Pr Z
UN(1,1)      schoolNR               8.2388      1.3388      6.15      <.0001
UN(2,1)      schoolNR              -0.7750      0.2778     -2.79      0.0053
UN(2,2)      schoolNR               0.1715     0.08615      1.99      0.0232
Residual     pupilNR     id 0      38.7210      1.6778     23.08      <.0001
Residual     pupilNR     id 1      36.2939      1.6428     22.09      <.0001

           Fit Statistics

-2 Log Likelihood             15004.4
AIC (smaller is better)       15024.4
AICC (smaller is better)      15024.5
BIC (smaller is better)       15004.4

                   Solution for Fixed Effects

                          Standard
Effect        Estimate       Error      DF    t Value    Pr > |t|
Intercept      39.5336      0.3143    2282     125.77      <.0001
GndC_verb       2.2641     0.08095    2282      27.97      <.0001
GndC_ses        0.1513     0.01434    2282      10.55      <.0001
sex             2.6415      0.2634    2282      10.03      <.0001
GrpMC_verb      1.0139      0.3221    2282       3.15      0.0017