Multilevel Analysis by Tom Snijders and Roel Bosker Chapter 6: Testing and Model Specification

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.

Furthermore, we will be creating the following variables: IQ_tilda which is equal to
GndC_verb – GrpMC_verb.

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;

Creating the within-group deviation variable IQ_tilda, p. 87.

data schools3;
  set schools3;
  IQ_tilda = GndC_verb - GrpMC_verb;
run;

Table 6.1, model 1, p. 87.

proc mixed data=schools3 noitprint noclprint covtest;
  model langpost = GndC_verb GndC_ses 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      8.3497      1.3742      6.08      <.0001
UN(2,1)      schoolNR     -0.7314      0.2862     -2.56      0.0106
UN(2,2)      schoolNR      0.1765     0.09321      1.89      0.0291
Residual                  39.3137      1.2253     32.08      <.0001

           Fit Statistics
-2 Res Log Likelihood         15114.7
AIC (smaller is better)       15122.7
AICC (smaller is better)      15122.7
BIC (smaller is better)       15134.2

                   Solution for Fixed Effects

                          Standard
Effect        Estimate       Error      DF    t Value    Pr > |t|
Intercept      40.7803      0.2901     129     140.55      <.0001
GndC_verb       2.2498     0.08274     130      27.19      <.0001
GndC_ses        0.1560     0.01468    2024      10.62      <.0001
GrpMC_verb      1.0866      0.3269    2024       3.32      0.0009

Table 6.1, model 2, p. 87.

proc mixed data=schools3 noitprint noclprint covtest;
  model langpost = IQ_tilda GndC_ses 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      8.3497      1.3742      6.08      <.0001
UN(2,1)      schoolNR     -0.7314      0.2862     -2.56      0.0106
UN(2,2)      schoolNR      0.1765     0.09321      1.89      0.0291
Residual                  39.3137      1.2253     32.08      <.0001

           Fit Statistics
-2 Res Log Likelihood         15114.7
AIC (smaller is better)       15122.7
AICC (smaller is better)      15122.7
BIC (smaller is better)       15134.2

                   Solution for Fixed Effects

                          Standard
Effect        Estimate       Error      DF    t Value    Pr > |t|
Intercept      40.7803      0.2901     129     140.55      <.0001
IQ_tilda        2.2498     0.08274    2024      27.19      <.0001
GndC_ses        0.1560     0.01468    2024      10.62      <.0001
GrpMC_verb      3.3365      0.3226    2024      10.34      <.0001

Example 6.2, testing a random slope, p. 89.

data temp;
  test_stat = abs(15251.8 - 15477.7);
  p_value = 1 - probchi(test_stat, 1);
run;
proc print data=temp noobs;
run;

test_
 stat    p_value
225.9       0

Example 6.3, testing the effect of a categorical variable, p. 89.


data temp1;
  test_stat = abs(15208.4 - 15193.6);
  p_value = 1 - probchi(test_stat, 3);
run;
proc print data=temp1 noobs;
run;

test_
 stat     p_value
 14.8    .00199579

Example 6.4, testing a random slope, p. 91.

data temp2;
  test_stat = abs(15227.5 - 15213.5);
  p_value = 1 - probchi(test_stat, 2);
run;
proc print data=temp2 noobs;
run;

test_
 stat      p_value
  14     .000911882