SAS/STAT 9.2 User's Guide: The MIXED Procedure (Book Excerpt)

Example 56.7: Influence in Heterogeneous Variance Model ✦ 4055
Example 56.7: Influence in Heterogeneous Variance Model
In this example from Snedecor and Cochran (1976, p. 256), a one-way classification model with
heterogeneous variances is fit. The data, shown in the following DATA step, represent amounts of
different types of fat absorbed by batches of doughnuts during cooking, measured in grams.
data absorb;
input FatType Absorbed @@;
datalines;
1 164 1 172 1 168 1 177 1 156 1 195
2 178 2 191 2 197 2 182 2 185 2 177
3 175 3 193 3 178 3 171 3 163 3 176
4 155 4 166 4 149 4 164 4 170 4 168
;
The statistical model for these data can be written as
Yij D C i C ij
i D 1; ; t D 4
j D 1; ; r D 6
ij D N.0; 2 i /
where Yij is the amount of fat absorbed by the j th batch of the ith fat type, and i denotes the
fat-type effects. A quick glance at the data suggests that observations 6, 9, 14, and 21 might be
influential on the analysis, because these are extreme observations for the respective fat types.
The following SAS statements fit this model and request influence diagnostics for the fixed effects
and covariance parameters. The ODS GRAPHICS statement requests plots of the influence diagnostics
in addition to the tabular output. The ESTIMATES suboption requests plots of “leave-one-out”
estimates for the fixed effects and group variances.
ods graphics on;
proc mixed data=absorb asycov;
class FatType;
model Absorbed = FatType / s
influence(iter=10 estimates);
repeated / group=FatType;
ods output Influence=inf;
run;
ods graphics off;
The “Influence” table is output to the SAS data set inf so that parameter estimates can be printed
subsequently. Results from this analysis are shown in Output 56.7.1.