Statistical Methods for Psychology

(some lines are higher than others) and it is this variance that we have here. For most of us

that variance is not particularly important, but there are studies in which it is.

As I said earlier, mixed model analyses do not require an assumption of compound

symmetry. In fact, that assumption is often incorrect. In Table 14.17 you can see the pat-

tern of correlations among trials. These are averaged over the separate groups, but give you

a clear picture that the structure is not one of compound symmetry.

There are a number of things that we could do to alter the model that we just ran, which

requested a solution based on compound symmetry. We could tell SPSS to solve the problem

without assuming anything about the correlations or covariances. (That is essentially what

the MANOVA approach to repeated measures does.) The problem with this approach is

that the solution has to derive estimates of those correlations and that will take away

degrees of freedom, perhaps needlessly. There is no point in declaring that you are to-

tally ignorant when you are really only partially ignorant. Another approach would be to

assume a specific (but different) form of the covariance matrix. For example, we could

use what is called an autoregressive solution. Such a solution assumes that correlations

between observations decrease as the times move further apart in time. It further assumes

that each correlation depends only on the preceding correlation plus some (perhaps

much) error. If the correlation between adjacent trials is, for example 0.5121 (as it is in

the study we are discussing), then times that are two steps apart are assumed to correlate

.5121^2 and times three steps apart are assumed to correlate .5121^3. This leads to a matrix

Section 14.12 Mixed Models for Repeated-Measures Designs 503

Time

1 2 3 4

Mean dv

300

250

200

150

100

Treatment

Control

Group

Figure 14.5 Means across trials for the two conditions

Table 14.17 Correlations among trials

Estimated RCorrelation Matrix for Subject 1

Row Col1 Col2 Col3 Col4

1 1.0000 0.5121 0.4163 2 0.08840
2 0.5121 1.0000 0.8510 0.3628
3 0.4163 0.8510 1.0000 0.3827
4 2 0.08840 0.3628 0.3827 1.0000