## Varying covariates in repeated measures

Often in a repeated measures analysis a covariate varies within subject e.g. mean blood flow varies between the left and right brain.

In version 7 and above this analysis can only be performed in SPSS using syntax and the MANOVA command. (The GLM procedure *cannot* fit varying covariates in repeated measures). In the following example we have four reaction times indexed by task and condition. There are two covariates cov and x and two between subject groups indicated by gp.

manova rtp1c1 rtp1c2 rtp2c1 rtp2c2 by gp(1,2) with cov1 cov2 cov3 cov4 x1 x2 x3 x4 /wsfactors prime(2) cond(2) /contrast(time)=polynomial /wsdesign /print=transform signif(univ hf gg averf).

Note that the first within subs factor (in this case prime) assigned using the wsfactors subcommand always changes *slowest* amongst the four responses entered.

In the special case of two varying covariates and two levels of a repeated measures variable this approach using MANOVA is equivalent to performing a simple regression with the *difference* between responses at the two levels, y1-y2, as the dependent variables and the *difference* in the covariate values at each level, x1-x2, as the predictor.

The contrast can be any of the repeated measures types available in the menu bar and is particularly useful if the repeated measures factor has more than two levels. The covariates are pooled together in the “regression” term in the output and each have one degree of freedom.

The print=transform helps interpret the Ts produced in the output.

One can also adjust for a varying covariate by using the SPSS MIXED procedure and fitting a random effects mixed model which give similar results to MANOVA in SPSS (see here). Illustration using MANOVA and MIXED with a single between subjects covariate is presented here.