I have a 2x2x2 design, where two of the variables are repeated measures and one is a between-subjects manipulation. I need to break down the interaction to look at the 2x2 mixed interactions (Repeated Var1 x Bwn-subjects var) at each level of Repeated Var2. How do I do this using a MIXED MODEL in SPSS (Not through ANOVA or GLM)?
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The TEST subcommand on the MIXED command is the way to go about this. It applies to fixed effects within the mixed model fitted in MIXED, and works similarly to the LMATRIX subcommand in GLM and UNIANOVA.
Using TEST or LMATRIX in general designs requires some understanding of estimable functions, which isn't exactly trivial. For a situation like this, there's a little trick I can recommend that makes things a bit easier.
Once you've fitted your model and found that you've got a three-way interaction, you can re-fit the same model with a simpler parameterization that results in one fixed parameter per cell, with no redundant or linearly dependent parameters as are usually involved in the overparameterized version of the model used by default in MIXED (and GLM/UNIANOVA). This makes it really simple to specify a TEST (or LMATRIX) subcommand that involves just one coefficient per cell in the fixed-effects design, so it's easy to get the comparisons you want.
So for a model like this, instead of specifying the factorial design on the FIXED subcommand or in the Fixed dialog, you suppress the fixed intercept and specify only the three-way interaction term. Compare the overall results for the model fit to the original fitting of the model and you'll see that everything matches up. Also, you can compare the fixed-effects parameter estimates from this modified parameterization to the EMMEANS for the three-way interaction in the original fitting to see that they match up and have the same standard errors.
This lays out the design so that you can specify any linear combination of the individual cell means quite easily. For getting simple interaction effects for a two-way interaction within each level of the third factor, you'd need something like a 1 -1 -1 1 pattern for the four cells that make up the two-way interaction of interest within each level of the third factor.
Suppose the three factors are named Rep_Var1, Rep_Var2, and Bet_Var. If you specify the FIXED subcommand as:
/FIXED Rep_Var1*Bet_Var*Rep_Var2
you can specify
/TEST ALL 1 -1 -1 1 0 0 0 0
/TEST ALL 0 0 0 0 1 -1 -1 1
to get interaction contrasts nested within each level of Rep_Var1. You can specify as many TEST subcommands as you want.
