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I conducted an experiment with three (categorical) within-subjects factors and a (continuous) between-subjects variable. Participants were presented with a number of political arguments that were experimentally varied by political issue and argument frame. Arguments adressed either achievement or security-related benefits and they adressed either gains or losses. So participant A might have received a gain / security argument for issue #1 and and loss / security argument for issue #2 etc... Also, personal conservatism was measured (between-subjects variable). The dependent variable is persuasiveness or argument strength.

I previously analyzed the data using repeated measures ANOVA but I realize this is not the ideal method. So I would like to re-analyze the data using SPSS linear mixed models.

So I have set up a model for repeated-measures and modelled my within-factors as Level 1 fixed factors. "Person" is the Level 2 variable.

MIXED ArgumentStrength BY Issue AchieveSecur GainLoss
 /CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0, 
ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
/FIXED=Issue AchieveSecur GainLoss Issue*AchieveSecur Issue*GainLoss 
AchieveSecur*GainLoss Issue*AchieveSecur*GainLoss | SSTYPE(3)   
/METHOD=REML
/PRINT=SOLUTION TESTCOV
/RANDOM=INTERCEPT | SUBJECT(Person) COVTYPE(VC).

This worked out fine. Results were very similar to the results I got using RM ANOVA. But now I would like to add personal conservatism and all interactions between conservatism and argument frames to the model. After all, loss / security arguments might be very persuasive for highly conservative people.

Theoretically, I think conservatism and all its interactions should be Level 2 variables and should be entered as random effects, right? If I do that, however, the Hessian Matrix gets very angry with me and SPSS all but collapses. So, how do I deal with this? I'm also really not sure which intercept and which slopes should vary or not vary. These models are so flexible, I'm really afraid of mis-specifying. Please help! :)

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