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I am unsure which statistical tests I should use in order to follow-up my three-way interaction. I used to split my file and run the analysis twice per group, but as I read in the paper by Hayes & Matthes, 2009, Behavior Research Methods, this is not a good approach.

I have a centered continuous variable (questionnaire score), one dichotomous variable and one variable called facetype with three categories. I have 6 trials per facetype condition per participant, so each participant has multiple lines in my SPSS file. My dependent variable is binary.

I use the generalized linear model to analyze this data. The fixed effects show a significant three-way interaction, and I would like to interpret the interaction by for example testing the significance of one slope. I have no idea how to do this with multilevel data.

GENLINMIXED
  /DATA_STRUCTURE SUBJECTS=id*trial
  /FIELDS TARGET=in_team_yes_no TRIALS=NONE OFFSET=NONE
  /TARGET_OPTIONS REFERENCE=0 DISTRIBUTION=BINOMIAL LINK=LOGIT
  /FIXED  EFFECTS=questionnairescore Treatment Facetype questionnairescore*Treatment questionnairescore*Facetype Treatment*Facetype **questionnairescore*Treatment*Face**type USE_INTERCEPT=TRUE
  /RANDOM USE_INTERCEPT=TRUE SUBJECTS=id COVARIANCE_TYPE=VARIANCE_COMPONENTS
  /RANDOM EFFECTS=trial USE_INTERCEPT=FALSE COVARIANCE_TYPE=VARIANCE_COMPONENTS
  /BUILD_OPTIONS TARGET_CATEGORY_ORDER=ASCENDING INPUTS_CATEGORY_ORDER=ASCENDING MAX_ITERATIONS=100 CONFIDENCE_LEVEL=95 DF_METHOD=RESIDUAL COVB=MODEL.
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Could you please explain what you mean by "follow up" on an interaction? If you're asking about how to interpret the interaction or what additional statistical analyses would be appropriate, this is the place for you and we are eager to help. But if your question is about how to structure SPSS files, then please turn to other resources. – whuber♦ Oct 22 '12 at 12:58
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Hi Whuber, with follow-up, I indeed mean which additional statistical analyses I need to conduct. When I plot the interaction, I can see that the interaction is driven by one steep line. How can I test the significance of that slope (in a multilevel design). I think I need to conduct a single slope analysis in order to interpret my 3-way interaction but I could be wrong. With splitting the file, I meant running the analyses twice, for example once per group, and than testing the 2-way interactions. Do you know what I mean? – user9203 Oct 22 '12 at 13:54
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I think I follow. It would help for you to edit your question to (a) include the points made in your comment and (b) to emphasize the results you have obtained (such as selected output and graphics) rather than the details of the code you used. In fact, I see little use for posting the code at all, if your interest focuses on the statistical questions--it seems to be more of a distraction than a help. – whuber♦ Oct 22 '12 at 14:03
Tt would help (at least to me) if you write down your model with equations. Something like: Pr(y_ij=1) = invlogit(a_j + bx1_ij +b*x2_ij) and a description of what is each variable. I, for instance, didn't understand how you may have one random intercept and a random incerpet for trial! – Manoel Galdino Oct 23 '12 at 13:07
Hi Manoel, thanks for your comment. I am not familiar with writing formulas and I am afraid that if I make a mistake, I will bring you and other readers on the wrong path. Instead, I included my syntax again. Is this clear? The interaction questionnairescore*Treatment*Facetype is sign. I read about pick and point approach to probe the interaction but don't know how to do it with my multilevel structure. – user9203 Oct 23 '12 at 14:07

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