Linear mixed models in SPSS with repeated measures

Question

I am trying to build some linear mixed models in SPSS, and am having a little trouble with the syntax - particularly with regards to the repeated measures aspects of my design.

I have around 40 participants, each of whom took part in 4 sessions: baseline, active, passive and control. I would like to find out if the relationship between my dependent variable - d-prime (behavioral performance on a task) and my independent variable - BOLD (brain activity) differs between session.

I think what I need to do first is specify a bunch of models i.e. a model with fixed slopes and intercepts, a model with random slopes and fixed intercepts and a model with random slopes and intercepts and compare the -2LL, but I'm struggling to specify these models correctly.

My data is arranged in a long format, and looks like this:

subject_ID	session	d-prime	bold
1	active	3.37	.97
1	passive	3.94	.18
1	control	3.34	.31
1	baseline	3.94	.63
2	active	3.30	.83
2	passive	3.46	1.33
2	control	4.23	.62
2	baseline	1.90	-.81

Answer 1

I don't think you need a random slope in your design, you'll get what you need with a random intercept mixed model with a session*BOLD interaction (though I must say you have very little data for testing an interaction, are you confident you have adequate power?). But technically, I'd use the following:

MIXED d-prime BY session WITH bold
  /FIXED=session bold session*bold | SSTYPE(3)
  /METHOD=REML
  /PRINT=SOLUTION
  /RANDOM=INTERCEPT | SUBJECT(subject_ID) COVTYPE(VC).

Then, if the interaction between session and bold is significant, it suggests that bold is related to d-prime in different way in different sessions and you can for instance plot the bold - d-prime slopes for different sessions.

If you want to run an unconditional model (e.g. to report the variance component for subject), you can use

MIXED d-prime 
  /PRINT=SOLUTION
  /RANDOM=INTERCEPT | SUBJECT(subject_ID) COVTYPE(VC).

And then you can compute subject ICC from the Estimates for covariance parameters.