Extending repeated measures ANOVA to linear mixed effects model

Hi, I currently have data on a group of participants undergoing an identical experiment in which they submit a rating after a given instruction/cue set at two separate timepoints that I have analyzed using repeated measures ANOVA:

t=table(inst1_cue1_pre_rating_mean_stack,inst1_cue1_post_rating_mean_stack,inst2_cue1_pre_rating_mean_stack,inst2_cue1_post_rating_mean_stack,inst1_cue2_pre_rating_mean_stack,inst1_cue2_post_rating_mean_stack,inst2_cue2_pre_rating_mean_stack,inst2_cue2_post_rating_mean_stack,'VariableNames',{'inst1_cue1_pre','inst1_cue1_post','inst2_cue1_pre','inst2_cue1_post','inst1_cue2_pre','inst1_cue2_post','inst2_cue2_pre','inst2_cue2_post'});   with instruction ("inst1/inst2"), cue ("cue1/cue2") and time (pre/post) as categorical variables
WithinStructure=table([1 1 2 2 1 1 2 2]',[1 1 1 1 2 2 2 2]',[1 2 1 2 1 2 1 2]','VariableNames',{'instruction','picture','time'});
WithinStructure.instruction = categorical(WithinStructure.instruction);
WithinStructure.picture = categorical(WithinStructure.picture);
rm=fitrm(t,'look_alc_pre-negative_food_post~1','WithinDesign',WithinStructure);
ranovatbl=ranova(rm,'WithinModel','instruction*picture*time')

My question is, I would like to extend this to a linear mixed effects model, where instead of pre and post I would like to have a continuous variable interval days between session ("intervals")

So I have gotten as far as setting up the table for the lme:

pre_table=table(inst1_cue1_pre_rating_mean_stack,inst2_cue1_pre_rating_mean_stack,inst1_cue2_pre_rating_mean_stack,inst2_cue2_pre_rating_mean_stack,intervals_baseline)

, where intervals_baseline is a column of zeros the size of the participant group

post_table=table(inst1_cue1_post_rating_mean_stack,inst2_cue1_post_rating_mean_stack,inst1_cue2_post_rating_mean_stack,inst2_cue2_post_rating_mean_stack,intervals_post) 

where intervals_post is the number of days for each participant between tests

tbl=[tbl_pre;tbl_post]

My question is how to extract (or code) the categorical variables for the linear mixed effects model, which I think should be rating~instruction+cue+intervals (and I would like the interaction terms instruction*intervals and cue*intervals) but I'm a little lost on how to set this up. Do I code the fixed effects as in the anova? And what about the dependent variable?

Thank you!

[Jeff Miller]

So each participant has a different pre/post interval that you wish to take into account numerically instead of just making a binary pre/post distinction? I don't see how this design is appropriate for a linear mixed effects model.

How many participants do you have and what does a frequency distribution of the pre/post intervals look like?

[bsriv]

Hi- thanks for the response

I have 22 particpants and here is a histogram (x axis = #days between sessions, y axis # of participants)

[Jeff Miller]

That's not a lot of participants, and they are mostly squished together in that 90-100 range, so I doubt you have much power to detect an influence of the interval length. If you want to try, I'd suggest using a median split on interval to divide the participants into two groups (short vs long interval) and then treating that division as a between-Ss factor in the ANOVA. If it is practical in a future study looking harder at interval, maybe randomly assign participants into more distinct short- and long-interval groups (e.g., 80-95 and 110-125).