I have preference ratings (integers from 1-to-7) for k=80 stimuli, obtained from N=30 subjects. I want to use a mixed-effects model to test how well the following variables - as fixed effects - can predict the responses(ratings):
Predictor 1, called "Parncutt" below = value describing each stimulus
Predictor 2, called "GMSI" below = score describing each subject
Subject and stimulus number are to be considered random effects.
I used the Matlab command:
lme = fitlme(tbl,formula)
where the input data (tbl) is arranged like this:
and where the model formula, in Wilkinson/R notation, is:
formula = 'ratings_pls ~ Parncutt + GMSI + (1|subjectNr) + (1|stimulusNr)';
The fitlme command produced this output:
lme = Linear mixed-effects model fit by ML Model information: Number of observations 2370 Fixed effects coefficients 3 Random effects coefficients 110 Covariance parameters 3 Formula: ratings_pls ~ 1 + Parncutt + GMSI + (1 | subjectNr) + (1 | stimulusNr) Model fit statistics: AIC BIC LogLikelihood Deviance 7066.8 7101.5 -3527.4 7054.8 Fixed effects coefficients (95% CIs): Name Estimate SE tStat DF pValue Lower Upper '(Intercept)' 4.7822 0.56266 8.4993 2367 3.3222e-17 3.6789 5.8856 'Parncutt' -4.7474 0.87128 -5.4488 2367 5.5949e-08 -6.456 -3.0389 'GMSI' 0.011938 0.0059983 1.9901 2367 0.04669 0.00017503 0.0237 Random effects covariance parameters (95% CIs): Group: subjectNr (30 Levels) Name1 Name2 Type Estimate Lower Upper '(Intercept)' '(Intercept)' 'std' 0.56507 0.43399 0.73574 Group: stimulusNr (80 Levels) Name1 Name2 Type Estimate Lower Upper '(Intercept)' '(Intercept)' 'std' 0.86879 0.73879 1.0217 Group: Error Name Estimate Lower Upper 'Res Std' 0.99594 0.96733 1.0254
As a first step, I initially computed correlations between the DV (rating) and each of the two factors (GMSI and Parncutt) - both correlations are moderately strong. I then wanted to do a multiple regression with these two predictors, but was led instead to the mixed-model, since the sample size is small and there are multiple items(stimuli), both of which pose a problem for multiple regression.
I am, however, not sure which output of the LME model to interpret that would give me information above&beyond the two correlations that I did.
Also, I am not sure whether to also add a term in the LME model for:
A) random slopes: if allowing for differences between subjects and stimuli (random intercepts in the model), then why not also allow the slopes for both factors to be random?
B) interaction terms between any of the subject-wise factors (SubjectNr and GMDI) and any of the stimulus-wise factors (StimulusNr and Parncutt)