# UPDATED: Multiple lme models or MANOVA with random effects? Problem with singular fit

hope you can help me with this issue! In my study I have 4 outcome variables which correspond to the ratings I collected for 4 different psychological dimensions (liking, comfort, approach, attractiveness). The 4 psychological dimensions are defined in the column ‘ratetype’ and the column 'ratings' reports the score. I also have 2 independent variables: 'paintingtype', which is a categorical variable with 3 experimental conditions, and ArtInterest, which is the self-rated measure on a 5-points Liker scale. This is my data structure:

Observations: 7,872
Variables: 14
$$X  1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16…$$ PID                  <fct> 571b712f5d40840009c44804, 5798f7a116020100010411ac, 5…
$$ArtInterest  4, 4, 4, 5, 4, 4, 3, 2, 3, 3, 5, 4, 4, 4, 4, 3, 5, 5,…$$ ratings              <int> 15, 72, 21, 80, 91, 13, 58, 36, 18, 70, 10, 49, 82, 1…
$$ratetype  Liking, Liking, Liking, Liking, Liking, Liking, Likin…$$ paintingtype     <fct> Angular, Angular, Angular, Angular, Angular, Angular,…
$paintingID <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…  At the moment I subsetted the data in 4 different datasets with the following code: # # Select data for ‘LIKING’ Liking <- subset(mdata, ratetype == "Liking", select=c("PID", “ArtInterest", "ratings", "paintingtype", "paintingID" ))  This is the data structure of the subsetted dataset: $$PID 571b712f5d40840009c44804, 5798f7a116020100010411…$$ ArtInterest <int> 4, 4, 4, 5, 4, 4, 3, 2, 3, 3, 5, 4, 4, 4, 4, 3, … $$ratings 15, 72, 21, 80, 91, 13, 58, 36, 18, 70, 10, 49, …$$ paintingtype <fct> Angular, Angular, Angular, Angular, Angular, Ang…$ paintingID   <int> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …


and then run 4 different analysis with the model below:

m1 <-  lme(ratings ~ paintingtype:ArtInterest, random= (~1|PID/paintingID), data=Liking, method = "ML")


Q1: Would be better to run one single MANOVA instead of 4 different lme models? Q2: As every participant ('PID') rated 16 items ('paintingID') for every experimental condition, how can I control for the random effect of those two variables in the MANOVA?

EDIT: Following the suggestions in the comments, I built the following model:

m <- lmer(ratings ~ paintingtype + ArtInterest + ratetype + (ratetype | PID/paintingID) , data=mdata)


however I receive the following warning message:

singular fit


What does it mean? Should I worry about it? Any suggestion will be much appreciated!

• You can always run a manova as a multilevel model. I don't quite understand your model -wnat are the 4 datasets? Perhaps include your subset command. Jul 31, 2019 at 15:59
• @JeremyMiles thanks for your suggestion. I updated the question as you suggested Aug 1, 2019 at 9:47
• @JeremyMiles I am not sure how to run a MANOVA as multilevel model: are you suggesting to add 'ratetype' as a fixed effect in my model? Aug 1, 2019 at 9:55
• Here's an article about it. link.springer.com/chapter/10.1007/978-3-319-20585-4_16 . I'm fairly sure that the book Serious Stats by Baguley covers it (as do many others). Aug 2, 2019 at 16:30
• @JeremyMiles thanks Aug 3, 2019 at 10:58

A short answer to the updated question: your model is too complex. You will need to either simplify your model (typically one removes more complex random effects) or to switch to a Bayesian approach to fitting your model. A more thorough explanation can be found here.

• thanks for the link. I am considering running a simple repeated-measures ANOVA using the 'aov' function in R, which might be enough to model my data. Aug 6, 2019 at 10:37
• @Nicole You can start by removing the random slopes, and then simplify it further as needed.
– mkt
Aug 6, 2019 at 10:38