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I have a dataset with participants' scores on three exams. Each participant completed each of the three exams. So the dataset looks something like (for a total of 945 rows):

SubjectCode    Exam    Score
1              A       70
1              B       44
1              C       80
2              A       62
2              B       50
2              C       89

I can run the following model without problem, using the nlme library:

lme(LD ~ 1, random = ~1|SubjectCode/Exam, data = ld_melted, method = "ML")

However, when I try the same with the lme4 library, I get an error:

lmer(LD ~ 1 + (1|SubjectCode/Exam), data = ld_melted)

Error: number of levels of each grouping factor must be < number of observations

Firstly, I don't understand the error. My dataset consists of 945 rows: 315 students * 3 exams. So it would seem that "the number of levels of each grouping factor" is 315 for SubjectCode, and 3 for Exam, both of them lower then the number of observations (945).

Secondly, the GLMM FAQ states that model specifications are used both by lme4 and nlme. So I also don't understand why one, but not the other, throws an error.

Thanks for any help!

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    $\begingroup$ (1|SubjectCode/Exam) is equivalent to (1|SubjectCode) + (1|SubjectCode:Exam). The interaction SubjectCode:Exam has 945 levels and you have 945 rows. So lme4 is right in complaining. No idea why nlme does not. $\endgroup$
    – amoeba
    Commented Jul 2, 2018 at 16:03
  • $\begingroup$ Thanks, that's really helpful. What would in your opinion then be the correct way to specify this model, considering the fact that I have repeated measures? (This is supposed to be a null model without fixed effects; I'll add the fixed effects later when I know that the null model is correct) $\endgroup$
    – Johanna
    Commented Jul 2, 2018 at 16:07
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    $\begingroup$ LD ~ 1 + (1|SubjectCode). You don't need random effect for Student/Exam if you only have 1 observation per Student/Exam combination. $\endgroup$
    – amoeba
    Commented Jul 2, 2018 at 16:14

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