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I have a language learning study with a few different dependent variables. For the majority of the tasks, responses to each item are either right (1) or wrong (0), and thus the data has been analysed with a mixed effects logistic regression.

However, I have one task that has allowed for partial scoring - so participants can score 0, 0.5, or 1. Is there any way to analyse this in a consistent way to the other tasks? I wondered about multinomial regressions but (a) these seem complicated (no lme4 option?), and (b) I'm not sure whether it's appropriate given that the categories are related? There are also very few 0.5 scores.

Any pointers would be much appreciated, many thanks in advance.

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  • $\begingroup$ How many is "very few" ? $\endgroup$
    – Robert Long
    Commented Aug 1, 2016 at 18:41
  • $\begingroup$ For my adult dataset, 152/4992 observations. For my child dataset, only 20/2353. Now I put it like that it seems even more daft to persist, but it would still be helpful to know. $\endgroup$
    – E James
    Commented Aug 2, 2016 at 12:21

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I have 2 broad suggestions:

  1. Use a logistic binary mixed effects model. There are 3 approaches, and you could compare the results of all three (I expect the results will not differ markedly)

    • collapse the 0.5 group into the 0 group.

    • collapse the 0.5 group into the 1 group

    • delete the 0.5 group

  2. Fit a logistic multinomial mixed effects model to the 3-level data, using clmm from the ordinal package or npmlt from the mixcat package.

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  • $\begingroup$ Thank you! Option 1 of collapsing the groups is what I have done thus far, I was just trying to work out if there were other options (especially in terms of planning ahead for future studies with data of this nature). I will give the 3 level data option a go to try - any guidance on which package is more beginner-friendly? $\endgroup$
    – E James
    Commented Aug 4, 2016 at 14:12
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    $\begingroup$ @EJames ordinal should be a bit more beginner-friendly $\endgroup$
    – Robert Long
    Commented Aug 4, 2016 at 15:30

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