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I'm struggling to figure out the right model specification for my data.

Here's my design: a between-subject longitudinal study, with two Type of participants (Test and Control), with 8 Subject in each Type, each of which is tested multiple times (different numbers of times across participants, unfortunately). At each test, subjects produce a lot of speech, from which I've derived a measure of their language development (MLU, continuous variable ranging from ~1 to ~3). The DV is, for each sentence they say, whether it contains a certain Word (binary, coded as 1 or 0).

I'm interested in whether the two Types of people change differently on the DV, as their MLU increases -- ie. the interaction between Type and MLU. I also want to account for random effects of Subject (though I'm not sure how possible this is with only 8 subjects per type).

I'm struggling to figure out the right 'maximal' model. I've come up with something like this, but I'm not sure if it's conceptually right:

Word ~ MLU*Type + (MLU|Type/Name)

One conceptual question I'm unclear about is that it seems there are, in principle, two different ways to test for an effect of Type in this design, and I'm not sure how different they are, or which one makes more sense. One approach is just to treat Type as a standard fixed effect. The other is to compare two models that differ on whether Type is included as a Random effect. E.g. something like: 

model1<- MLU + (MLU|Type/Name)
model2<- MLU + (MLU|Name)
anova(model1, model2)
amoeba
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Roder
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  • `Word ~ MLU*Type + (MLU|Type/Name)` is wrong. You cannot have `Type` as both fixed and random. From your description it should clearly be fixed. So you should use `Word ~ MLU*Type + (MLU|Name)`. – amoeba Jun 22 '17 at 11:12
  • Hm... the discussion here seems to say otherwise, along with others I've seen? https://stats.stackexchange.com/questions/70556/have-i-correctly-specified-my-model-in-lmer – Roder Jun 22 '17 at 22:52
  • I don't see anything there contradicting what I said above. Can you point me to the exact statement that you think is contradictory? – amoeba Jun 23 '17 at 07:22
  • Just to clarify: `MLU*Type + (MLU|Type:Name)` would be okay, but presumably your `Names` are different for `Type=Test` and `Type=Control`, and if so, it's equivalent to `MLU*Type + (MLU|Name)`. If you can have the same names in both groups, e.g. a John there and a John here, then you need `(MLU|Type:Name)`. The only thing that does NOT make sense is `(MLU|Type/Name)` because it contains `(MLU|Type)` which contains `(1|Type)` which cannot be in the formula together with `Type`. – amoeba Jun 23 '17 at 07:26
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    Ah, thank you! That helps clear up my confusion quite a bit. – Roder Jun 25 '17 at 20:49

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