[R-sig-ME] Nested random effects in mgcv gam/bam

[Cesko Voeten]

Replies inline.

Op 24-06-2019 om 18:07 schreef Mathew Guilfoyle:
> Cesko, thanks for the reply.
> 
>> If the subjects are each in one group only, the 'by=G' in the two re smooths in m2b is redundant, and therefore m2a is correct.
> 
> Does the addition of a by-factor argument not allow different variance in the random effects for each group? (Incidentally each subject is in one group only)

I believe it should, but I'm not sure if this would actually give you a different fit, given that the groups perfectly separate the subjects? I've tried both constructions on some toy data of my own and the fits are exactly the same up to rounding error (in which case the non-by version is more parsimonious). But I guess this question would be answered for your data by a likelihood-ratio test.

> 
>> Note that this is not entirely equivalent to your gamm model, for two reasons. One is, as you note correctly, that gamm includes correlations between intercept and A which bam doesn't. The second reason is that nlme interprets subsequent grouping factors as nested, meaning that your model actually has random effects for G and G %in% ID, not for G and ID separately. (This could be overcome with a complicated pdBlocked() argument, or by using gamm4 instead of gamm.)
> 
> So does this imply that the random effects on intercept and slope will necessarily be uncorrelated in gam/bam, i.e. equivalent to a pdDiag() argument in lme/gamm?

Yes, precisely.

> 
> Secondly, does a random effect smooth with two factors [e.g. s(G, ID, A, bs=‘re’)] not create a nested structure? - the mgcv random.effects documentation page implies that the random effect applies to the interaction of the two factors?

Ahh, sorry, I mistakenly thought you did not want nesting in your gamm model (I usually write the %in% explicitly if I use lme). Yes, of course, this is completely correct.

> 
> Thanks.
>>
>> Good luck,
>> Cesko
>>
>> -----Messaggio originale-----
>> Da: R-sig-mixed-models <r-sig-mixed-models-bounces using r-project.org> Per conto di Mathew Guilfoyle
>> Inviato: maandag 24 juni 2019 14:34
>> A: r-sig-mixed-models using r-project.org
>> Oggetto: [R-sig-ME] Nested random effects in mgcv gam/bam
>>
>> I have a dataset comprising of subjects with a unique identifier ‘ID’ who are each in one of two groups ‘G’ .  I am looking to find the smooth relationship between numerical variables A and B that are both evaluated at multiple times in each subject.
>>
>> Ignoring the grouping for the moment, a GAM formula including random intercept and ’slope’ for each subject would be:
>>
>> m1 = bam(B ~ s(A, bs=‘cr’, k=10) + s(ID, bs=‘re’) + s(ID, A, bs=‘re’))
>>
>> Now, I believe the smooth is different in each group therefore I want to obtain separate smooths based on G, and also include random intercepts and ‘slope’ for each subject but nested within each group.
>>
>> Which of the following constructions is correct? (G is a factor)?:
>>
>> m2a = bam(B ~ G + s(A, bs=‘cr’, k=10, by=G) + s(G, ID, bs=‘re’) + s(G, ID, A, bs=‘re’))
>>
>> m2b = bam(B ~ G + s(A, bs=‘cr’, k=10, by=G) + s(ID, bs=‘re’, by=G) + s(ID, A, bs=‘re’, by=G))
>>
>>
>> I have tried do this more explicitly using gamm:
>>
>> m3 = gamm(B ~ G + s(A, bs=‘cr’, k=10, by=G), random = list(G=~1+A, ID=~1+A))
>>
>> but this takes a lot longer (hours) to run given the size of the dataset and as I don’t need/want to specify the correlation structure of the random effects I hoped that one of the bam calls above was equivalent.  I have tried the various models on a subset of the data and model m2a gives qualitatively very similar smooths to model m3.
>>
>> Thanks.
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