[R-sig-ME] Multivariate mixed models with different outcome distributions
Ben Bolker
bbo|ker @end|ng |rom gm@||@com
Sat Dec 17 01:25:14 CET 2022
Is your multivariate response 256-dimensional (i.e. you have 256
responses from each individual which you want to treat as correlated)?
That's *very* unlikely to work if you just stick it into a standard
multivariate framework, as you'll have to estimate a 256×256 covariance
matrix (almost 33,000 parameters). A factor-analytic or reduced-rank
model could work (e.g. glmmTMB now allows this -- although it's not well
tested and definitely not with examples this large!), but doesn't do
multi-type models).
I'm not quite sure what you intend to do with nlme::lme() here.
It may well be that just doing something like an arcsine-sqrt
transform (or logit, if you prefer and have no exact 0/1 values) for
your proportion data and then modeling everything as a multi-response
Gaussian would be good enough ...
On 2022-12-15 12:20 p.m., Timothy MacKenzie wrote:
> Dear Ben,
>
> Thank you for your confirmation. There are two things that I want to
> better understand.
>
> First, brms::brm() etc. require wide-format data. For my data (below
> see long-format data from a single student), wide-formatting it will
> create 256 columns for each subject (attached)! Is using brm() etc.
> really practical here?
>
> Second, nlme::lme() allows modeling the residuals. If I model the
> residuals from my responses (CAL_type) on their current scale (some
> proportions, some normal ones) with lme() and find a relatively good
> fitting model, would that be a second best solution?
>
> Thanks,
> Tim M
>
> LONG-FORMAT="
> Class Person Task_order Task_type Time Score CAL_type Mot_ex Mot_inr
> Mot_ide Mot_int Mot_amot Eng_leng_txt Eng_time_on_tsk
> 1 1 S-C simple 1 5 com_mult 4 2
> 3 3 1 300 20
> 1 1 S-C simple 1 .3 com_dc/t 4 2
> 3 3 1 300 20
> 1 1 S-C simple 1 2 com_cn/t 4 2
> 3 3 1 300 20
> 1 1 S-C simple 1 3 com_cn/c 4 2
> 3 3 1 300 20
> 1 1 S-C simple 1 .4 ac 4 2
> 3 3 1 300 20
> 1 1 S-C simple 1 1 lex_vo 4 2
> 3 3 1 300 20
> 1 1 S-C simple 1 5 lex_fr 4 2
> 3 3 1 300 20
>
> 1 1 S-C complex 2 2 com_mult 3 4
> 2 1 2 200 25
> 1 1 S-C complex 2 .3 com_dc/t 3 4
> 2 1 2 200 25
> 1 1 S-C complex 2 4 com_cn/t 3 4
> 2 1 2 200 25
> 1 1 S-C complex 2 3 com_cn/c 3 4
> 2 1 2 200 25
> 1 1 S-C complex 2 .4 ac 3 4
> 2 1 2 200 25
> 1 1 S-C complex 2 4 lex_vo 3 4
> 2 1 2 200 25
> 1 1 S-C complex 2 5 lex_fr 3 4
> 2 1 2 200 25
>
> 1 1 S-C simple 3 4 com_mult 5 2
> 3 4 3 100 10
> 1 1 S-C simple 3 .2 com_dc/t 5 2
> 3 4 3 100 10
> 1 1 S-C simple 3 3 com_cn/t 5 2
> 3 4 3 100 10
> 1 1 S-C simple 3 3 com_cn/c 5 2
> 3 4 3 100 10
> 1 1 S-C simple 3 .6 ac 5 2
> 3 4 3 100 10
> 1 1 S-C simple 3 6 lex_vo 5 2
> 3 4 3 100 10
> 1 1 S-C simple 3 6 lex_fr 5 2
> 3 4 3 100 10
>
> 1 1 S-C complex 4 1 com_mult 1 3
> 2 5 4 400 35
> 1 1 S-C complex 4 .1 com_dc/t 1 3
> 2 5 4 400 35
> 1 1 S-C complex 4 1 com_cn/t 1 3
> 2 5 4 400 35
> 1 1 S-C complex 4 3 com_cn/c 1 3
> 2 5 4 400 35
> 1 1 S-C complex 4 .3 ac 1 3
> 2 5 4 400 35
> 1 1 S-C complex 4 5 lex_vo 1 3
> 2 5 4 400 35
> 1 1 S-C complex 4 5 lex_fr 1 3
> 2 5 4 400 35
> "
>
> On Wed, Dec 14, 2022 at 12:12 PM Ben Bolker <bbolker using gmail.com> wrote:
>>
>> I didn't realize that brms does multi-type models, but apparently it
>> does:
>>
>> https://cran.r-project.org/web/packages/brms/vignettes/brms_multivariate.html
>>
>> ... so yes, I would go for brms in this case.
>>
>> cheers
>> Ben
>>
>>
>> On 2022-12-14 12:09 p.m., Timothy MacKenzie wrote:
>>> Dear Ben,
>>>
>>> Thank you for the hint. Regarding MCMCglmm, I couldn't find "beta" in
>>> the family of allowable distributions in the package. Did you have a
>>> specific set of distribution families in mind to handle normal and
>>> beta responses simultaneously?
>>>
>>> Also, I noticed the brms package apparently can handle different
>>> response distributions, is there a reason, in your expert opinion, to
>>> opt for MCMCglmm?
>>>
>>> Many thanks,
>>> Tim M
>>>
>>> On Tue, Dec 13, 2022 at 9:28 PM Ben Bolker <bbolker using gmail.com> wrote:
>>>>
>>>> MCMCglmm can handle this case
>>>>
>>>> On Tue, Dec 13, 2022, 10:14 PM Timothy MacKenzie <fswfswt using gmail.com> wrote:
>>>>>
>>>>> Hello Colleagues,
>>>>>
>>>>> I have a multivariate data structure (below) where the dependent
>>>>> variables (DV) seem to have different distributions.
>>>>>
>>>>> For instance, *ac* is measured in proportions and perhaps
>>>>> beta-distributed, but *fl* and *le* may be normally distributed.
>>>>>
>>>>> Would it make methodological sense to fit such DVs in a multivariate
>>>>> mixed model given that they are theoretically related but practically
>>>>> measured on different scales?
>>>>>
>>>>> Any resources to provide mixed model strategies in such a situation?
>>>>>
>>>>> Many thanks for your help,
>>>>> Tim M
>>>>>
>>>>> Score ~ DV + (1 | subj_id) ## Would this make sense?
>>>>>
>>>>> # Data structure:
>>>>> subj_id DV Score
>>>>> 1 ac .5
>>>>> 1 fl 23.1
>>>>> 1 le 1.4
>>>>> 2 ac .7
>>>>> 2 fl 19.6
>>>>> 2 le 2.1
>>>>>
>>>>> _______________________________________________
>>>>> R-sig-mixed-models using r-project.org mailing list
>>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>> --
>> Dr. Benjamin Bolker
>> Professor, Mathematics & Statistics and Biology, McMaster University
>> Director, School of Computational Science and Engineering
>> (Acting) Graduate chair, Mathematics & Statistics
>> > E-mail is sent at my convenience; I don't expect replies outside of
>> working hours.
--
Dr. Benjamin Bolker
Professor, Mathematics & Statistics and Biology, McMaster University
Director, School of Computational Science and Engineering
(Acting) Graduate chair, Mathematics & Statistics
> E-mail is sent at my convenience; I don't expect replies outside of
working hours.
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