[R-sig-ME] Random effects in multinomial regression in R?

[Souheyla GHEBGHOUB]

Dear René,

Thank you for the feedback. Actually, my model was originally like you
suggested now (except for slopes I had PrePost without 1 in both words and
subjects. I called PrePost as "Time". I will read more about the 1+prepost
form you mentioned.

The reason why I gave up this model and looked for something else is the
fact that each subject has 28 words tested twice (pre&post) and I was not
too sure whether such model will take into consideration differences
between pre & post at the level of every word of each participant (which is
what I want) instead of merely comparing every participant's pre mean sores
of 28 words against his post mean score (which is what i should avoid), here
is a short example as to why:

 If a participant has  got 5 correct words out of 28 in both pretest and
posttest, there will be multiple interpretations:  e.g. They could refer to
the same words (i.e. 0 gain), or they could be totally new words (i.e. 5
gains) ...etc , hence I am not sure whether such model of pretest vs
posttest will compare each subject score of each word from pretest to
posttest then base its analysis on these score changes instead of comparing
the sum scores between pre and post and which likely skew results.

I posted about this in stackexchange 3 months ago and was told that it does
compare word to word for every participant, but I am still not confident
enough to use it because all the accurateness of the results and discussion
chapters of my PhD thesis will be based on this decision.

I look forward to receive feedback from you and any member reading this,
Souheyla
University of York

On Sat, 23 Mar 2019, 10:01 René, <bimonosom using gmail.com> wrote:

> Hi Souheyla,
>
> Well, I guess in your case it is simply more elegant to leave the measured
> predictor out of the fixed effects, because there is also another implied
> question (i.e. about the strength of change between pre and post).
>
> So, another possibility to re-define your model (as logistic regression)
> allowing for better interpretations:
> mod3<-brm(score~PrePost*Group+(1+PrePost | subject)+(1+group | words),...)
>
> score = 0 or 1 for a given testitem
> PrePost = Pre vs. Post  (basically just an indicator of the measurement
> time point)
> Thus, the PrePost main effect will tell, whether there is a change from
> pre to post (e.g. a gaint), and you can also tell how strong it is (in odds
> ratios).
> And if PrePost interacts with Group, then the change (e.g. a gain) is
> moderated by the treatment, which seems to be your main question.
>
> Now in this model, you can also have by-subject random slopes for PrePost
> of course (because the fixed effect of PrePost is present for every
> subject).
>
> Best, René
>
>
> Am Sa., 23. März 2019 um 10:12 Uhr schrieb Souheyla GHEBGHOUB <
> souheyla.ghebghoub using gmail.com>:
>
>> I read that in multinomial regression, all independent variables should be
>> variables that we manipulate. Can I still have pretest as IV without
>> skewing my results?
>>
>> Best,
>> Souheyla
>>
>> On Fri, 22 Mar 2019, 23:31 Souheyla GHEBGHOUB, <
>> souheyla.ghebghoub using gmail.com>
>> wrote:
>>
>> > Thank you both. I will look into this and see :)
>> >
>> > Best,
>> > Souheyla
>> >
>> > On Fri, 22 Mar 2019, 22:02 Uanhoro, James, <
>> uanhoro.1 using buckeyemail.osu.edu>
>> > wrote:
>> >
>> >> In standard regression models, the assumption is predictor variables
>> are
>> >> measured without error. Test scores will have measurement error, hence
>> >> Doran's comment when test scores are used as covariates. See: Hausman,
>> J.
>> >> (2001). Mismeasured Variables in Econometric Analysis: Problems from
>> the
>> >> Right and Problems from the Left. *Journal of Economic Perspectives*,
>> >> *15*(4), 57–67. https://doi.org/10.1257/jep.15.4.57
>> >> I will note that many practitioners ignore this issue, and it is quite
>> >> common to use predictors measured with error. Consider the number of
>> times
>> >> people use polychotomized income measures, or SES measures as
>> predictors,
>> >> or some other "construct".
>> >> On Mar 22 2019, at 5:39 pm, Souheyla GHEBGHOUB <
>> >> souheyla.ghebghoub using gmail.com> wrote:
>> >>
>> >> Dear Doran,
>> >>
>> >> Could you explain more this point to me, please?
>> >>
>> >> Thank you,
>> >> Souheyla
>> >>
>> >> On Fri, 22 Mar 2019, 21:19 Doran, Harold, <HDoran using air.org> wrote:
>> >>
>> >> Yes, but conditioning on the pre-test means you are using a variable
>> >> measured with error and the estimates you obtain and now inconsistent,
>> and
>> >> that¹s a pretty big sin.
>> >>
>> >> On 3/22/19, 3:49 PM, "Souheyla GHEBGHOUB" <
>> souheyla.ghebghoub using gmail.com>
>> >> wrote:
>> >>
>> >> Dear René,
>> >>
>> >> Thank you for your feedback to me. You are right, dropping the pretest
>> >> from
>> >> covariate if I predict change definitely makes sense to me! But the
>> fact
>> >> that i need to control for the starting levels of participants makes it
>> >> obligatory for me to chose the second way, which is predicting posttest
>> >> instead of change to have pretest scores controlled for.
>> >>
>> >> You also chose (1+group | word) , which is new to me. Does it intend to
>> >> assume the effect of group to vary across words, which is something
>> >> applicable to my data, right?
>> >> I will discuss all this with my supervisor, and may reply here again in
>> >> few
>> >> days if you do not mind.
>> >> Thank you very much
>> >> Souheyla
>> >> University of York
>> >>
>> >>
>> >> On Fri, 22 Mar 2019 at 13:42, René <bimonosom using gmail.com> wrote:
>> >>
>> >> Hi Souheyla,
>> >>
>> >> it seems to me that you will run into problems with your coding of
>> >> change
>> >> (gain, no gain and decline) because the 'change' is by
>> >> definition/calculation depending on the predictor pretest.
>> >> See, according to your coding scheme:
>> >> Change = decline can only occur if pretest=1 (not by pretest=0).
>> >> Change = gain can only occur if pretest = 0 (not by pretest=1)
>> >> Change = No Gain can occur if pretest= 1 or 0
>> >> In other words:
>> >> If pretest = 1 then the possible outcomes can be decline or no gain
>> >> If pretest = 0 then the possible outcomes can be gain or no gain
>> >>
>> >> And if the model result shows you then that the pre-test is
>> >> significantly
>> >> related to p(change-outcome), I guess there is no surprise in it, is
>> it?
>> >>
>> >> So the first solution to this would be simply kicking the pre-test
>> >> predictor out of the model completely, and predict:
>> >> mod1 <- brm(Change ~ Group + (1|Subject) + (1+Group|Word),...)
>> >> (Btw.: actually the first Hierarchical Bayes Model question I see on
>> the
>> >> mixed-effects mailing list :))
>> >>
>> >> Attempt for a further clarification on which random slopes would
>> reflect
>> >> the model's design:
>> >> If you have a within-subjects design, by-subject random slopes are
>> >> possible for the within-subject variable (e.g. if there are two sets of
>> >> words/lists [e.g. abstract vs. concrete words] for each participant,
>> and
>> >> you test whether there is a performance-difference between these
>> >> word-lists, then you can implement by-subject random slopes for words,
>> >> because each participant has seen both sets.) If each participant has
>> >> seen
>> >> only one list (i.e. between subjects design) by subject random slopes
>> >> for
>> >> words are not appropriate, because there is no 'slope' by participant
>> >> (i.e.
>> >> by definition, having a slope requires at least two observations...).
>> >> This
>> >> is always a good rule of thumb without thinking about it too heavily :)
>> >> Ans as you see: you can define a random slope for words:
>> >> (1+Group|Word),
>> >> because each word has been presented in each group (i.e. there can be a
>> >> slope for each word). And intuitively speaking the Treatment-effect can
>> >> vary depending on the stimuli you use, and the slope makes sense. (You
>> >> also
>> >> see in this example that the treatment effect can also vary by
>> subjects,
>> >> but in fact, this subject effect variation IS EQUAL to the effect you
>> >> want
>> >> to test, and having by subject group random slopes would eliminate the
>> >> fixed effect...)
>> >>
>> >> Anyway, there is a second possibility to define your model, depending
>> on
>> >> how you want to interpret it. In the previous model you can say
>> >> something
>> >> about the type-of-change likelihoods depending on the treatment group.
>> >> But
>> >> you could implement the model as binomial as well (i.e. logistic
>> >> regression)
>> >>
>> >> mod2 <- brm(posttest ~ pretest*Group + (1|Subject) +
>> (1+Group|Word),...)
>> >>
>> >> And what you would expect here would be an interaction between pre-test
>> >> and Group. For instance; if pretest=0 & treatment 1 then posttest
>> larger
>> >> than with pretest=0 & treatment 2; but not when pretest=1 (because this
>> >> is
>> >> a plausible no gain situation). And so on...
>> >> (And in this model there are no also no further random slopes hidden in
>> >> your design :))
>> >> Hope this helps.
>> >>
>> >> Best, René
>> >>
>> >>
>> >> Am Do., 21. März 2019 um 14:01 Uhr schrieb Souheyla GHEBGHOUB <
>> >> souheyla.ghebghoub using gmail.com>:
>> >>
>> >> Dear Philip,
>> >>
>> >> I understand , here is the structure of my data in case it could help.
>> >>
>> >> I have 3 groups of participants (control, treatment1, treatment2). Each
>> >> group was tested twice, once before treatment (pretest) and once after
>> >> treatment (posttest).
>> >> In each test, they were tested on knowledge of 28 words, scores are
>> >> dichotomous (0 = unknown , 1 = known). Tests are the same.
>> >>
>> >> I calculated change from pretest to posttest :
>> >> if pretest 0 and posttest 0 = no gain
>> >> if pretest 1 and posttest 1 = no gain
>> >> if pretest 0 and posttest 1 = gain
>> >> if pretest 1 and posttest 0 = decline
>> >> So I ended up with a dependent variable called Change with 3 levels
>> >> (no_gain, gain, decline) and I tried to predict it using Group and
>> >> Pretest
>> >> as covariates using multinomial logit model. mod0 <- brm(Change ~
>> >> Pretest
>> >> +
>> >> Group) I would like to add random effects for subjects but don't know
>> >> what's the best form when Time factor is absent.
>> >>
>> >> I hope other statisticians who read this could help
>> >> Thank you
>> >> Souheyla
>> >>
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>> >>
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