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

[René]

Hey, things clear up. Thanks for the picture. I want to challenge your
concerns:
First, you see that observing a main effect of PrePost (or "Time") in mod3
can only mean two things: 1) performance goes up (positive effect); or 2)
performance goes down (negative effect), in general. Saying something like
this, is what the model is defined for. The conclusion will be this
"general increase" or "general decrease" or "no evidence here". If you have
a different question from that (i.e. on an item level), then you should
specify it in more detail (see below).
There are three issues in-between the lines of your questions:
1. is it a statistical concern you have?
2. is it an actual theoretical question you have?
3. is it a matter of making a non-result to a result?

1. The statistical view:
Counter-question: who would ever assume that a 1 score for a word in a
pre-test will remain constant until eternity. And why should it? The answer
is: Nobody, and this is the reason statistics (probability theory) exists
:). So the first simple answer to your question is you do not need to test
whether observed gains from pre-to-post are 'genuine' (only from 0 to 1,
without decline cases) because 'nature' guarantees that there will be
decline somewhere. That's "randomness" :)  But the question is, what's
stronger, gain or decline? See... and there is no problem in it: a general
main effect (e.g. an overall gain) still is an overall gain, even if some
cases decline.

2. Theoretical view:
If, however, such special item dynamics are theoretized in advance, then
simply test it :) For instance, the assumption whether the treatment leads
to gain on abstract words, but to decline on concrete words, then should
find into the model by coding the factor AbsCon (abstract vs. concrete
words)  as fixed effect (assuming a within participants manipulation).
mod4<-brm(score~PrePost*Group*AbsCon+(1+PrePost*AbsCon| subject) +
(1+group|words),...)
(Note: the 1+XX|subject just means random intercept  for subject (1+) plus
slope for XX on subject; and writing (1+group|words) is the same as
writing (group|words),
but you can estimate the slope without the (word) intercept by writing
(0+group|words))

Without having such a theoretical account testing for can also be done via:
mod4<-brm(score~PrePost*Group*words+(1+PrePost*words| subject),...)
But you will hardly be able to interpret the interactions in this model
because words alone has 28 levels.

3. But, your example seems to suggest a special case... (i.e. an actual
Null-Effect):
"If a participant has  got 5 correct words out of 28 in both pretest and
posttest"
then there would be no general effect of PrePost in the model above
(generalizing to all participants now). And searching for "deeper" model
checks looks like rescuing all effects you can get (post hoc). But of
course, making an argument like there still is an effect, namely for 5
specific words, which is not observable because there is also a detriment
for other 5 words is possible, but requires a solid theory which explicitly
predicts this interaction, and an experiment which was explicitly designed
to test this interaction. (point 2)

So... if it is point 2 you got... Then go ahead :) test it in a meaningful
way. Otherwise, simply treat this "effect by words" interaction as random
slope (1+group|words), or btw. (1+PrePost*Group|words) is also possible...,
which is basically 'statistically' integrating the idea that the
treatment*time effects vary (randomly) between stimuli. And doing this in
the random effects has the notion of "generalizing" estimation error in the
population, and should be preferred to implementing those in the fixed
effects, if the 28 words can be seen as a random (non-special) stimulus
sample. If this is not the case, then consider coding the "special" thing
about the words as fixed effects (e.g. if you want to use the same design
again, for testing something, while controlling for stimulus specifics).

Best, René

Am Sa., 23. März 2019 um 11:59 Uhr schrieb Souheyla GHEBGHOUB <
souheyla.ghebghoub using gmail.com>:

> 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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