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

[Uanhoro, James]

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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