[R-sig-ME] Changing reference level in clmm() ordinal regression
Jessie Barker
jessiebarker at gmail.com
Tue Sep 26 11:55:45 CEST 2017
Hi Emmanuel,
Thanks very much for your reply! Your example is very helpful.
All the best,
Jessie
On 25 September 2017 at 11:30, Emmanuel Curis <
emmanuel.curis at parisdescartes.fr> wrote:
> Hello Jessie,
>
> Imagine a two-factors design, let's say sex and tobacco status. You
> can imagine the results as spanned in a 2×2 table :
>
> Sex
> F M
> Tobacco N µ0 µ1
> Y µ2 µ3
>
> The concept of "reference level" is to be meant on the basis of the
> cells of this table, not on the margins.
>
> That is, with the default orders of levels in R (alphabetical order),
> the reference value will be here µ0, and the coefficients will be a1 =
> (µ1-µ0) [change only Sex], b1 = (µ2-µ0) [change only Tobacco] and i =
> (µ3-[µ0+a1+b1]), interaction.
>
> If you change the reference level for Sex, for instance, then the
> reference value becomes µ1, and the coefficients are now a1' = (µ0-µ1)
> = -a1, b1' = (µ3-µ1) and i' = (µ2 - [µ1+a1'+b1']).
>
> So, as you can see, changing the reference level of one factor changes
> the coefficients for all factors — because you change in fact the
> reference cell in your table, and not only in the margin.
>
> Best regards,
>
> On Fri, Sep 22, 2017 at 05:24:59PM +0200, Jessie Barker wrote:
> « Hi Thierry,
> «
> « Thank you for your reply.
> «
> « I see that when changing the reference from say, a1 to a2, the estimate
> for
> « a3 will be different.
> « However, I'm still not sure why, when I change the reference of the other
> « factor from, say, q1 to q2, the estimate for a3 will be different
> (because
> « a3 is is still being compared to the same reference level of a,
> regardless
> « of what the reference level of q is). Or am I misinterpreting that?
> «
> « Thanks again,
> «
> « Jessie
> «
> « On 22 September 2017 at 14:38, Thierry Onkelinx <
> thierry.onkelinx at inbo.be>
> « wrote:
> «
> « > Dear Jessie,
> « >
> « > All models have an identical fit. They only differ in the
> « > parametrisation. "a3" estimates the difference between "a3" and the
> « > reference. Hence, changing the reference results in a different
> « > interpretation of the parameter and thus a different estimate.
> « >
> « > Best regards,
> « >
> « > ir. Thierry Onkelinx
> « > Statisticus/ Statiscian
> « >
> « > Vlaamse Overheid / Government of Flanders
> « > INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE
> « > AND FOREST
> « > Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
> « > thierry.onkelinx at inbo.be
> « > Kliniekstraat 25, B-1070 Brussel
> « > www.inbo.be
> « >
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> « >
> « > 2017-09-22 11:41 GMT+02:00 Jessie Barker <jessiebarker at gmail.com>:
> « > > I have a couple of questions that I asked on StackExchange and
> someone
> « > > suggested that I ask this mailing list. The post on StackExchange is
> « > here (
> « > > https://stats.stackexchange.com/questions/304092/changing-
> « > reference-level-in-clmm-ordinal-regression-in-r),
> « > > but I am summarizing it below:
> « > >
> « > > I’m analyzing data from a questionnaire where participants had to
> rank
> « > > three answers to each question (e.g. 1 = most likely, 3 = least
> likely).
> « > > They had to give a different rank to each answer, so each question
> has
> « > one
> « > > answer ranked 1, one ranked 2, and one ranked 3. The set of three
> answers
> « > > is the same for each questions, and there were seven questions.
> « > >
> « > > I want to know whether participants give different ranks to different
> « > > answers, and whether that is affected by question. Here's my model:
> « > >
> « > > model1 <- clmm(rank ~ answer + answer:question +
> (1+answer|participant),
> « > > data = mydata)
> « > >
> « > > (I don’t have question as a fixed effect, because for each question
> « > > participants had to give a 1, 2 and 3 rank, so question alone does
> not
> « > > affect rank.)
> « > >
> « > > My first question is whether I’ve set up the model correctly, as I
> don’t
> « > > have any experience with ordinal regression. When I look at
> coef(model1),
> « > > all participants seem to have the same intercepts and coefficients
> for
> « > the
> « > > different answers, which is not what I thought should happen (I
> thought I
> « > > was setting up a model with random intercepts and random slopes).
> « > >
> « > > My second question is about changing the reference level of question
> and
> « > > answer. When I look at summary(model1), it uses answer a1 and
> question q1
> « > > as the reference levels, so I ran the model again using different
> answers
> « > > and questions as reference levels.
> « > >
> « > > When I run the model again using a different answer as the reference
> « > level,
> « > > the coefficients for the fixed effects are the same, but the random
> « > effects
> « > > and threshold coefficients are quite different.
> « > > When I run the model using a different question as the reference
> level,
> « > the
> « > > coefficients for the fixed effects are quite different, but the
> random
> « > > effects are exactly the same, and the threshold coefficients
> relatively
> « > > similar.
> « > >
> « > > Could someone please help me understand what’s going on here?
> « > >
> « > > Thanks in advance,
> « > > Jessie Barker
> « > >
> « > > [[alternative HTML version deleted]]
> « > >
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> « >
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> --
> Emmanuel CURIS
> emmanuel.curis at parisdescartes.fr
>
> Page WWW: http://emmanuel.curis.online.fr/index.html
>
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