[R-sig-ME] choice of reference category only changes coefficient with uncorrelated random intercept and slope

[Fox, John]

Dear David and Ben,

I haven't worked out the implications specifically, but even in a linear model fit by least-squares, with no constraints on the inter-coefficient correlations, the correlation between the coefficients is influenced by the choice of reference level for a factor. That suggests to me that constraining the correlation to zero would affect the coefficients.

As I said, this is far short of a proof, but the result seems intuitively plausible.

Best,
 John

--------------------------------------
John Fox, Professor Emeritus
McMaster University
Hamilton, Ontario, Canada
Web: socserv.mcmaster.ca/jfox



> -----Original Message-----
> From: R-sig-mixed-models [mailto:r-sig-mixed-models-bounces at r-
> project.org] On Behalf Of David Sidhu
> Sent: Friday, September 8, 2017 8:19 PM
> To: Ben Bolker <bbolker at gmail.com>
> Cc: r-sig-mixed-models at r-project.org
> Subject: Re: [R-sig-ME] choice of reference category only changes
> coefficient with uncorrelated random intercept and slope
> 
> Hi Ben
> 
> Thanks for the reply.
> Just to follow up, I tried running an lmer instead of a glmer and the
> same thing happens: when a random slope and intercept are uncorrelated,
> the choice of the reference category affects the absolutely value of
> that predictor’s coefficient.
> 
> Dave
> 
> ---
> David M. Sidhu, MSc<http://davidmsidhu.com/> PhD Candidate Department of
> Psychology University of Calgary
> 
> 
> 
> 
> 
> 
> On Sep 8, 2017, at 12:04 PM, Ben Bolker
> <bbolker at gmail.com<mailto:bbolker at gmail.com>> wrote:
> 
> Not sure, but ...
> 
> I think this is real. (If I were going to pursue it further I would
> probably try running some simulations.)  I think the asymmetry you're
> seeing is most likely related to the nonlinearity inherent in a GLMM; if
> that's true, then the effect should go away if you were using a LMM
> instead of a GLMM ...
> 
> 
> On Tue, Sep 5, 2017 at 7:45 PM, David Sidhu
> <dsidhu at ucalgary.ca<mailto:dsidhu at ucalgary.ca>> wrote:
> 
> Hi Everyone
> 
> I have noticed something strange...
> 
> I am running a glmer with a single dichotomous predictor (coded 1/0).
> The model also includes a random subject intercept, as well as a random
> item intercept and slope.
> 
> Changing which level of the predictor serves as the reference category
> doesn’t change the absolute value of the coefficient, EXCEPT when the
> random intercept and slope are uncorrelated.
> 
> This happens whether I keep the predictor as a numeric variable, or
> change the predictor into a factor and use the following code:
> 
> t1<-glmer(DV~IV+(1|PPT)+(0+dummy(IV, "1")|Item)+(1|Item), data = data,
> family = "binomial”)
> 
> Is this a genuine result? If so, can anyone explain why the uncorrelated
> random intercept and slope allow it to emerge? If not, how can I run a
> model that has an uncorrelated random intercept and slope that would
> prevent the choice of reference category from affecting the result?
> 
> Thank you very much!
> 
> Dave
> 
> ---
> David M. Sidhu, MSc<http://davidmsidhu.com/> PhD Candidate Department of
> Psychology University of Calgary
> 
> 
> 
> 
> 
> 
> 
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