[R] Linear model vs Mixed model

[Cade, Brian]

Your lm() estimates are using the default contrasts of contr.treatment,
providing an intercept corresponding to your subject 308 and the other
subject* estimates are differences from subject 308 intercept.  You could
have specified this with contrasts as contr.sum and the estimates would be
more easily compared to the lmer() model estimates.  They are close but
will never be identical as the lmer() model estimates are based on assuming
a normal distribution with specified variance.  They rarely would be
identical.

Brian

Brian S. Cade, PhD

U. S. Geological Survey
Fort Collins Science Center
2150 Centre Ave., Bldg. C
Fort Collins, CO  80526-8818

email:  cadeb at usgs.gov <brian_cade at usgs.gov>
tel:  970 226-9326


On Tue, Jul 12, 2016 at 12:10 PM, Utkarsh Singhal <utkarsh.iit at gmail.com>
wrote:

> Hello Thierry,
>
> Thank you for your quick response. Sorry, but I am not sure if I follow
> what you said. I get the following outputs from the two models:
> > coef(lmer(Reaction ~ Days + (1| Subject), sleepstudy))
> Subject    (Intercept)     Days
> 308    292.1888 10.46729
> 309    173.5556 10.46729
> 310    188.2965 10.46729
> 330    255.8115 10.46729
> 331    261.6213 10.46729
> 332    259.6263 10.46729
> 333    267.9056 10.46729
> 334    248.4081 10.46729
> 335    206.1230 10.46729
> 337    323.5878 10.46729
> 349    230.2089 10.46729
> 350    265.5165 10.46729
> 351    243.5429 10.46729
> 352    287.7835 10.46729
> 369    258.4415 10.46729
> 370    245.0424 10.46729
> 371    248.1108 10.46729
> 372    269.5209 10.46729
>
> > coef(lm(Reaction ~ Days + Subject, sleepstudy))
> (Intercept)  295.03104
> Days          10.46729
> Subject309  -126.90085
> Subject310  -111.13256
> Subject330   -38.91241
> Subject331   -32.69778
> Subject332   -34.83176
> Subject333   -25.97552
> Subject334   -46.83178
> Subject335   -92.06379
> Subject337    33.58718
> Subject349   -66.29936
> Subject350   -28.53115
> Subject351   -52.03608
> Subject352    -4.71229
> Subject369   -36.09919
> Subject370   -50.43206
> Subject371   -47.14979
> Subject372   -24.24770
>
> Now, what I expected is the following:
>
>    - 'Intercept' of model-2 to match with Intercept of Subject-308 of
>    model-1
>    - 'Intercept+Subject309' of model-2 to match with Intercept of
>    Subject-309 of model-1
>    - and so on...
>
> What am I missing here?
>
> If it is difficult to explain this, can you alternately answer the
> following: "Is it possible to define the 'lm' and 'lmer' models above so
> they produce the same results (at least in terms of predictions)?"
>
> Thanks again.
>
> Utkarsh Singhal
> 91.96508.54333
>
>
> On 12 July 2016 at 19:15, Thierry Onkelinx <thierry.onkelinx at inbo.be>
> wrote:
>
> > The parametrisation is different.
> >
> > The intercept in model 1 is the effect of the "average" subject at days
> ==
> > 0.
> > The intercept in model 2 is the effect of the first subject at days == 0.
> >
> > ir. Thierry Onkelinx
> > Instituut voor natuur- en bosonderzoek / Research Institute for Nature
> and
> > Forest
> > team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
> > Kliniekstraat 25
> > 1070 Anderlecht
> > Belgium
> >
> > To call in the statistician after the experiment is done may be no more
> > than asking him to perform a post-mortem examination: he may be able to
> say
> > what the experiment died of. ~ Sir Ronald Aylmer Fisher
> > The plural of anecdote is not data. ~ Roger Brinner
> > The combination of some data and an aching desire for an answer does not
> > ensure that a reasonable answer can be extracted from a given body of
> data.
> > ~ John Tukey
> >
> > 2016-07-12 15:35 GMT+02:00 Utkarsh Singhal <utkarsh.iit at gmail.com>:
> >
> >> Hi experts,
> >>
> >> While the slope is coming out to be identical in the two methods below,
> >> the
> >> intercepts are not. As far as I understand, both are formulations are
> >> identical in the sense that these are asking for a slope corresponding
> to
> >> 'Days' and a separate intercept term for each Subject.
> >>
> >> # Model-1
> >> library(lmer)
> >> coef(lmer(Reaction ~ Days + (1| Subject), sleepstudy))
> >>
> >> # Model-2
> >> coef(lm(Reaction ~ Days + Subject, sleepstudy))
> >>
> >> Can somebody tell me the reason? Are the above formulations actually
> >> different or is it due to different optimization method used?
> >>
> >> Thank you.
> >>
> >> Utkarsh Singhal
> >> 91.96508.54333
> >>
> >>         [[alternative HTML version deleted]]
> >>
> >> ______________________________________________
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> >> and provide commented, minimal, self-contained, reproducible code.
> >>
> >
> >
>
>         [[alternative HTML version deleted]]
>
> ______________________________________________
> R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
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> PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

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