[R] Linear model vs Mixed model

Utkarsh Singhal
Tue, 12 Jul 2016 18:10:21 -0000

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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