[R-sig-ME] Model diagnostics show slope in residuals plot and slope on the observed vs fitted plot is different than y = x

[Carlos Familia]

Dear Thierry,

The image can be found here https://s4.postimg.org/lj5xf0rpp/Screen_Shot_2016_10_03_at_09_44_28.png <https://s4.postimg.org/lj5xf0rpp/Screen_Shot_2016_10_03_at_09_44_28.png>

Let me add another thing to the discussion, I was trying different models, and I tried the following

lmer( Y ~ X + (1 | C), data = df)

For which the residuals are distributed in a form I was expecting, however I am missing the part of the same individual being measured for different conditions, the plots can be found here, https://s25.postimg.org/oupckrapr/Screen_Shot_2016_10_03_at_09_49_20.png <https://s25.postimg.org/oupckrapr/Screen_Shot_2016_10_03_at_09_49_20.png> 

Thank you,
Carlos Família



> On 3 Oct 2016, at 09:40, Thierry Onkelinx <thierry.onkelinx at inbo.be> wrote:
> 
> Dear Carlos,
> 
> Can you show us a plot of the residuals versus W for each level of C? It looks like either the relation of Y and W is not linear, or you are missing an important covariate.
> 
> Best regards,
> 
> 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
> 
> 2016-10-03 10:34 GMT+02:00 Carlos Familia <carlosfamilia at gmail.com <mailto:carlosfamilia at gmail.com>>:
> Hello,
> 
> The image can be found here https://s18.postimg.org/rbx2vh2ex/Pasted_Graphic_4.png <https://s18.postimg.org/rbx2vh2ex/Pasted_Graphic_4.png>
> 
> Best regards,
> Carlos Família
> 
>> On 3 Oct 2016, at 08:50, Thierry Onkelinx <thierry.onkelinx at inbo.be <mailto:thierry.onkelinx at inbo.be>> wrote:
>> 
>> Dear Carlos,
>> 
>> Your plot got stripped from your mail. Try sending it as pdf or put it someone online and send us the URL.
>> 
>> Best regards,
>> 
>> 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
>> 
>> 2016-10-02 17:57 GMT+02:00 Carlos Familia <carlosfamilia at gmail.com <mailto:carlosfamilia at gmail.com>>:
>> Hello,
>> 
>> I have in hands a quite large and unbalanced dataset, for which a Y continuous dependent variable was measured in 3 different conditions (C) for about 3000 subjects (ID) (although, not all subjects have Y values for the 3 conditions). Additionally, there is continuous measure W which was measured for all subjects.
>> 
>> I am interested in testing the following:
>> 
>> - Is the effect of W significant overall
>> - Is the effect of W significant at each level of C
>> - Is the effect of C significant
>> 
>> In order to try to answer this, I have specified the following model with lmer:
>> 
>> lmer( Y ~ W * C + (1 | ID), data = df)
>> 
>> Which seems to proper reflect the structure of the data (I might be wrong here, any suggestions would be welcome).
>> However when running the diagnostic plots I noticed a slope in the residuals plot and a slope different than y = x for the observed vs fitted plot (as shown bellow). Which made me question the validity of the model for inference.
>> 
>> Could I still use this model for inference? Should I specify a different formula? Should I turn to lme and try to include different variances for each level of conditions (C)? Any ideas?
>> 
>> I would be really appreciated if anyone could help me with this.
>> 
>> Thanks in advance,
>> Carlos Família
>> 
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