Model diagnostics show slope in residuals plot and slope on the observed vs fitted plot is different than y = x

Dear Thierry,

The image can be found here 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

Thank you,
Carlos Fam?lia



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>:

Hello,

The image can be found here https://s18.postimg.org/r
bx2vh2ex/Pasted_Graphic_4.png

Best regards,
Carlos Fam?lia

On 3 Oct 2016, at 08:50, Thierry Onkelinx <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>:

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 Fam?lia