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About computing covariances between two fixed effects with 4 and 5 levels respectively.

3 messages · Julian Gaviria Lopez, Thierry Onkelinx

Original
Julian Gaviria Lopez
# 
Hello,


I want to assess the correlation of 4 kinds of brain activation patterns (CAP: c1, c2, c3, c4) from 20 subjects, across 5 different conditions (Condition: base,  neu, pneu, aff, paff). In total, the count data contains 380 observations, and has the next structure:


     ID       Observations         CAP          Condition

     1                  6                       c1              base

    ...                 ...                      ...                 ...

    20                 0                       c1              base

    ...                 ...                       ...                 ...

     1                  3                       c4              base

    ...                 ...                       ...                 ...

   20                  0                       c4             base

    1                   4                       c1              neu

    ...                 ...                       ...                ...

   20                  2                       c1              neu

    ...                 ...                       ...                ...

    1                   0                       c4              neu

    ...                 ...                       ...                ...

   20                  5                       c4              neu

    ...                 ...                       ...                ...

   20                  0                       c4              paff


I am trying to compute the covariance structures proposed by Kasper Kristensen:

https://cran.r-project.org/web/packages/glmmTMB/vignettes/covstruct.html


When I compute the unstructured covariance:
I obtain the following result:
Conditional model:
 Groups    Name     Std.Dev. Corr
Condition  c1         0.86527
                    c2         0.34487   0.116
                    c3         0.16450  -0.951  0.164
                    c4         0.36269   0.414 -0.719 -0.545
 Residual           1.98011


As you might appreciate, the results are either wrong or uncompleted, since the right output would yield a 5x4 cov matrix, expressing the correlation of the CAPs (c1, c2, c3, c4) across all the conditions (base, neu, pneu, aff, paff). One rapid solution is to compute the cov matrix per condition. However, apart of  being penalized by model deficiency (I guess),  the problem is still present, since the question to answer is how the brain activation patterns (CAP) are correlated across all conditions (e.g. correlation between "CAP c1 - Condition aff",  and "CAP c4 - Condition paff").

Thanks in advance for any comment on this regard.

Best,

Julian Gaviria
Neurology and Imaging of cognition lab (Labnic)
University of Geneva. Campus Biotech.
9 Chemin des Mines, 1202 Geneva, CH
Tel: +41 22 379 0380
Email: Julian.GaviriaLopez at unige.ch
Thierry Onkelinx
# 
Dear Julian,

The described covariance structures relate to a _random_ effect. You are
looking for _fixed_ effect covariances.

You are probably looking for a model like glmmTMB(Observations ~ CAP *
Condition + (1|ID), data=sdf, ziformula=~1)

I'd also recommend to contact a local statistician about your problem.

Best regards,

ir. Thierry Onkelinx
Statisticus / Statistician

Vlaamse Overheid / Government of Flanders
INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE AND
FOREST
Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
thierry.onkelinx at inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

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than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
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ensure that a reasonable answer can be extracted from a given body of data.
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Op do 24 okt. 2019 om 15:05 schreef Julian Gaviria Lopez <
Julian.GaviriaLopez at unige.ch>:

  
  


  


      

    

    
3 days later

    

      
      

        


  

        

      Julian Gaviria Lopez
    

    

      
      #
    

  


  

      
Dear Thierry,


Thank you so much for your comment. In fact, it was the first step of the analysis:

Mol<- glmmTMB(Observations ~ CAP * Condition  + (1|ID), data=mDATA, ziformula=~ 1, family=nbinom1)

I aimed to investigate  the differences between the CAPs (CAP: c1, c2, c3, c4), across 5 conditions (Condition: base, neu, pneu, aff, paff). For this purpose, implemented the Anova function (glmmTMB), and the emmeans package for assessing the interactions.

Another question to answer is how related (i.e., Pearson coefficients for normally distributed and independent data)  are those CAPs to each other,  across conditions (Condition: neu, pneu, aff, paff), being from the same individuals (N=20).  In the previous email, you were right when pointing my confusion between fixed  and random effects.  So, I went on solving my problem, and I found two alternative solutions:

1)   Taking the previous model:
Mol<- glmmTMB(Observations ~ CAP * Condition  + (1|ID), data=mDATA, ziformula=~ 1, family=nbinom1)

We can compute the corr/cov

(vcov(Mol)$cond)

I assume that the output covariance structure is autoregresive (AR1).(Question aside: Is there any way to change the structure when using his function?)

2) Following the previously cited vignette:
https://cran.r-project.org/web/packages/glmmTMB/vignettes/covstruct.html

I found the following alternative:
fit.us <- glmmTMB(Observations ~ us(CAP * Condition +  0 | group), data=mDATA)

Where the"group "variable" is just a 1 in every row of the data, and "us" corresponds to the"heterogeneous unstructured" covariance structure.

Regardless of the method, I obtain a correlation values (-1 to 1), of the covariances of the random effect (ID). Therefore, my questions to solve are:
1) Would it be right to interpret the output "correlation" values as the evaluation of the relationship between the factors "CAP" and "Condition" (fixed effects), based on the number of counts  reported in "Observations" (random effect)?

2) I do not manage to obtain the cov/corr values from the intercept. For instance, if the intercept values corresponds to"CAP:c1, Condition: base" how can I obtain the corr/cov values corresponding to the regressors from itself? e.g.:

CAP:c1, Condition: base" - CAP:c1, Condition: neu"
CAP:c1, Condition: base" - CAP:c1, Condition: pneu"
CAP:c1, Condition: base" - CAP:c1, Condition: aff"
CAP:c1, Condition: base" - CAP:c1, Condition: paff"

Thank you so much in advance for any comment.



Julian Gaviria
Neurology and Imaging of cognition lab (Labnic)
University of Geneva. Campus Biotech.
9 Chemin des Mines, 1202 Geneva, CH
Tel: +41 22 379 0380
Email: Julian.GaviriaLopez at unige.ch