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List:       r-sig-mixed-models
Subject:    [R-sig-ME] About computing covariances between two fixed effects with 4 and 5 levels respectively.
From:       Julian Gaviria Lopez <Julian.GaviriaLopez () unige ! ch>
Date:       2019-10-24 13:05:33
Message-ID: ee6e0316ec60433ea6f5bdca0df8320d () unige ! ch
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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:

> fit.us <- glmmTMB(Observations ~ us(CAP + 0 | Condition), data=sdf, ziformula=~1)

I obtain the following result:
> VarCorr(fit.us)
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@unige.ch

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