[R-sig-ME] About computing covariances between two fixed effects with 4 and 5 levels respectively.

[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:

> 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 using unige.ch

	[[alternative HTML version deleted]]