Negative values for Cohen's f^2

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Gang,

Hi. Thank you again for adding the -R2 option to 3dLMEr. I used it to calculate an effect size for my quantitative variable (auditory arousal threshold [AAT]) in my LME model. To refresh your memory, I measure AAT periodically during all-night functional MRI sleep studies and currently use the last four minutes of functional MRI data before each arousal. I would like your thoughts on a few things, and please give me a little latitude in this discussion.

Using the same mathematical steps outlined for this procedure when using SAS [1], I estimated Cohen's f^2 by subtracting the proportion of variance explained by R^2 in a reduced model without AAT from a full model with AAT. See below for my code.

Is the R^2 value produced by 3dLMEr ordinary or adjusted (i.e., adjusted for the number of fixed-effects coefficients)? From my previous request [2], I assume you used the r.squaredGLMM function in R's MuMIn package. From my reading of its documentation [3], I was able to deduce with relative confidence that it is ordinary. Is that your understanding? Either way, might you know why the majority of my obtained Cohen's f^2 values across all voxels in my maps would be negative? It is possible for the variance explained by a model to decrease when adding a variable to it, but this is rare.

The reason I am starting with ordinary versus adjusted R^2 as the possible cause is that my colleague and I, mostly my colleague Nils Yang, did a similar analysis on the same data with Matlab's fitlme function and experienced something similar. When using adjusted R^2, most Cohen's f^2 values were negative. When this was changed to ordinary R^2, most were positive as I would expect.

Sincerely,

Dante

REFERENCES:
[1] Selya, A. S., Rose, J. S., Dierker, L. C., Hedeker, D., & Mermelstein, R. J. (2012). A practical guide to calculating Cohen's f(2), a measure of local effect size, from PROC MIXED. Frontiers in Psychology, 3, 111. https://doi.org/10.3389/fpsyg.2012.00111

[2] https://discuss.afni.nimh.nih.gov/t/effect-size-for-3dlme

[3] https://cran.r-project.org/web/packages/MuMIn/MuMIn.pdf

CODE:

...
my_model=(
    "cond+AAT+cond:AAT+(AAT|Subj)"
    "cond+cond:AAT+(AAT|Subj)"
)
my_suffix=(
    ""
    _reduced
)
for (( h=0 ; h<${#my_model[@]} ; ++h )) ; do
    3dLMEr \
        -prefix output_lme_audaro_${region}${regsiz}_${prepro}_${statin}${my_suffix[h]}.nii \
        -jobs 32 \
        -model "${my_model[h]}" \
        -qVars 'AAT' \
        -R2 \
        -SS_type 3 \
        -gltCode AATeff 'AAT : ' \
        -dataTable \
        Subj    cond    AAT     InputFile \
...
    sb=(5 6)
    sb_reduced=(4 5)
    my_suffix=(fix fixplusran)
    for (( j=0 ; j<${#my_suffix[@]} ; ++j )) ; do
        3dcalc \
            -a ${my_olay[i]}"[${sb[j]}]" \
            -b $(echo ${my_olay[i]} | sed 's/\.nii//')_reduced.nii"[${sb_reduced[j]}]" \
            -expr "(a-b)/(1-a)" \
            -prefix ${my_prefix}_aatf2_${my_suffix[j]}.nii
...

Hi Dante,

Is the R^2 value produced by 3dLMEr ordinary or adjusted (i.e., adjusted for the number of fixed-effects coefficients)?

The R^2 values presented by 3dLMEr rely on the r.squaredGLMM function from R's MuMIn package, as per your suggestion. The 3dLMEr output includes two types of R^2 values: conditional and marginal. Do these align with the two categories (ordinary or adjusted) you're mentioning?

Gang Chen

Gang,

Hi again. Happy New Year. Thank you for your help and dedication.

No, it does not. With some help from Nils, I discovered that both marginal and conditional are ordinary R^2. Please let me think about this. I still very much do not understand why most of my Cohen's f^2 values are negative.

Sincerely,

Dante