[R-sig-ME] How to fix a gamma model with poor fit?

Wed Jul 14 01:18:05 CEST 2021

Dear all,

I am sorry for reposting here after posting on cross validated here
<https://stats.stackexchange.com/questions/534098/glmer-gamma-model-good-fit>
but I am still not sure what would be the best way of going about fixing
this model. It seems to have poor fit if you look at the plots as they have
extremes on both sides, which would not fit well with a gamma distribution.
Despite this, the results are consistent across packages (lme4, nlme...).

I have 209062 rows of data and this is response time data.
I want to determine whether there are differences between groups (Groups -
2 levels) on the learning of a task (Probability - 2 levels) across time
(within sessions - Block - 4 levels / across sessions - Session - 2
levels). It doesn't have zero response times, but some close to zero.

Do you have any suggestions for how one can improve a model like this or
whether I should just use another distribution that fits the data a bit
better?

Thank you!

Catia

Model:

    glmer(RT ~ Prob * Bl * Session * Gr + (1  | Participant), data=
Data.trimmed, family = Gamma(link =
"log"), control=glmerControl(optimizer="bobyqa"))
Model summary:

    Generalized linear mixed model fit by maximum likelihood (Adaptive
Gauss-Hermite Quadrature, nAGQ = 0) ['glmerMod']
     Family: Gamma  ( log )
    Formula: RT ~ Probability * Block * Session * Group + (1 | Participant)
       Data: Data.trimmed
    Control: glmerControl(optimizer = "bobyqa", optCtrl = list(maxfun =
1e+06))

         AIC      BIC   logLik deviance df.resid
     2456107  2456538 -1228012  2456023   209020

    Scaled residuals:
       Min     1Q Median     3Q    Max
    -4.297 -0.625 -0.158  0.440 35.691

    Random effects:
     Groups      Name        Variance Std.Dev.
     Participant (Intercept) 0.002203 0.04694
     Residual                0.053481 0.23126
    Number of obs: 209062, groups:  Participant, 130

    Fixed effects:
                                            Estimate Std. Error  t value
Pr(>|z|)
    (Intercept)                            6.024e+00  4.182e-03 1440.439  <
2e-16 ***
    Probability1                          -2.835e-02  7.041e-04  -40.265  <
2e-16 ***
    Block2-1                              -2.925e-02  2.077e-03  -14.084  <
2e-16 ***
    Block3-2                              -3.676e-03  2.131e-03   -1.725
0.084500 .
    Block4-3                               4.085e-03  2.307e-03    1.771
0.076577 .
    Block5-4                              -1.220e-02  2.380e-03   -5.125
2.98e-07 ***
    Session1                               4.795e-02  7.323e-04   65.478  <
2e-16 ***
    Group1                                -4.616e-02  4.182e-03  -11.037  <
2e-16 ***
    Probability1:Block2-1                 -7.228e-03  2.077e-03   -3.480
0.000501 ***
    Probability1:Block3-2                 -5.332e-03  2.131e-03   -2.503
0.012331 *
    Probability1:Block4-3                 -2.076e-02  2.307e-03   -8.999  <
2e-16 ***
    Probability1:Block5-4                  6.044e-03  2.380e-03    2.539
0.011104 *
    Probability1:Session1                  1.656e-03  7.046e-04    2.351
0.018743 *
    Block2-1:Session1                     -1.972e-02  2.077e-03   -9.494  <
2e-16 ***
    Block3-2:Session1                     -8.521e-03  2.131e-03   -3.999
6.35e-05 ***
    Block4-3:Session1                      4.380e-05  2.308e-03    0.019
0.984856
    Block5-4:Session1                     -3.768e-03  2.380e-03   -1.583
0.113389
    Probability1:Group1                    1.515e-03  7.041e-04    2.151
0.031478 *
    Block2-1:Group1                       -6.161e-03  2.077e-03   -2.966
0.003015 **
    Block3-2:Group1                       -1.129e-02  2.131e-03   -5.301
1.15e-07 ***
    Block4-3:Group1                        7.095e-03  2.307e-03    3.076
0.002101 **
    Block5-4:Group1                       -4.055e-03  2.380e-03   -1.704
0.088414 .
    Session1:Group1                        3.782e-03  7.323e-04    5.164
2.41e-07 ***
    Probability1:Block2-1:Session1         5.729e-05  2.077e-03    0.028
0.977997
    Probability1:Block3-2:Session1         3.543e-03  2.131e-03    1.663
0.096363 .
    Probability1:Block4-3:Session1        -6.877e-03  2.308e-03   -2.980
0.002886 **
    Probability1:Block5-4:Session1         4.329e-03  2.380e-03    1.819
0.068952 .
    Probability1:Block2-1:Group1          -1.238e-03  2.077e-03   -0.596
0.550980
    Probability1:Block3-2:Group1           1.022e-02  2.131e-03    4.795
1.63e-06 ***
    Probability1:Block4-3:Group1          -6.532e-03  2.307e-03   -2.831
0.004634 **
    Probability1:Block5-4:Group1           2.351e-03  2.380e-03    0.988
0.323373
    Probability1:Session1:Group1          -1.805e-03  7.046e-04   -2.562
0.010412 *
    Block2-1:Session1:Group1              -2.060e-04  2.077e-03   -0.099
0.920984
    Block3-2:Session1:Group1              -4.211e-03  2.131e-03   -1.977
0.048094 *
    Block4-3:Session1:Group1               3.339e-03  2.308e-03    1.447
0.147888
    Block5-4:Session1:Group1              -3.956e-03  2.380e-03   -1.662
0.096539 .
    Probability1:Block2-1:Session1:Group1 -1.270e-03  2.077e-03   -0.611
0.540933
    Probability1:Block3-2:Session1:Group1  1.678e-03  2.131e-03    0.788
0.430929
    Probability1:Block4-3:Session1:Group1 -4.640e-03  2.308e-03   -2.010
0.044392 *
    Probability1:Block5-4:Session1:Group1  4.714e-03  2.380e-03    1.980
0.047649 *
    ---
    Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

    Correlation matrix not shown by default, as p = 40 > 12.
    Use print(x, correlation=TRUE)  or
        vcov(x)        if you need it

Plots:

  [1]: https://i.stack.imgur.com/XPdtl.png
  [2]: https://i.stack.imgur.com/zUNRX.png
  [3]: https://i.stack.imgur.com/6slYG.png
  [4]: https://i.stack.imgur.com/LlRwT.png
  [5]: https://i.stack.imgur.com/TNYCP.png
  [6]: https://i.stack.imgur.com/45l0P.png

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