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I am trying to fit a mixed model (person as random effect) on data which has heteroscedasticity and non-normality. I log-transformed the Y-variable but it did not fix the problem. Normality and heterogeneity test and residuals plot with Y and log(Y) transformations are shown below. I will be grateful for any comments:

Shapiro-Wilk normality test

data:  resid
W = 0.4458, p-value < 2.2e-16


Bartlett test of homogeneity of variances

data:  resid and test$person
Bartlett's K-squared = 442.58, df = 8, p-value < 2.2e-16

Model Y not transformed: mod1

Model Y log transformed:enter image description here

EDIT

Here I add more information, I measure time of reaction (seconds) for 9 persons in differents variables (some dummys other continous), below show table of model, variance (residiual and intercept) and plot residuals for each person

> person = pdLogChol(1) 
            Variance   StdDev   
(Intercept) 0.03864167 0.1965749
Residual    3.64527198 1.9092595

I think that variance intercept its so low and residual variance so high, the person dont give variance in my results??. This is some results from my mixed model:

                         Value  Std.Error   DF   t-value p-value
    (Intercept)        0.5962784 0.12821014 2334  4.650789  0.0000
    dummy21           -0.8913013 0.24000557 2334 -3.713669  0.0002
    countback2        -0.0322950 0.00923287 2334 -3.497829  0.0005
    countspace2        0.8046936 0.18837571 2334  4.271748  0.0000
    action             0.0001028 0.00001484 2334  6.926781  0.0000
    pauseTime          0.0003853 0.00002582 2334 14.923275  0.0000
    Duration           0.0007586 0.00003112 2334 24.377110  0.0000
    Time2              0.0006724 0.00023442 2334  2.868323  0.0042 

Below I show residual normalised from model por each person

resid

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    $\begingroup$ Could you provide more context? Namely, what is your outcome variable, e.g., is it only positive, does it have bounds, is it perhaps discrete, and what is the model you’re fitting. $\endgroup$ – Dimitris Rizopoulos Apr 20 at 4:03
  • $\begingroup$ Why not use a nonlinear multilevel model? $\endgroup$ – Peter Flom Apr 20 at 10:34
  • $\begingroup$ Dimitris Rizopoulos, Thanks I add more information upper. $\endgroup$ – Rodrigo Apr 20 at 13:21
  • $\begingroup$ Thanks Peter Flom I will try to use nonlinear multilevel model $\endgroup$ – Rodrigo Apr 22 at 12:30
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You could attempt to do a robust linear mixed model using package robustlmm. https://cran.r-project.org/web/packages/robustlmm/index.html

Or you can try it in lme4 with glmer() based on the appropriate family and link. https://www.rdocumentation.org/packages/lme4/versions/1.1-21/topics/glmer

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  • $\begingroup$ Thanks Craig for your comment I am trying with glmer family(Gamma, link(log)). Do you know some book or link to fit this kind of models (assumptions, etc)... $\endgroup$ – Rodrigo Apr 25 at 21:07

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