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
EDIT
I measure time of reaction (seconds) for 9 people in differents variables (some dummy variables, others are continuous). Below I show the model table, variance (residual and intercept), and plot the residuals for each person.
> person = pdLogChol(1)
Variance StdDev
(Intercept) 0.03864167 0.1965749
Residual 3.64527198 1.9092595
I think that the variance intercept is low and the residual variance is high. So person
doesn't add 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 for each person: