Solved – ANOVA – when homogeneity of variance is violated

heteroscedasticitymixed model

My data was a repeated measurement (3-4 measuring times) with one fixed factor (4 doses) and nested (Please find an example below).

I would like to ran ANOVA but the assumption of homogeneity of variance was violated for some of the measuring times (e.g. Day1). Transformation of data did not fix the problem, what test could I use? Should I use Welch–Satterthwaite adjustment for F value, or use generalized mixed model or ran non-parametric test? I saw these three methods were use when Levene test is significant, or any other method would be better?

Thank you deeply for all the generous help!

ID   Location Dose  Day1    Day 3    Day 7
1     A       0.1    2.3     3.1      3.07
2     A       0.1    2.02    2.9      3.02
3     B       0.1    2.5     3.5      5.12
4     B       0.1    2.3     4.05     5.07
5     C       0.2    2.2     6.1      6.55
6     C       0.2    2.5     3.1      3.07
7     D       0.2    2.1     5.1      5.25
8     D       0.2    2.4     3.3      4.07

Best Answer

Since you assume is homogeneity is violated, data transformation is only alternative to minimize the variation in the data obtained. I have this kind of same problem like you, and I tried the Generalized Linear mixed model with dependent follow to poisson distribution. For your case, I think the dependent follow any distribution such exponential or else, just see the pattern. Good luck..

Here is the sample to analyze GLMM using R enter image description here

Related Solutions

Solved – Homogeneity of variance in regression

You don't "correct" your covariates; the heterogeneity is in the residuals.
If you're simply running Levene's test as a factorial ANOVA & finding heterogeneity for some of your explanatory variables, you probably have interactions with those variables that you're currently missing & need to add to your model.
Transformations of the response variable are a good place to start once you've accounted for possible omitted variables (such as interactions).

lmer Models – Testing for Homogeneity

Yes you could use for example Levene's test using the leveneTest() function from the car package. Here's an example with the Machines dataset from the nlme package:

library(lme4)
library(nlme); data(Machines)
library(car)

mod <- lmer(score ~ Machine + (1|Worker), data=Machines)

> leveneTest(residuals(mod) ~ Machines$Machine)

Levene's Test for Homogeneity of Variance (center = median)
      Df F value Pr(>F)
group  2  0.0811 0.9222
      51

Since the result is not significant, the assumption of equal variances (homoscedasticity) is met.

Also check ?leveneTest for more options.

Let's compare this with a boxplot of the residuals:

boxplot(residuals(mod) ~ Machines$Machine)

Since the reviewer seems to want a "formal test", it will probably be difficult to convince him accepting your visual inspection, despite, in my opinion, this would be the way to go. Maybe someone else has an actual reference why checking those assumptions visually is superior compared to "formal tests".

Edit to address comment by @D_Williams below:

A good and strongly cited paper by Zuur et al. 2010 may help to convince your reviewer regarding visual inspection of residuals to test for homogeneity of variances. Also here's is the link to the book Mixed Effects Models and Extensions in Ecology with R.

Best Answer

Related Solutions

Solved – Homogeneity of variance in regression

lmer Models – Testing for Homogeneity

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