I am trying to model log reaction times (logRT) as a function of movement direction (categorical with two levels: 'right' and 'left') and reward (categorical with two levels: 'reward' and 'control'). As fixed effects, I enter direction and reward (with interaction term) into the model. As random effects, I have random intercepts and slopes by session number for the effects of both direction and reward. Additionally, given that the variance across levels of reward is clearly different, I allow the model to assume different variances for different levels of reward. Visual inspection of residuals plotted against predicted logRT as well as residuals plotted against predictors (see the figure below) reveals an obvious deviations from homoscedasticity.
var_reward
Masih -
I think what you really want to know is "how much" heteroscedasticity you have. A "test" that says you do or don't have it would be triggered by what effect level? and Impacted by sample size how? What would you do if you 'found' heteroscedasticity?
When you use a log transformation you complicate interpretation. And your model is more complex than what I want to show you. But what is below may give you some ideas:
In a regression, we can expect heteroscedasticity where variance increases with increased predicted-yi (the size measure). Modeling the heteroscedasticity in a weighted least squares regression can work very well. You might consider the following:
https://www.researchgate.net/publication/320853387_Essential_Heteroscedasticity, as bounded by Ken Brewer,
https://www.researchgate.net/publication/333642828_Estimating_the_Coefficient_of_Heteroscedasticity,
and
Knaub, J.R., Jr.(2021), "When Would Heteroscedasticity in Regression Occur?" Pak. J. Statist., Vol. 37(4), 315-367, https://www.pakjs.com/,
https://www.researchgate.net/publication/354854317_WHEN_WOULD_HETEROSCEDASTICITY_IN_REGRESSION_OCCUR
Best wishes - Jim
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