The variance in my dependent variable changes with a changing value in an important independent variable and is hence probably distorting the measured effect of the treatment. Can I combat this form of heteroscedasticity by introducing an interaction term?
I'm analyzing the influence of the scoring procedure in online challenges on the predictability of the challenges. I measure predictability as the absolute difference between the rank percentile of a participant in a challenge and the overall rating percentile of a participant at that time. If a challenge is predictable that means that highly rated participants also rank highly (i.e. low difference between these two values).
Each observation (n = 1425) in my dataset is the participation of an individual in a challenge. Hence, I have partially crossed data as not all participants contribute in all of the challenges. Further, the data is divided into strata of comparable challenges that only differ significantly in the treatment variable (i.e. scoring procedure). Therefore, I fit a mixed effects model with random effects for the individual and the strata as well as an interaction between the random effects.
Based on the answers in the following thread, I have used a linear model, a model with a log-transformed dv and a beta regression in comparison, all yielding similar results: Regression with bounded non-normal dependent variable
I have observed that the variance of the dv changes with a change in the independent variable "rating" which I included as a control and which is a strong predictor of predictability. It seems that participants with a high rating are more consistent. See this plot:
Also, the precision model of the beta regression indicates that there is a lower variance in the dv with a rising value in rating.
So this is probably a cause of heteroscedasticity. To deal with this and to account for the fact that the effect of the treatment does not seem to be purely additive, but depending on the value of rating, I introduced an interaction term between rating and treatment. My question is: Is this a sensible approach or are there any arguments against introducing such an interaction term?
