I am running monte carlo simulations to calculate power for a proposed study. I have 2 groups (treatment vs. control) and a count outcome (number of days of marijuana use). I used the example code for a poisson regression and found that when the mean and variance of u=1 and the mean of x is .5 and the variance of x is .25, and beta = .2, the power is .90 and coverage is .93. However, now I want to explain the meaning of this beta in terms of Cohen's d effect size. How is the beta and Cohen's d related, if at all? Grant reviewers prefer effect sizes, so I am trying to explain beta in terms of number of days difference between the two groups.
As far as I know, Cohen's d effect size has not been defined for count outcomes so you have to come up with your own understandable effect size measure. For instance, you can consider the difference in the estimated probability of zero counts (we describe how to do that in our RMA book) across the two groups. Or you can consider the difference in estimated expected count (the count mean).
Thank you for your recommendations. I will need to look up the way to look at the difference in estimated probability of zero counts in your book.
I also wanted to calculate power for another model. I will have 16 continuous variables that represent number of days of marijuana use over 16 months of pregnancy and postpartum. I think the curve will be quadratic and will be different in terms of both linear and quadratic terms between the intervention and control groups. You had said that 10 timepoints are the recommended maximum for growth models, so perhaps I need to switch over to using Dynamic Structural Equation Modeling. I have used the cross-classified analysis in an article that is in press, but I have not seen monte carlo input for it. Is there syntax for running power for a DSEM model with the specifications I described above?