For my thesis, I'm analyzing some mediation models. My dependent variable is a count variable, thus I used poisson regression. I want to calculate an effect size for the indirect effect (path a * path b) to compare my models for mothers and fathers. I can only find effect sizes for either an indirect effect or a poisson distribution. Which one should I use?
Hello Tessa,
Here are a some possible paths:
1. Estimate C at two fixed points on "A" (A = antecedent variable on the 'path a', C = DV on 'path b'), as outlined in this paper: https://stefanycoxe.weebly.com/uploads/2/4/3/7/24372766/coxe_asa_csp_020618.pdf
2. Compare log likelihood of model with the mediation vs. that of model without the mediation.
3. Compare reduction in AIC or BIC from intercept only model to final model for a model with the mediation (e.g., includes the indirect path) vs. one without, or from model without the indirect path to a model with the indirect path.
Good luck with your work.
Hi all,
if the X -> M effect is linear and the M -> Y part is the count part, then the indirect effect (product of both direct effects) should have the same interpretation as a direct effect in a poisson regression (the increase in the log(counts) of Y when X changes one unit mediated by M). The key as always is to get the standard errors of that effect which should work via boostrapping (as always).
Perhaps the work by Imai can help
Imai, K., Keele, L., Tingley, D., & Yamamoto, T. (2010). Causal mediation analysis using R. In D. V. Hrishikesh (Ed.), Advances in social science research using R (pp. 129-154). Springer.
Imai, K., Keele, L., & Tingley, D. (2010). A general approach to causal mediation analysis. Psychological Methods, 15(4), 309-334. http://imai.princeton.edu/research/files/BaronKenny.pdf
And of course, the more important question is about the causal identification of X and M via control variables and/or instruments...
HTH
Holger
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