Power analysis for multinomial logistic regression

Question

I am planning a regression analysis where a continuous independent variable predicts 3 categorical outcomes of a dependent variable. I believe this is done using multinomial logistic regression. Before I go ahead and collect my data I would like to get an idea of the sample size I will need to to have an adequately powered analysis. I have not been able to find much information about how to conduct a power analysis for a multinomial logistic regression.

My questions are as follows:

1. is a multinomial logistic regression the right statistic for this scenario?
2. if so, how to conduct a power analysis for multinomial regression?

Answer 1

1. Yes, you can use multinomial logistic regression to predict a categorical outcome with a continuous predictor.

2. Power analyses for multinomial logistic regression are complex, but possible. Here is a recent publication proposing a method for conducting a power analysis for multinomial logistic regression.

Pate, A., Riley, R. D., Collins, G. S., van Smeden, M., Van Calster, B., Ensor, J., & Martin, G. P. (2023). Minimum sample size for developing a multivariable prediction model using multinomial logistic regression. Statistical Methods in Medical Research, 32(3), 555–571. https://doi.org/10.1177/09622802231151220

Although the publication promises to provide the methodology via the R package pmsampsize, the authors have unfortunately not done so as of May, 2024. The authors do provide code with the manuscript, though, which could be modified to fit your scenario.