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I am looking to conduct a power analysis for a multinomial logistic regression. Categorical outcome variable (3-response measures) and two continuous predictor variables (and an interaction of them both). I also have 7 covariates (gender, age, ethnicity, education, employment status, political orientation, household income). Can anyone advise me as to how I should run a power analysis? I have 151 participants (I'd imagine the study will be quite underpowered given the number of variables).

Any help appreciated! Thanks!

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  • $\begingroup$ You should probably run a simulation. $\endgroup$
    – Jeremy Miles
    Commented Feb 13, 2021 at 21:40
  • $\begingroup$ Thank you! How would I do this? $\endgroup$
    – Rionagh
    Commented Feb 28, 2021 at 12:47
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    $\begingroup$ It's not easy to describe, because it's a long process. Generate the data that matches your alternative hypothesis (including all variances and covariances (perhaps using mvrnorm from the MASS package in R), then analyse, and see if you get significant results. Then repeat (something like) 10,000 times. $\endgroup$
    – Jeremy Miles
    Commented Feb 28, 2021 at 22:18

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Pate et al. propose a method for conducting a power analysis for multinomial logistic regression in a recent publication:

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.

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