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I'm an undergrad student completing my dissertation research proposal. I am trying to calculate a sample size for my multinomial logistic regression analysis. The criterion variable is degree type with 3 categories and the predictor variables are value type with 4 variables. I am also proposing to do a moderation analysis in introducing another covariate (Not sure if that will have an impact on the sample size). Any guidance or advice is appreciated :)

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There are two reasons I can think of to be working on a sample size: 1) Power and 2) Avoiding overfitting

For Power:

I don't know of a prepackaged program to do power analysis for multinomial logistic. However this page from the U. of Virginia (title is "simulating multinomial logistic regression data, in case of link rot) shows how to to this by simulation. Although it's somewhat involved, the page goes step by step.

Alternatively, you could try to adapt a program that does power analysis for binomial logistic regression, but the programs I have seen that do this are not very flexible.

For avoiding overfitting There are various "rules of thumb" but the one I have seen most often is that you need 10 observations per variable in the least common response level. So, you would need 50 observations of the least common degree.

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    $\begingroup$ You can also think of making $m$ large enough where $m$ is the lowest frequency predictor variable category for which you care to get class membership probability estimates. $m$ will need to be 96 or larger to get a margin of error of 0.1 or smaller in estimating a single Y category probability. To estimate all Y category probabilities jointly, minimizing the worst error in estimating any one of them, will require even larger sample sizes. $\endgroup$ Commented May 9 at 12:42

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