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I have a categorical dependent variable that involves four clusters of positions. In descriptive analysis, I noticed that first cluster covered about 5% of the participants, second 6%, third 60%, and fourth 29%. I have four continuous independent variables and I am thinking of using multinomial logistic regression.

Do you think that low percentages in the first two clusters would be a problem? Should I omit the first two and turn the model into a binary logistic regression model predicting the probability of belonging to either the third or fourth cluster?

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It's not so much the percentage of participants as the number that is important. The rule of thumb is that you want 10 people in the smallest class per independent variable. So, with 4 IVs, you want at least 40 people in cluster 1 and 40 in cluster 2.

Whether you should combine clusters is really a substantive matter. Does it make sense to combine them? Whether you should omit clusters is also a substantive issue: Do you want to distinguish between clusters 3 and 4? Would that be interesting?

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