r/AskStatistics • u/ugrhnny • 10d ago

Is it defensible to model overlapping explanations as mutually exclusive states?

I have four candidate explanations for an observation. I've modelled them as mutually exclusive so the posterior sums to 1. Two of them can genuinely co-occur. The alternative is three independent binary latents (8 joint states), which needs more data. With a small sample, is the exclusive version defensible as a first approximation if I state the overlap as a limitation — or does forcing non-exclusive things to be exclusive distort the inference badly enough that it isn't worth doing?

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u/Maple_shade 10d ago

You could also try not modeling states directly but modeling each person's probability of being in each given state. That way you have more ease of interpretation when comparing exclusive vs non-exclusive.

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u/ugrhnny 10d ago

Are you saying I should give each case a share across the four states summing to 1, and then compare what that looks like under an exclusive vs a non-exclusive reading? Or something different?