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I am trying to estimate an ordered probit model, where the data in question comes from two separate counties. I was thinking that I should use fixed effects to account for unobserved heterogeneity across the counties, but apparently a fixed effects ordered probit model is not possible to estimate. I read somewhere else that you can approximate the fixed effects model by estimating a random effects model AND including a dummy for the variable in question.

Am I on the right path with my thinking here? Is it possible to estimate a random effects ordered probit model with 2 different outcomes for the random variable? Or am I ok to estimate a regular ordered probit model and simply include an indicator variable for "county"?

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