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I'm trying to model an ordered probit model on my dataset with a (3-level) ordinal dependent variable. The independent variables are categorical and numeric.

I did some research and I've read about 3 assumptions: 1) the normal distribution of error terms 2) parallel odds assumption 3) no multicolinearity

which of those 3 are absolutely necessary to have a valid and reliable model? what do these assumptions implies? As far as I know 1) implies that normal distributed error terms assures us that the p-value of the coefficients are reliable. 2) the coefficients of the variables are the same across the levels (e.g. beta2 is the same for all the output levels) 3) variables are not correlated, we do not have 2 variables representing the same variability in the data. (I'm planning to model this in R with the polr function)

is this correct? Thanks in advance!

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