I have a data set comprising of real valued variables X (Range :-200
to 200 approximately) and ordered categorical response variables Y
[1,2,3,4 or 5].

I want to predict the probability of getting response Yi given an
input X.

My question concerns whether a probit or logit model is more
appropriate, i.e.  on what basis(es) I should make this decision.

If the log-likelihood is higher for one of the models does that imply
that it is better, or am I being too simplistic?

Do I need to look at the distribution of the independent variable X?

If I introduce another input variable X2, which causes the
log-likelihood to decrease, does this imply the single variable model
is a better predictor of Y?

Many thanks for your help, as you can probably tell I am not a
statistician!
.
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