Stata: Data Analysis and Statistical Software

David said

"Unless the counts are high, count data can't be realistically modeled
as the outcome of a single underlying process consisting of a linear
functional plus a normally distributed error."

That was his advice about using -cmp-. He's the author and an expert.
If you want to go against his advice, that's your call, but in the
only example you have given, your counts have a maximum of 5.

Whether your count data can be treated as ordered probit is something
on which experts have different tastes and judgements. Counts that can
go 0,...,5 could be treated as graded variables 0 < 1 < 2 < 3 < 4 < 5.
I can't comment on the example you refer to, as I have not studied it.

On terminology: I wouldn't describe a counted variable as a
categorical variable, although counted variables do certainly appear
in categorical data analysis texts.

Nick

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