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I'm writing a codebook that defines variables in a data set. Should the verb of the following sentence be singular or plural (refer/refers)? (Note that the italics appear in original; they are, obviously, the variable name.)
Other types of residential treatment facility refers to facilities not licensed as a psychiatric hospital, whose primary purpose is ...
This is a case where the way English handles the "use/mention distinction" is important. See, without the italics, quotes, or any other distinguishing marks, you could use the words directly just as you normally do and make a grammatical and almost semantically coherent sentence like this (verb bolded):
Other types of residential treatment facility refer to facilities not licensed as a psychiatric hospital, whose primary purpose is ...
The only problem with this would be that the types here do not in fact refer; they actually are.
So what you're really trying to do is say this (verb bolded, elided phrase in brackets):
[The label/codeword/phrase/term] "other types of residential treatment facility" refers to facilities not licensed as a psychiatric hospital, whose primary purpose is ...
Once you realize that there's implicitly a singular noun that introduces the mention of the phrase you italicized, but is elided in the actual sentence, it becomes much clearer how this sentence should be written (verb bolded):
Other types of residential treatment facility refers to facilities not licensed as a psychiatric hospital, whose primary purpose is ...
A phrase that you are mentioning, not using, is considered one phrase. It's singular. So you use singular conjugations with it. (This is a little clearer when using quotes, since that's a more common way to mention a phrase, but italics, bold, underlines, and even different font families have been used for the purpose as well, so there's nothing wrong with the sentence being written this way.)
Subject NOUN of the sentence is TYPES. "Of residential treatment facility" is a prepositional phrase that does not determine verb tense. REFER is the appropriate verb.
The head noun of the noun phrase Other types of residential treatment facility is types which is plural. Thus, it takes refer
