The word "due" is a funny little thing. The etymology is that the Latin debere produced the Anglo-French dever which has the participle form deu. In effect, English borrows (or has stolen) this participle without regard to the rest of the French verb.*
This answer to an ELL question states that the construction "due to" is best understood as a compound preposition. I am not sure whether that is the case, and, even if it is, that doesn't directly address how best to understand the word "due" on its own.
Since it comes from a participle, it would be easy to assume that it remains a participle. However, we're all familiar with the phrase etymological fallacy. It might well have started its career in English as a defective verb with only a single participle form, but that wouldn't count as evidence that it remains so.
My question is simple: To what grammatical category or categories should I assign the word "due". I don't think I'm confused about the word's use or its semantics. I am only trying to determine whether there is a better way to regard this word's grammatical form and function in English than to simply retain a label that happens to make sense in reference to its origin.
My reason for asking is also simple. The phrase in question in the ELL posting is "compared to the DART model". Immediately following is "due to the imprecise modeling". My initial reaction was "aha, those are both participial phrases". I only checked the derivation of "due" after having that reaction and realizing that the base form of the verb seems to be missing.
I intend to post my own answer to this question so that the merits of each may be regarded separately. If my question seems incomplete, consider my attempted answer as a supplement.
* Some regard for the root exists. English also obtained the verb "to debit" from Latin, although I couldn't say whether the verb debere or the noun debitum deserves more credit. I mention this only because it does not matter. Whatever "due" is, it is not a synonym for the participle "debited".