The analysis in "I" results from my personal deductions.
I - He is the same as the dog is.
Collins tells you that you can replace "the same as" by "just as", but "just" is a mere emphasizer, and so "as" is semantically very similar to "the same as". It follows that the sentence is very much like the one below.
Such constructions, as the following two references show, are idiomatic.
(ref.) Besides, if they are as the ones who came before . . of course they have Scrolls of their own!” “Does that mean they are . . . gods?”
(ref.) have taken the time to live with these people and understand why they are as they are and do as they do.
In the transformed sentence, and the ones given in reference "as" is evidently a conjunction. Since "the same as" fills in syntactically the place of "as" in the same way as "as", ie without changing appreciably the meaning, the grammatical nature of both must be the same. The question is what this nature is. In the following sentences, there is no doubt that "as" is a conjunction meaning "in the way in which", "the way". All these sentences answer to a how-question: "How is he?", "How do they do?",…, "How were the papers to be left?".
- They do as they do when the weather is warm.
- They did as he had done.
- Leave the papers as they are.
There is stumbling block in this analysis so far, that being so because if in those cases where the first verb is not the copula (to be) there is no problem in parsing the clause introduced by "as" as a subordinate, there is no such possibility when the verb is "to be": the subject complement of the copula cannot be a subordinate.
(Wikipedia) The predicative expression accompanying the copula, also known as the complement of the copula, may take any of several possible forms: it may be a noun or noun phrase, an adjective or adjective phrase, a prepositional phrase (as above) or another adverb or adverbial phrase expressing time or location.
There is only one alternative; the clause "as the dog is" is to be analysed (in similarity to the process that leads to nominal clauses taking on the functions of the noun phrases), as having an adjective vor an adverb value. In this case the conjunctive clause would be an "adverbo-adjectival conjunctive clause". It will function as an adjective if the context has it that "as the dog is" means being "lazy", "mean", "watchful", etc., or simply a dog (dog-like, he is dog-like.). It will function as an adverb if "as the dog is" means being "in the way of everybody, slowing down people's activity", for instance.
Calling "as" or "the same a" a preposition makes no sense. The object of a preposition is never the subject of a verb.
(Wikipedia) A preposition or postposition typically combines with a noun phrase, this being called its complement, or sometimes object. The phrase formed by a preposition or postposition together with its complement is called a prepositional phrase (or postpositional phrase, adpositional phrase, etc.) – such phrases usually play an adverbial role in a sentence.
It is therefore correct, according to the present analysis to call "the same as" a conjunctive locution, or to call "as" a conjunction.
II - He is the same as the dog.
An analysis as initiated in "I" leads to considering "the same as" as a preposition. "Same" cannot be an adjective, the traditional analysis in the absence of noun being qualified by "same" results in calling "same" a pronoun.
The necessary noun is also found in all the examples found in lexico
The following idiomatic sentences in which appear a phrase that is incontestably a a prepositional phrase show that it is not possible to consider the sentence in "II" to have a different structure since "as" is a preposition.
○ he is for independence" (support)
○ he is on the hill" (place)
○ he is past the obstacle (resultative)
○ he is as his brother, greedy (manner)
○ he is the same as his brother, greedy
III - He is (just) like the dog.
"Like" in the sentence can't be an adjective because it is followed by a determiner (the). As all adjectives, "like" has to be followed by a noun or a noun phrase not preceded by determiners (OALD, like [only before noun] (formal)). It is a preposition and "like the dog" is a prepositional phrase expressing a manner. Notice that in the same way as "as", the preposition "like" is used for expressing manner.
IV - He is similar to the dog.
In this sentence "to" can be considered to be a preposition, "the dog" its object, and the prepositional phrase "to the dog" is the complement of the adjective "similar". There seems to exist no alternative analysis consisting in considering that "similar to" should be a complex preposition: I found none.
- ahead of, exclusive of, outside of, … close to, according to, prliminary to, subsequent to, thanks to, …