Where should I place the citation in this sentence? I have the following sentence, where the citation refers to the first part of the sentence. Because of how it appears in the formatting of my paper, and how it reads, I would like to have the citation at the end of the sentence as below. Is this acceptable in APA style formatting?

However, location controls should control for variation common across regions, while my placebo test does not provide evidence that an unseen trend in weight gain is responsible for my results (Mincy &amp; De la Cruz Toledo, 2014).

The citation refers to a study which uses location controls, while the placebo test refers to something I did myself, but that I mention here to provide additional support to the plausibility of my results.
Even if it's not your personal preference, would it be OK by APA to have this reference at the end of the sentence?
I think the bigger problem is with your sentence structure.

However, location controls should control for variation common across
regions, while my placebo test does not provide evidence that an
unseen trend in weight gain is responsible for my results (Mincy &amp; De
la Cruz Toledo, 2014).

By starting the sentence with &quot;However&quot; a contrast is implied.  I'm assuming the contrast is against a (hopefully simple) point made in the prior sentence.
What really kills comprehension is the &quot;while&quot; in conjunction with the &quot;however&quot;.  &quot;While&quot; is &quot;coexisting in time&quot; and since we have two items in contrast, it is not clear if the commentary is referring to the placebo test or the contrasted item.  This uncertainty impacts the citation, making it equally ambiguous.
I'd just start with the subject, the placebo test:

The placebo test does not support that an unseen trend in weight gain is responsible for
the results.

With this simple idea as an independent sentence, it is easier to place the citation with it or not.  The citation will be fully clear if placed in this sentence, as it is only supporting one idea; not a portion of a compound idea containing a contrast where one of those items occur simultaneously with a third item.
Incredibly long sentences and complex grammar are superficially brilliant; true brilliance is making a complex idea simple.