You need something stable and firmly attached to your head, to 'pin your hat on'. In the case of the original hatpin, that was women's hair: the long pin was driven through the hat, then through the hair. More pins might also be used for greater stability.
In the figurative sense in your case, the thing the hat is pinned on is evidence [the hair] that supports analysis of or conclusions about factors contributing to comparative longevity [the hat].
Expectably, given your own failure to find information with Google, this idiom is not so common as I'd supposed from its immediate familiarity to me. Another instance of the same general meaning in use is this:
It protects me as a trial judge and it gives the courts of appeals something to pin their hat on when they write their decisions.
(From Inclusion Probabilities in Parentage Testing, American Association of Blood Banks, 1983.)
A third instance:
As an aside, the retroactive "fitting" of the model output to fit previous temps is what the AGW scientists pin their hats on when they exclaim, "the models are accurate."
(From "Are human influences on the climate really small?".)
Perhaps diluting the sense of the 'pin one's hat on' idiom, two very similar idioms are frequently confused with it. The sense of one or another or both of the similar idioms is sometimes intended when 'pin one's hat on' is used. Those idioms are
A. hang one's hat on something;
B. pin one's hopes on something.
Their meanings are, respectively,
A. hang your hat on something
1. to depend on something The company's earnings were up 70% last year, but I don't think you can hang your hat on that kind of growth.
2. to believe something It's hard to hang your hat on a lack of money as the real reason they didn't take the trip.
B. pin one's hopes on
Also, pin one's faith on. Put one's hope or trust in someone or something, as in She'd pinned her hopes on an early acceptance to the college but it didn't materialize. This term, dating from the 1500s, originated as pin one's faith on another's sleeve and may have alluded to the practice of soldiers wearing their leader's insignia on their sleeves. By the 1800s, however, it acquired its present form.
[From Cambridge Dictionary of American Idioms. S.v. "hang hat on." Retrieved February 16 2016 from http://idioms.thefreedictionary.com/hang+hat+on and The American Heritage Dictionary of Idioms by Christine Ammer. S.v. "pin one's hopes on." Retrieved February 16 2016 from http://idioms.thefreedictionary.com/pin+one%27s+hopes+on ]