- is this a product that involves a lot of personal time to get started with and migrate away from? (example: cloud hosting for files and photos)? With this type of product, I'm going to spend more time on the initial 30 day evaluation, and if it suits my needs then I go right for the (multi)year contract. The personal investment is large (get all those photos uploaded, e.g.) so my chances of leaving after a few months are statistically unlikely.
- is this a product that I can walk away from with no real loss? (music streaming service) well this a service which quality can vary month over month, I'm more likely to use monthly pricing just so I can cancel at any time if I don't like it. I have no real investment to your brand, yeah it's nice but there's 100 others out there I can move too easily.
Usually with a multi-year discount, I'll buy the first year just to be sure and if I still like it after the first year, I'll buy multiple years. Just so I never have to worry about randomly missing a payment or somehow "losing" it (my login, my access, my files, etc.) but balance that against "how long will this company be around, really?" - it's a sense of security over time because I've invested a lot of personal time into the product. Walking away is not in my plans at the time.
Third reason that doesn't fit for you but is also a thought: is this a donation to (open source project)? Will I give them more money - less recurring middle-man processing fees - by paying one lump yearly sum instead of donating monthly? I use Liberapay for some FOSS donations and they tell you to do this straightaway, one lump sum is better for the receiver than monthlies.
Only if you can differentiate value meaningfully also. And I don't think it's a strong signal of anything.