How do you change the culture of your company so that product marketers have more of a voice to influence the product roadmap?

It's hard to answer this in the abstract (w/o knowing more about your current culture), but these two cultural components have been critical to the influence creds PMM has earned at Ironclad: (1) empathy and (2) (a derivative thereof) "win as one" mindset. 

Empathy means the ability to see things from your counterparty's point of view. "Win as one" culture is something we really care about at Ironclad, and it basically means committing to driving the best results for the company. It means always looking for the highest common ground instead of devolving to the lowest common denominator. It's the opposite of factionalism (e.g., my team's needs versus your team's needs).

This "win as one" mindset is really important for product marketing because we are the connective tissue b/w so many teams. When the company is trying to "win as one," PMM can be a powerful company linchpin, greasing the GTM engine for all the teams we connect. Rather than making your goal "influencing the roadmap," you can focus on the higher order goal of making the product successful by your agreed-upon metric. (See above answer.) This makes us better partners to each other, which ultimately helps us achieve our goals. 

On the flip side, without "win as one," PMM can easily end up in a state of perpetual reactivity, serving this or that team, unable to be proactive/strategic. 

How do you change your culture to be more empathetic, to actually win as one? I believe product marketing has to exemplify both empathy and "win as one," earning trust and credibility the hard way, i.e. the right way. Set an intention is to drive the right result for the company, versus to merely influence the roadmap, and prove out that intention with excellent results. 

First, changing a culture is hard. You can do your best by setting an example, being curious, solving hard problems and helping your peers grow the business. Second, you do not have a product without adoption. PMMs usually own or share the adoption goals with product management. PMM is in a unique position to capture and unify qualitative and quantitative data to increase adoption and usage. This process never ends and should be injected in every step of the product life cycle not just the start.

We have established a process whereby we partner closely with engineering to condut both qualitative and quantiative market research on areas where we believe there may be an opportunity for growth/or closure of gaps. Partnering closely allows us to leverage the results to both influnce the roadmap as well as our outbound marketing messaging. 

The hard way - you earn it. 

First, I should clarify that when I think about influencing roadmap, I'm not thinking about it as "getting a feature I think is important onto the roadmap" - if that's the approach you're putting yourself in the same category as every other person who lobs requests at a product manager and they'll see it as just more clamouring for more, more, more.

When I think about influencing the roadmap, I think about building a real partnership with product. Understanding the tradeoffs they're trying to make, the limitations they're facing. What are the factors that go into their decision making and then what information does my PMM team have to add to that conversation.

This starts with listening. Ask to join a planning meeting (or two or more) as a silent observer. Listen to how they're making decisions and note what factors are going into their decision making. After the meeting, follow up with some of the product leaders and offer to help. Over time, ask for a role in planning where you/your team can present information / input into that planning session. Over more time, you'll notice you get questions proactively from product and they'll seek your team's advice, over more time you'll be an integral part of that planning process with an assigned role to play.