"determining influence" is correct and usable in written English.
You can use it when you are referring to something that has a significant impact on a result or outcome. For example, "Social media has had a determining influence on the way we communicate today."
In contrast, determining influence is more tricky.
What his neighbors and friends felt and believed was always a powerful, and often a determining, influence on his judgment.
Unconscious psychic processes refer to feelings, desires, images, fantasies, etc., that occur outside of awareness and likely have a determining influence on our conscious mentation and behavior.
These examples illustrate the determining influence of photographs in shaping what catastrophes and crises we pay attention to, what we care about, and ultimately what evaluations are placed on these conflicts.
The appointment of his successor, which under the constitution lies with the president, and of that successor's confirmation, which belongs to the Senate, will have an unpredictable but determining influence on the politics of the next decade.
While acknowledging Coltrane as a determining influence on composer Steve Reich - who saw him play about 50 times - Ratliff tends to confine himself to jazz as a narrowly defined and increasingly atrophied musical form.
To be free is to be absolved from all determining influences – to be self-generating, self-dependent and absolutely self-responsible.
The number and strength of links among novels determine influence, much the way Google ranks Web sites.
VX: We are trying to determine influence.
Social IQ tracks Facebook, Twitter, LinkedIn, and MySpace to determine influence.
To determine influence, the interviewers stressed that all types of influence are considered financial, formal influence, communication, advice, or voice in determining the final influence level.
