I’m building a model to estimate whether a population of animals is in decline. I previously asked a question about how to test this.

Following on from that I was wondering whether the Probability of Direction is equivalent to taking the mean(coefficient<0) i.e. the probability that the coefficient is negative?

Essentially, I think yes. Although note that the probability of direction says it is bounded between .5 and 1 (or 50% and 100%) because it takes the most likely probability as its reference point. So if your mean(coefficient<0) was .25, I think the probability of direction would be ‘.75 that the parameter is positive’.