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I'm doing this, and it works. I know it has to have a name.

(background) I'm using a linear model (glm) and I get parameter estimates of various magnitude. My general formula is $ y = \alpha_1 \cdot x_1 ... + \alpha_n \cdot x_n + \epsilon $. Y is a binomial valued, and I am using logit-link.

(what I do) When I want to find parameters that, all else being equal, more strongly impact the variable of interest after fitting, I look at mean values of the measure, and multiply it by the parameter estimate. That is to say, the fit gives me the $\alpha_i$ values then I find the product $\alpha_i \cdot E\left(x_i\right)$ and use them to compare strength of $x_i$ on $y$.

What is the proper term for what I am doing?

I am tempted to use words like "importance", "leverage", "significance" or "impact" but those all have very narrowly defined meanings that might not necessarily apply here.

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You're trying to assess and compare the economic significance of the variable. I've seen more often the standard deviation used instead of the means.

The reason why the expectation might not be a good choice for what you're doing is this. Consider the expected value of the dependent variable: $$ E[y] = \alpha_1 E[ x_1] ... + \alpha_n E[ x_n]$$ As you can see your measure of strength can be interpreted as the contribution of the variable to the mean of the dependent variable.

This could be exactly what you're looking for in your particular situation, however, let's just change one of the variable, maybe introduce an offset: $\tilde x_1=x_1-C$, now we get: $$ E[y] = \alpha_1 E[ \tilde x_1] + \alpha_1 C ... + \alpha_n E[ x_n]$$ All of a sudden the contribution (strength) changed by simply changing the variable's starting point. Is this desirable? Again, it may be in your case, but in most cases it would not be a desired feature.

Also, often we're not very interested in the mean of dependent variable, but we're interested in its response to an input. If variable $x_1$ typically varies a lot, then $\alpha \sigma_{x_1}$ would indicate how much this variable contributes into the variation if $y$. Of course, this would ignore the covariances, so it's not a perfect measure either.

There is not standard way of measuring the strength of the variable or its economic significance. It depends on the application.

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