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In short, I am working with a classification problem where I have conducted a logistic regression. The dependent variable is a binary variable with the five explanatory variables being ratios ranging from 0 to 1. This is done using the caret package utilizing the train()-function. Furthermore, I have used the margins package and the margins()-function in order to obtain the Average Marginal Effects. For example, for one of the explanatory variables the AME is -0.05 and significant.

How do I interpret this? Is it so that a 1 unit increase (which equals a 100% increase?) in the explanatory variable will yield a 5% lower probability for an outcome of Y = 1?

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  • $\begingroup$ Hi Jonas, I would suggest not using the margins package to interpret a logistic regression model, and instead interpret the logistic regression coefficients on the odds scale. $\endgroup$
    – JTH
    Dec 14 '20 at 16:44
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The average marginal effect of a continuous variable is the average of the marginal effects of that variable across units. A marginal effect is the instantaneous rate of change of the probability of the event corresponding to a small change in the predictor for an individual unit.

Imagine a race, with many runners running at different speeds toward the finish line. If you were to take a snapshot at a single time point, you could, for each runner, describe their speed at that single time point. This is the rate of change of the distance corresponding to a small change in the position of each runner. The average of all the runners' speeds would be the average speed. In this analogy, the individual runners' speeds correspond to the marginal effects, and the average of these speeds corresponds to the average marginal effect. You can think of the snapshot as your dataset with its observed values.

If we were to measure each runner's speed at the chosen time point in miles per hour (e.g., 12 miles per hour), that would not imply that if the runner were to run for an hour straight they would have a constant speed and run 12 miles. The race may only be 500 meters and last a few minutes. It would not make sense to say, "if the runner were to run for an hour, they would run 12 miles". The runner isn't running for an hour, and even if they did, their speed would likely change at various time points along the race. This is all to say that just because the rate is measured in miles per hour doesn't mean we have to interpret the speed at a single time point as occurring over the range of an hour. We can talk about a runner's instantaneous speed at a specific moment in time. The instantaneous speed doesn't tell us how far the runner would run in an hour or even how long it will take to finish the race because that runner's speed changes at various points along the race; it only describes the speed at a single moment.

Analogously, if the marginal effect for a unit in your sample was .07, that would not mean that going from 0 to 1 would yield a change in the probability of the event of .07. It means that the instantaneous rate of change of the probability of the event is .07 for the individual at the snapshot that is the data you collected on them. A rate of change of ".07 units in probability per unit change in the predictor" doesn't mean we have to (or even can) talk about changing the predictor a whole unit to interpret the rate. In the same way that we can talk about speed (in miles per hour) at a single time point, we can talk about a rate of change in probability per unit change in the predictor at a single value of that predictor. We don't have to "traverse" an entire unit of the predictor to interpret a marginal effect, in the same way a runner doesn't have to run for an hour to interpret an instantaneous speed in miles per hour, so you don't have to think about going from 0 to 1 to interpret an average marginal effect of -.05.

So how are you supposed to interpret the average marginal effect of -.05? There is no obviously intuitive way. It is the average of the marginal effects across units, each of which is the instantaneous rate of change in the probability of the event corresponding to a small increase in the value of the predictor. This is not really an easily interpretable value. It gives you a vague sense that on average, a decrease in the probability of the event accompanies increases in the predictor. It doesn't tell you what would happen if you were to increase each unit's value of the predictor by 1 (which wouldn't make sense anyway since it is a proportion). It's honestly not that much more interpretable than an odds ratio except that it's in probability units.

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    $\begingroup$ Thank you, kind sir. This was very helpful! $\endgroup$ Dec 14 '20 at 18:39

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