Solved – Interpretation of average marginal effects for categorical and continuous variables

marginal-modelstata

I'd like to make sure I'm interpreting average marginal effects for categorical and continuous variables correctly (interpretation of binary variables seems straightforward).

Using Stata, I ran a logistic regression to model a binary outcome as a function of Census region (1 = Northeast, 2 = Midwest, 3 = South, and 4 = West) and age category (values 1-5; modeled as a continuous variable). Northeast is the reference category for region.

logistic outcome i.region agecategory

Categorical variable – using this Stata code…
```
margins, dydx(region)
```

Stata provides an average marginal effect of 0.1 for South (region = 3) vs Northeast (region = 1). Does this mean that the difference between the predicted probability of the outcome is 0.1 percentage points when assuming everyone has a value of region = 3 vs region = 1 (holding age category at its observed value)?

Using this Stata code…
```
margins, dydx(agecategory)
```

Stata provides an average marginal effect is 0.5. Does this mean that the change in predicted probability of the outcome is 0.5 percentage points for all possible one-unit increments in agecategory: 2 vs 1, 3 vs 2, 4 vs 3, 5 vs 4?

Thanks.

Best Answer

Stata provides an average marginal effect of 0.1 for South (region = 3) vs Northeast (region = 1). Does this mean that the difference between the predicted probability of the outcome is 0.1 percentage points when assuming everyone has a value of region = 3 vs region = 1 (holding age category at its observed value)?

Yes. More precisely, it gives the average of each individual difference, since the effect varies with the age category.

Stata provides an average marginal effect is 0.5. Does this mean that the change in predicted probability of the outcome is 0.5 percentage points for all possible one-unit increments in agecategory: 2 vs 1, 3 vs 2, 4 vs 3, 5 vs 4?

No. The effect of the variable on the probability is not assumed to be linear in a logit. It will vary across observation with the value of the age category and of the other variable.

It calculates the average marginal effect, that is, the average change in the probability among all observation in the sample.

If you want to look at how this predicted effect changes at different values of the agecategory, you can use the at option of the margin command.

Related Solutions

Solved – overall effects of categorical variables

Given your comments I will assume that you do not want an estimate of the size of the effect but instead a statistical test whether the expected (possibly adjusted) count for each of the categories are the same. This may or may not be wise depending on your circumstances, but this is an example of how you do it in Stata:

webuse dollhill3
poisson deaths smokes i.agecat, exposure(pyears)
testparm i.agecat

If you want something like a single effect size you could look into sheaf coefficients. In case of interaction terms this generalizes to a model with parametrically weighted covariates. A brief discussion on how to do those in Stata can be found here.

Solved – The difference between average and marginal treatment effect

As some of the information you provided states, the two are not the same. I like better the terminology of conditional (on covariates) and unconditional (marginal) estimates. There is a very subtle language problem that clouds the issue greatly. Analysts who tend to love "population average effects" have a dangerous tendency to try to estimate such effects from a sample with no reference to any population distribution of subject characteristics. In this sense the estimates should not be called population average estimates but instead should be called sample average estimates. It is very important to note that sample average estimates have a low chance of being transportable to the population from which the sample came or in fact to any population. One reason for this is the somewhat arbitrary selection criteria for how subjects get into studies.

As an example, if one compared treatment A and treatment B in a binary logistic model adjusted for sex, one obtains a treatment effect that is specific to both males and females. If the sex variable is omitted from the model, a sample average odds ratio effect for treatment is obtained. This in effect is a comparison of some of the males on treatment A with some of the females on treatment B, due to non-collapsibility of the odds ratio. If one had a population with a different female:male frequency, this average treatment effect coming from a marginal odds ratio for treatment, will no longer apply.

So if one wants a quantity that pertains to individual subjects, full conditioning on covariates is required. And these conditional estimates are the ones that transport to populations, not the so-called "population average" estimates.

Another way to think about it: think of an ideal study for comparing treatment to no treatment. This would be a multi-period randomized crossover study. Then think about the next best study: a randomized trial on identical twins where one of the twins in each pair is randomly selected to get treatment A and the other is selected to get treatment B. Both of these ideal studies are mimicked by full conditioning, i.e., full covariate adjustment to get conditional and not marginal effects from the more usual parallel group randomized controlled trial.

Best Answer

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Solved – overall effects of categorical variables

Solved – The difference between average and marginal treatment effect

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