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malcolmbarrett committed Dec 23, 2024
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Expand Up @@ -441,7 +441,7 @@ For example, using a propensity score method can be more statistically efficient
Second, it can sometimes be challenging to get the estimate we are targeting with outcome models---an answer to a precise question---something we will probe more deeply in @sec-estimands.

Relatedly, outcome models give us *conditional* coefficients.
In other words, when describing the estimated coefficient, we often say something like "a one-unit change in the exposure results in a `coefficient` change in the outcome *holding all other variables in the model constant*. In causal inference, we are often interested in **marginal effects**. Mathematically, this means that we want to average the effect of interest across the distribution of factors in a particular population for which we are trying to estimate a causal effect. In the case where the outcome is continuous, the effect is linear, and there are no interactions between the exposure effect and other factors about the population, the distinction between a conditional and a marginal effect is largely semantic. The estimates will be identical.
In other words, when describing the estimated coefficient, we often say something like "a one-unit change in the exposure results in a `coefficient` change in the outcome *holding all other variables in the model constant*". In causal inference, we are often interested in **marginal effects**. Mathematically, this means that we want to average the effect of interest across the distribution of factors in a particular population for which we are trying to estimate a causal effect. In the case where the outcome is continuous, the effect is linear, and there are no interactions between the exposure effect and other factors about the population, the distinction between a conditional and a marginal effect is largely semantic. The estimates will be identical.

If there *is* an interaction in the model, that is, if the exposure has a different impact on the outcome depending on some other factor, we no longer have a single coefficient to interpret.
We may want to estimate a marginal effect, taking into account the distribution of that factor in the population of interest.
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