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I am using the coarsened exact matching (CEM) package in R. I'm trying to understand the non-homogenous treatment effects.

I've attached what an image of the linear model looks like and the model with random effects. 1The package also use allows you to use the random forest option.Linear Model Random forest

But how does one interpret the output? The random forest and effects models look the same as the output for the linear model (different values). How do I know what the different treatment effects are for different values of the other variable? They also offer a way to plot the SATT, but I think that's for the linear model and I also am confused on how to interpret that.

The link to the guide is here: https://scholar.harvard.edu/files/gking/files/cem.pdf

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"Homogeneous treatment effect" refers to an assumption that the treatment effect is the same for all units, i.e., it does not depend on other factors. "Non-homogeneous treatment effect" allows that the treatment effect might differ across units. Certain methods of estimating the treatment effect are only compatible with a homogeneous treatment effect. If that assumption is incorrect, then the estimate will be biased. Other methods are compatible with either a homogeneous or non-homogeneous treatment effect and can be used in either scenario.

If the treatment effect is indeed homogeneous, then your estimate will be more precise if you use a method for homogeneous treatment effects. In general, though, this is a bad assumption to make, so you should generally use a method that is compatible with both homogenous or non-homogeneous treatment effects, such as the random forest or linear-RE methods. (That is, it's worse to assume a homogeneous treatment effect and be wrong than it is to assume a non-homogeneous treatment effect and be wrong.)

Even if the treatment effect is estimated as non-homogeneous, the att function estimates the average treatment effect, which is the average of the individual treatment effects (which are allowed to vary with the models compatible with non-homogeneous treatment effects). This is why the output looks the same regardless of which assumption you make: you are estimating the same single quantity but under one assumption or another.

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