There is an issue on chapter 11, in the following paragraph (missing comma + it creates)
We can simplify this further, but let’s take a look at it like this because it gives us some nice intuition of what the propensity score is doing. The first term is estimating Y_1. It is taking all those that are treated and scaling them by the inverse probability of treatment. What this does is it makes those with very low probability of treatment have a high weight. This makes sense right? If someone has a low probability of treatment, that individual looks like the untreated. However, that same individual was treated. This must be interesting. We have a treated that looks like the untreated, so we will give that entity a high weight. What this does is create a population with the same size as the original, but where everyone is treated. By the same reasoning, the other term looks at the untreated and gives a high weight to those that look like the treated. This estimator is called the Inverse Probability of Treatment Weighting (IPTW), since it scales each unit by the probability of receiving some treatment other than the one it received.
It should be
We can simplify this further, but let’s take a look at it like this because it gives us some nice intuition of what the propensity score is doing. The first term is estimating Y_1. It is taking all those that are treated and scaling them by the inverse probability of treatment. What this does is it makes those with very low probability of treatment have a high weight. This makes sense, right? If someone has a low probability of treatment, that individual looks like the untreated. However, that same individual was treated. This must be interesting. We have a treated that looks like the untreated, so we will give that entity a high weight. What this does is it creates a population with the same size as the original, but where everyone is treated. By the same reasoning, the other term looks at the untreated and gives a high weight to those that look like the treated. This estimator is called the Inverse Probability of Treatment Weighting (IPTW), since it scales each unit by the probability of receiving some treatment other than the one it received.
matheusfacure
commented
2 years ago
There is an issue on chapter 11, in the following paragraph (missing comma +
it creates)We can simplify this further, but let’s take a look at it like this because it gives us some nice intuition of what the propensity score is doing. The first term is estimating Y_1. It is taking all those that are treated and scaling them by the inverse probability of treatment. What this does is it makes those with very low probability of treatment have a high weight. This makes sense right? If someone has a low probability of treatment, that individual looks like the untreated. However, that same individual was treated. This must be interesting. We have a treated that looks like the untreated, so we will give that entity a high weight. What this does is create a population with the same size as the original, but where everyone is treated. By the same reasoning, the other term looks at the untreated and gives a high weight to those that look like the treated. This estimator is called the Inverse Probability of Treatment Weighting (IPTW), since it scales each unit by the probability of receiving some treatment other than the one it received.
It should be
We can simplify this further, but let’s take a look at it like this because it gives us some nice intuition of what the propensity score is doing. The first term is estimating Y_1. It is taking all those that are treated and scaling them by the inverse probability of treatment. What this does is it makes those with very low probability of treatment have a high weight. This makes sense, right? If someone has a low probability of treatment, that individual looks like the untreated. However, that same individual was treated. This must be interesting. We have a treated that looks like the untreated, so we will give that entity a high weight. What this does is it creates a population with the same size as the original, but where everyone is treated. By the same reasoning, the other term looks at the untreated and gives a high weight to those that look like the treated. This estimator is called the Inverse Probability of Treatment Weighting (IPTW), since it scales each unit by the probability of receiving some treatment other than the one it received.