How To Obtain The Propensity Score Weights From Gradient Boosted Model In R

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Introduction

In the field of statistics and machine learning, propensity score weighting is a widely used technique for reducing bias in observational studies. The propensity score is the probability of a unit being assigned to a particular treatment given a set of observed covariates. In this article, we will discuss how to obtain the propensity score weights from a gradient boosted model in R.

What are Propensity Scores?

Propensity scores are a key concept in causal inference and are used to estimate the effect of a treatment on an outcome. The propensity score is defined as the probability of a unit being assigned to a particular treatment given a set of observed covariates. In other words, it is the probability of a unit being in the treatment group given the observed characteristics of the unit.

What is a Gradient Boosted Model?

A gradient boosted model is a type of machine learning algorithm that combines multiple weak models to create a strong predictive model. Gradient boosting is an ensemble learning technique that combines multiple weak models to create a strong predictive model. It is a popular algorithm for classification and regression tasks.

Multinomial Regression with Gradient Boosting

In this article, we will focus on multinomial regression with gradient boosting. Multinomial regression is a type of regression analysis that is used to model the probability of a categorical response variable. In this case, we will use a multinomial regression model with a gradient boosted algorithm to estimate the propensity scores.

Obtaining Propensity Score Weights from Gradient Boosted Model

To obtain the propensity score weights from a gradient boosted model in R, we can use the following steps:

Step 1: Load the necessary libraries

library(gbm)
library(dplyr)
library(purrr)

Step 2: Load the data

data <- read.csv("data.csv")

Step 3: Create a gradient boosted model

gbm_model <- gbm(class ~ ., data = data, distribution = "multinomial", n.trees = 1000, 
                interaction.depth = 3, shrinkage = 0.1, n.minobsinnode = 10, 
                verbose = FALSE)

Step 4: Extract the propensity scores from the model

propensity_scores <- predict(gbm_model, type = "probability")

Step 5: Calculate the propensity score weights

propensity_weights <- propensity_scores[, 1] / sum(propensity_scores[, 1])

Step 6: Apply the propensity score weights to the data

weighted_data <- data %>% 
  mutate(weight = propensity_weights[match(class, levels(class))])

Example Use Case

Let's consider an example use case where we want to estimate the effect of a treatment on an outcome. We have a dataset with the following variables:

  • class: a categorical response variable with four levels (A, B, C, D)
  • age: a continuous covariate
  • sex: a categorical covariate with two levels (male, female)
  • treatment: a binary treatment variable

can use the gradient boosted model to estimate the propensity scores and then apply the propensity score weights to the data.

Conclusion

In this article, we discussed how to obtain the propensity score weights from a gradient boosted model in R. We used a multinomial regression model with a gradient boosted algorithm to estimate the propensity scores and then applied the propensity score weights to the data. This technique can be used to reduce bias in observational studies and estimate the effect of a treatment on an outcome.

Code

The code used in this article is available on GitHub.

References

  • Friedman, J. (2001). Greedy function approximation: A gradient boosting machine. Annals of Statistics, 29(5), 1189-1232.
  • Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning: Data mining, inference, and prediction. Springer.
  • Hill, J. L. (2011). Bayesian nonparametric modeling for causal inference. Journal of the American Statistical Association, 106(494), 633-644.

Future Work

In future work, we plan to explore the use of gradient boosted models for other types of propensity score weighting, such as inverse probability weighting and doubly robust estimation. We also plan to investigate the use of gradient boosted models for other types of causal inference, such as instrumental variables and mediation analysis.