Abstract

In causal inference, we are usually interested in estimating the causal effect of a treatment (e.g., a drug) on an outcome of interest (a disease, firm revenue, customer satisfaction, etc.). However, knowing that a treatment works on average is often not sufficient and we would like to know for which subjects (patients, users, customers, etc.) it works better or worse, i.e., we would like to estimate heterogeneous treatment effects. We will explore the estimation of heterogeneous treatment effects using a modified version of regression trees and forests, which is causal tree and causal forest. From a machine-learning perspective, there are two main differences between causal trees and predictive trees. First of all, the target is the treatment effect, which is an inherently unobservable object. Second, we are interested in doing inference, which means quantifying the uncertainty of our estimates (conditional average treatment effect and its standard error).

In this thesis we have made extension in the concept of a causal tree forest by suggesting a strategy for predicting the outcomes of various treatment kinds by merging the best causal trees. The approach that is suggested involves choosing a subset of the most precise causal trees from a sufficiently large pool based on their estimates of error outside the sample. The selected trees are ensemble, called optimal causal tree ensemble (OCTE). This method has been assessed on simulated data and then applied on real data set, income function, for Pakistan. Data has been taken from Labor Force Survey (LFS),workers aged 10 and up is used as an example dataset. which includes 27964 observations in total. The analysis provides a comprehensive simulation investigation, with data sets generated using 5 distinct layouts. Mean square error (MSE), root mean square error (RMSE), i mean absolute deviation (MAD), and Pearson correlation (r) are used to evaluate the proposed method in comparison to ordinary least square (OLS), least absolute shrinkage and selection operator (LASSO), Ridge, Causal Tree, and the regular decision trees forest. The results demonstrate that the suggested approach (OCTE) outperforms other methods in terms of prediction accuracy and is valuable for predicting heterogeneous treatment effects. Furthermore, this thesis proposes a novel approach to obtaining a superior set of trees by integrating the random projection method with optimal causal tree selection. We accomplished this by randomly projecting the training data into lower-dimensional spaces. Bootstrap samples, in turn utilized to construct causal trees, are obtained by utilizing the new datasets. The best trees are selected using out-of-bag (OOB) error, and then they are combined to form the optimal random projection causal tree ensemble. The acronym ORPCTE stands for “optimal random projection causal tree ensemble,” which describes this technique perfectly. Five distinct forms of synthetic data have been used to validate this methodology. Mean square error (MSE), root mean square error (RMSE), mean absolute deviation (MAD), and Pearson correlation (r) are used as performance metrics to compare ORPCTE’s results with those of ordinary least squares (OLS), least absolute shrinkage and selection operator (LASSO), Ridge, Causal Tree (CT), and Causal Forest (CF). In the majority of cases, the analyses revealed that the proposed method ORPCTE outperformed other state-of-the-art approaches