A unified and user-friendly framework for applying the principal sufficient dimension reduction methods for both linear and nonlinear cases. The package has an extendable power by varying loss functions for the support vector machine, even for an user-defined arbitrary function, unless those are convex and differentiable everywhere over the support (Li et al. (2011) <doi:10.1214/11-AOS932>). Also, it provides a real-time sufficient dimension reduction update procedure using the principal least squares support vector machine (Artemiou et al. (2021) <doi:10.1016/j.patcog.2020.107768>).

Provides propensity score weighting methods to control for confounding in causal inference with dichotomous treatments and continuous/binary outcomes. It includes the following functional modules: (1) visualization of the propensity score distribution in both treatment groups with mirror histogram, (2) covariate balance diagnosis, (3) propensity score model specification test, (4) weighted estimation of treatment effect, and (5) augmented estimation of treatment effect with outcome regression. The weighting methods include the inverse probability weight (IPW) for estimating the average treatment effect (ATE), the IPW for average treatment effect of the treated (ATT), the IPW for the average treatment effect of the controls (ATC), the matching weight (MW), the overlap weight (OVERLAP), and the trapezoidal weight (TRAPEZOIDAL). Sandwich variance estimation is provided to adjust for the sampling variability of the estimated propensity score. These methods are discussed by Hirano et al (2003) <DOI:10.1111/1468-0262.00442>, Lunceford and Davidian (2004) <DOI:10.1002/sim.1903>, Li and Greene (2013) <DOI:10.1515/ijb-2012-0030>, and Li et al (2016) <DOI:10.1080/01621459.2016.1260466>.

Supports propensity score weighting analysis of observational studies and randomized trials. Enables the estimation and inference of average causal effects with binary and multiple treatments using overlap weights (ATO), inverse probability of treatment weights (ATE), average treatment effect among the treated weights (ATT), matching weights (ATM) and entropy weights (ATEN), with and without propensity score trimming. These weights are members of the family of balancing weights introduced in Li, Morgan and Zaslavsky (2018) <doi:10.1080/01621459.2016.1260466> and Li and Li (2019) <doi:10.1214/19-AOAS1282>.