I did some research and I’m coming to you with a few books that I found maybe the proper way to understand Causal Inference.

The first introductory book would be: “An Introduction to Statistical Learning”. It’s a companion to the MOOC from Stanford, which offers it on its ‘lagunita’ platform along with a free certificate:

An Introduction to Statistical Learning

Free book in PDF format

‘Statistical Learning’ MOOC on ‘lagunita’

Terran M’s Review on goodreads.com:

Adequate preparation for understanding “Principles and Practice of Structural Equation Modeling” would be a basic treatment of multivariate regression, such as Gelman and Hill. Introduction to Statistical Learning would also be sufficient. If you want to understand confirmatory factor analysis, you should probably already know something about factor analysis as well; I liked Gorsuch.

Data Analysis Using Regression and Multilevel/Hierarchical Models

by Andrew Gelman, Jennifer Hill

See on goodreads.com

A Mig’s review on goodreads.com

A go-to book for multilevel modeling but far from my favorite books on statistics. First, one should pass all the sections on probability distributions and linear regression, since there is much better elsewhere on the same topic (and with R codes), such as ‘An Introduction to Statistical Learning: With Applications in R’

Principles and Practice of Structural Equation Modeling, Fourth Edition

Terran M’s Review on goodreads.com:

This is the correct first book to read on causal inference. It covers structural equation modeling (SEM), confirmatory factor analysis (CFA), and Pearl’s structured causal modeling (SCM).
Although this book claims to cover various software packages, the treatment is cursory and the code examples (online) are mostly uncommented; don’t expect to learn how to use the software from this book. Read this book for the principles and then also read the software manual for whatever tool you’re going to use.
Ironically, this book, whose title claims to be about SEM only, actually covers most of the modern causal inference, whereas Pearl’s book, with the grand title “Causality”, covers only his narrow work. This is definitely the one you want.

For a brief introduction to using causal graphs to select your controls, see Chapter 17 of “Statistical Modeling — A Fresh Approach”. That chapter is available free from the author at http://www.mosaic-web.org/go/Statisti...

For more about inferring causal graphs from the data, look for a series of papers by Colombo and Maathuis at ETH Zurich. Here are a couple of papers:

https://projecteuclid.org/euclid.aos/...
https://projecteuclid.org/euclid.aos/...

These papers are also on ArXiv, and there are more from the same authors. Also, they wrote an R package:

https://cran.r-project.org/web/packag...

The Elements of Statistical Learning: Data Mining, Inference, and Prediction

https://web.stanford.edu/~hastie/ElemStatLearn/

The challenge of understanding vast amounts of data in a variety of fields such as medicine, biology, finance, and marketing has led to the development of new tools in the field of statistics and spawned new areas such as data mining, machine learning, and bioinformatics. Many of these tools have common underpinnings but are often expressed with different terminology. This book describes the important ideas in these areas in a common conceptual framework. While the approach is statistical, the emphasis is on concepts rather than mathematics. Many examples are given, with liberal use of color graphics. It should be a valuable resource for statisticians and anyone interested in data mining in science or industry. The book’s coverage is broad, from supervised learning (prediction) to unsupervised learning. The many topics include neural networks, support vector machines, classification trees and boosting — the first comprehensive treatment of this topic in any book. Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at Stanford University. They are prominent researchers in this area: Hastie and Tibshirani developed generalized additive models and wrote a popular book of that title. Hastie wrote much of the statistical modeling software in S-PLUS and invented principal curves and surfaces. Tibshirani proposed the Lasso and is co-author of the very successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, and projection pursuit.

Terran M’s Review on goodreads.com:

This is an excellent second or third book on statistical modeling after you have read something with code examples and done a few real projects. It is mathematically deeper and more comprehensive than An Introduction to Statistical Learning: With Applications in R and does more to tie together how and why algorithms work. It provides no code examples, and it is also correspondingly more demanding in the mathematical background of the reader. Even if you never read all of it, it’s worthwhile owning as a reference, and a PDF is even available for free from the author: https://web.stanford.edu/~hastie/ElemStatLearn/