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Addendum on Lord’s Paradox

lord's paradox

causal inference

A couple of years ago, I wrote a post on Lord’s paradox in which I argued that introducing a causal model, as Judea Pearl does in his article on the subject (Pearl 2016)…

Notes on GLMs: Part 2

generalized linear models

statistics

Continuing where we left off in Chapter 3 of Wood (2017), we begin with a discussion of residuals in GLMs.

Notes on GLMs

generalized linear models

statistics

In this post and the following, I go through Chapter 3 of Simon Wood’s textbook Generalized Additive Models (2017), which covers GLMs (as a prerequisite for understanding…

Linear Regression

linear regression

statistical inference

I’m going back to the basics to discuss something that has confused me for a while about the “error term” in linear regression in the hopes that it might be helpful to…

Lord’s paradox is explained by regression to the mean, not a causal model

lord's paradox

causal inference

regression to the mean

Here’s the original formulation, appearing in a 1967 article published in Psychological Bulletins entitled “A Paradox in the Interpretation of Group Comparisons” (Lord 1967):

External Validity Part 5: Conclusion

causal inference

external validity

In these blog posts, following Erin Hartman’s chapter in Advances in Experimental Political Science titled “Generalizing Experimental Results,” I have investigated how one…

External Validity Part 4: Sensitivity Analysis

causal inference

external validity

Recall the following figure:

External Validity Part 3: Estimation

external validity

causal inference

This is the third in a series of blog posts for a causal inference project on external validity. To summarize the previous posts if you are just joining us, we are…

External Validity Part 2: Identification

causal inference

external validity

identification

In my previous blog post, I motivated the issue of external validity (or lack thereof) and introduced a formal framework for defining the target population average treatment…

Intro to External Validity: Sampling bias and causal inference

external validity

causal inference

What can you do when the sample you’ve collected doesn’t represent the population you’re interested in studying? When such a disconnect between sample and population of…

Pivoting a cdf

statistical inference

confidence intervals

The title of this post refers to a technique for constructing confidence sets for real-valued parameters that is extremely general. The generality of the techinque came as…

Randomization Inference Part 2: Attributable Effects

causal inference

randomization inference

In the last post, I presented a framework for performing causal inference in a matched-pair randomized experiment. The Wilcoxon signed rank statistic was introduced, and we…

Randomization Inference Part 1: The Wilcoxon Signed Rank Statistic

causal inference

randomization inference

Last semester, I made my way through the first half of Paul Rosenbaum’s textbook Design of Observational Studies (2010). Rosenbaum is a leading expert in causal inference…