Causal Analysis in Theory and Practice

David Kenny’s website <http://davidakenny.net/cm/mediate.htm> has recently been revised to include a section on the Causal Inference Approach to Mediation. As many readers know, Kenny has pioneered mediation analysis in the social sciences through his seminal papers with Judd (1981) and Baron(1986) and has been an active leader in this field. His original approach, often referred to as the “Baron and Kenny (BK) approach,” is grounded in conservative Structural Equation Modeling (SEM) analysis, in which causal relationships are asserted with extreme caution and the boundaries between statistical and causal notions vary appreciably among researchers.

It is very significant therefore that Kenny has decided to introduce causal mediation analysis to the community of SEM researchers which, until very recently, felt alienated from recent advances in causal mediation analysis, primarily due to the counterfactual vocabulary in which it was developed and introduced. With Kenny’s kind permission, I am posting his description below, because it is one of the few attempts to explain causal inference in the language of traditional SEM mediation analysis and, thus, it may serve to bridge the barriers between the two communities.

Next you can find Kenny’s new posting, annotated with my comments. In these comments, I have attempted to further clarify the bridges between the two cultures; the “traditional” and the “causal.” I will refer to the former as “BK” (for Baron and Kenny) and to the latter as “causal” (for lack of a better word) although, conceptually, both BK and SEM are fundamentally causal.

Click here for the full post.

From Melanie Wall, University of Minnesota:

I am teaching a course in latent variable modeling (to biostatistics and other public health students) and was yesterday introducing path analysis concepts including direct and indirect effects.

I showed them how to calculate indirect effects by taking the product of direct paths. Then a student asked about how to interpret the indirect effect and I gave the answer that I always give, that the indirect effect ab (in the following simple model) is the effect that a change in x has on Z through its relationship with Y.

After chewing on this for a second, the student asked the following:

Student: "The interpretation of the b path is: b is the increase we would see in Z given a unit increase in Y while holding X fixed, right?"

Me: "That's right"

Student: "Then what is being held constant when we interpret an indirect effect?"

Me: "Not sure what you mean"

Student: "You said the interpretation of the indirect effect ab is: ab is the increase we would see in Z given a one unit increase in X through its causal effect on Y. But since b (the direct effect from Y to Z) requires X to be held constant how can it be used in a calculation that is also requiring X to change one unit"

Me: "Hmm. Very good question, I'm not sure I have a good answer for you. In the case where the direct path from X Z is zero I think we have no problem since the relationship between Y and Z then has nothing to do with X. But you are right, here if "c" is non-zero then we must interpret b as the effect of Y on Z when X is held constant. I understand that this sounds like it conflicts with the interpretation of the ab indirect effect where we are examining what a change in X will cause. How about I get back to you. As I have told you before, the calculations here aren't hard, its trying to truly understand what your model means that's hard."

(Quoted from Jacques A. Hagenaars' comments on my SMR paper (Pearl, 1998a), dated February 24, 2000. Full text accessible through http://www.knaw.nl/09public/rm/koster1.pdf.)

In general, researchers are interested in the nature and sizes of direct, total and indirect effects. In a way (but see below), Pearl shows how to compute direct and total effects in the general (nonparametric) model, but is silent about indirect effects. …. indirect effects do occupy an important place in substantive theories. Many social science theories `agree' on the input (background characteristics) and output (behavioral) variables, but differ exactly with regard to the intervening mechanisms. To take a simple example, we know that the influence of Education on Political Preferences is mediated through `economic status' (higher educated people get the better jobs and earn more money) and through a `cultural mechanism' (having to do with the contents of the education and the accompanying socialization processes at school). It is important what the causal directions (signs) of these two processes are and which one is the dominant one (at least in The Netherlands they did tend to go into different directions, one leading to a right wing preference, the other to a left wing). We need to know and separate the nature and consequences of these two different processes, that is, we want to know the signs and the magnitudes of the indirect effects. In the parametric linear version of structural equation models, there exists a `calculus of path coefficients' in which we can write total effects in terms of direct and several indirect effects. But this is not possible in the general nonparametric cases and not, e.g., in the loglinear parametric version. For systems of logit models there does not exist a comparable `calculus of path coefficients' as has been remarked long ago. However, given its overriding theoretical importance, the issue of indirect effects cannot be simply neglected.

In line with my own proposals (Hagenaars, 1993, see below), maybe something might be derived from collapsing tables over one but not the other intervening variable; formulated in terms of the `do-operator', maybe some assessment of indirect effects might be obtained by setting not only the `causal factor' (here: Education) to a particular value, but also one of the two intervening variables. Or maybe we must simply conclude that only given particular definitions (parameterizations) of causal effects it makes sense to talk about indirect effects, e.g., only if we take differences between distributions as our causal measure, but not when we use ratios.

Reference: Hagenaars, Jacques A., Loglinear Models with Latent Variables, Sage University Papers Series, Newbury Park, CA: Sage, 49–50, 1993.