'Causal' mediation great intro

I came across this great writing, which tackles 2 complex topics, causal mediation, and then this g-formula, not an easy feat...

They present a sweeping overview of current 'causal' mediation understanding, wonderfully summarized in some tables, especially 1:

and 2 (a bit 'thicker' for newcomers...)

* Note that g-formula has been incorporated in Stata (SAS too), see: http://www.stata-journal.com/article.html?article=st0238 .

References:
Wang, A., & Arah, O. A. (2015). G-computation demonstration in causal mediation analysis. European Journal of Epidemiology, 30(10), 1119-1127. doi: 10.1007/s10654-015-0100-z http://link.springer.com/article/10.1007/s10654-015-0100-z
Daniel RM, De Stavola BL, Cousens SN. gformula: estimating causal effects in the presence of time-varying confounding or mediation using the g-computation formula. Stata J. 2011;11(4):
479–517.

Causal hypotheses:from qualitative to quantitative (SEM style)

The statistical testing of hypotheses about causal sequencing of variables seems to more clearly show nowadays the 2-step process directly stated in Ch. 10 in Conrady & Jouffe, (chapter written with Felix Elwert), process mentioned in my Semnet posting:
1. Causal Identification, followed by
2. Computing the Effect Size.

I found a good example of this approach, within the SEM (Structural Equation Modeling) approach, in a a recent article in Computers in Human Behavior, by Yen & Wu, the sequence is simply: 1. A 'qualitative' (i.e. no numbers!) part: how variables/concepts are expected to 'string themselves' out; and 2. A quantitative part, the post-SEM estimation phase, with numbers attached this time.
1.What one expects:

 2. What one finds (numerically):

References:

Conrady, S. and L. Jouffe, Bayesian Networks and BayesiaLab: 

A Practical Introduction for Researchers. 2015: Bayesia USA: 

free online: http://www.bayesia.com/book

Yen, Y.-S., & Wu, F.-S. (2016). Predicting the adoption of mobile financial services: 

The impacts of perceived mobility and personal habit. Computers in Human Behavior, 

65, 31-42. doi: http://dx.doi.org/10.1016/j.chb.2016.08.017 

Mediation: from 3 variables to 6 and 27 models

We all know the 3 variable model (X->M->Y & X->Y) with M being an intermediate variable (hence both cause and effect) is 'the simplest' possible 'statistical model', besides the bare-bone 2 variable one (X->Y).
Many have delved into its intricacies however, which are many in fact, dealing with specification alternatives. For instance, as Felix Thoemmes e.g. showed, there are 6 alternative statistically indistinguishable models that link all 3 variables (these are then all 'saturated models': no test of fit to data in SEM can be done).

Another take on this is the Conrady & Jouffe (2015) display of all 27 possible causal specifications one may contemplate when analyzing such 'simple' model (They use N1, N2, N3): this makes clear that the researcher/analyst 'gets married' to a specific causal structure s/he believes to operate behind the data, i.e. that generated it; In BayesiaLab this is obvious by asking the user for direct input ('drawing an arrow', much like in AMOS).

Of course, with >3 variables, the number of possibilities quickly get out of hand! Some can be ruled out by theory and prior findings, others by 'hunches', others by 'strong beliefs' (more so the case in practice, I'd say).

Conrady, S., & Jouffe, L. (2015). Bayesian Networks and BayesiaLab: A Practical Introduction for Researchers. http://www.bayesia.com/book
Thoemmes, F. (2015). Reversing Arrows in Mediation Models Does Not Distinguish Plausible Models. Basic and Applied Social Psychology, 37(4), 226-234. doi:10.1080/01973533.2015.1049351 www.tandfonline.com/doi/pdf/10.1080/01973533.2015.1049351

nested_CF-s

Here is the worked example from the article below; they showed how to 'process' such data, in the classical manner (standard adjustment), and in the causal modeling way (structured adjustment). Very simple side-by-side application.

Kaufman, J. S., & Kaufman, S. (2001). Assessment of Structured Socioeconomic Effects on Health. Epidemiology, 12(2), 157-167. doi:10.2307/3703617

Change patterns

Notice anything interesting in this?

There are some interesting cyclical patterns here... For context related to SEMNET, see below.

Changes-leading-to-changes

A quick illustration of how talking about changes in a variable X leading to changes in another variable Y can be simplified.

Changes-leading-to-changes makes language difficult, because we are used to talk about ‘imaginary changes in X leading to imaginary changes in Y’ to describe Y(X) relations from cross-sectional/timeless regressions X->Y, whereas in reality there are no actual changes to talk about in the same-time Y-on-X regression, only potential ones.

The problem comes when talking about what a model 'change-in-X->change-in-Y' tells us; here, you run into the problem of having cases that belong to 4 different quadrants of a scatter plot change-in-Y(change-in-X), see figure above: those increasing in both (Q2), those decreasing in both (Q4), and those increasing in 1: Y/X and decreasing in the other one: X/Y (Q1 / Q3, respectively).
You can still talk about all of these, with some help from peeking at where the averages for change-in-X & change-in-Y are (see the big green dot), whether they are positive or negative.

A simple way of describing these graphs where the changesX->changesY slope is >0 , is to say that if one increases in X, then we expect their Y to also increase, even though the 2 graphs show that the Y actual mean shows an average Y increase, then an average Y decrease: the only difference is that the slope was 'pushed down' by the 2 means, as the slope naturally crosses the (MeanX, MeanY) dot.

PatientDoctor

Here's an adaptation of Dave Kenny's social relations approach to patient-doctor relations, some of these may be forced... I add his original look for proper context

Kenny, D. A. (1994). Interpersonal perception: A social relations analysis: Guilford Press.