{gcm} Informative plot of SCM fit results

[elikling]

I have written some code that uses bootrapping to estimate the gcm/scm effect pvalues. I am devising a plot with the information usign graphviz.

I would like to disuss a few aspects and thougths. The first is the shape convnetions. I have seen a few. for example https://cjvanlissa.github.io/tidySEM/articles/sem_graph.html. but they do not cover all apects relevant to Casality graphs - such as a shape for the outcome variabel. I am thinking of something like this:

• Nodes
  - Exhogenous (no parents) : Triangle
  - Variable (with parents and children): Square [box]
  - Latent variable (not in the data) : Circle
  - Outcomes (no children) : Inverted triangle
  - Edges
  - Causal/Regression efects: straingt arrow
  - Covariance: dashed curve
  - (Residual) variance: double headed arrow

currently my code prodcuces

So

1. Is there a convention I sould be aware of?
2. Should we turn this into a functionality of Do Why?
3. will this be something to ask the NetworkX?

Eli

[kailashbuki]

Thank you for this thoughtful suggestion, Eli.

There are 3 key points on your proposal:

1. We restrict to a linear SCM.
2. We resort to a data modelling approach in statistics with a pre-conceived hypothesis on the data generating process (DGP), instead of an algorithmic approach.
3. We define a new convention on the visual representation of a causal graph.

Currently in the gcm package, we take an algorithmic approach to learning DGPs leveraging ML algorithms. We do not restrict to linear SCMs. And the convention proposed does not seem standard in academic literature.

Typically, researchers use circles for nodes, and outline latent variables by dashed edges or fill the latent node with grey. But I would love to understand a concrete use case where such a convention would help, as opposed to simply renaming a variable or highlighting the nodes with different colours. Note that causal graphs are not always constructed with effect estimation in mind. As such, using different visual signals for different roles seems to cater only to effect estimation. networkx already supports manipulation of visual elements of a graph. Is there a strong reason why networkx should natively support a new convention on displaying graph for a niche use case?

Having said that, your proposal surfaces the difficulty to obtain model fit diagnostics from the gcm package. We can definitely work on that. In principle, however, if model fit statistics (e.g., linear regression coefficients and their p-values, R2 score) are desirable, the design is flexible enough to enable that with gcm by writing appropriate wrappers (e.g., around statsmodels). Let us mark this as a todo.

[elikling]

:-) interesting points @kailashbuki,

I think I need to work thgouth them one by one.

The first point you make is that my approach implies "We restrict to a linear SCM." I am not sure what you mean by that. Do you think my approach can only work when the relationships are modeled as OLS regressions? I chose that form to make my calcualtions and expalantion simple. I do have a way to generalise. Here is an extact form the summary section of a paper I am workong on:

"The example presented in section 4 used liner regression as the functional form modelling the causal relationship effect. This is not a constraint on the discussion in this paper. The statistical modeller does have to specify some form of modelling the conditional probability and choose some measures of variable (parent node) contribution. For instance the modeler may chose a random forest for the functional representation and the variable importance as the contribution measure. The hypothesis about the parameters discussed in section 3 should be replaced with a more generalised null hypotheses family: the parent variable is not contributing to modelling the child. In this case two bootstrap loops should be employed as recommended by Westfall & Young (1992) and Yekutieli & Benjamini (2001):

1. [Outer] Bootstrap distribution of p-values and FDR adjustment
2. [Inner] Bootstrap distribution of contribution measures or regression parameters deriving p-values
   The statistical modeller should balance the complexity of the modelled relationships with expandability. Granted the Casual Graph form provides a communicable and intuitive explanation. A full explanation should also cover the effects size and sign.
   "

As to getting the model sumaries but - there is alot that should be developed in Do-Why. for now I am using somthing like:
print("--- Rain_Ind ---")
print(scm.causal_mechanism('Rain_Ind_Cat').classifier_model.sklearn_model.intercept_)
print(scm.causal_mechanism('Rain_Ind_Cat').classifier_model.sklearn_model.coef_)
print("--- Speed_KMpH ---")
print(scm.causal_mechanism('Speed_KMpH').prediction_model.sklearn_model.intercept_)
print(scm.causal_mechanism('Speed_KMpH').prediction_model.sklearn_model.coef_)
print("--- Fuel_Consumption_LpKM ---")
print(scm.causal_mechanism('Fuel_Consumption_LpKM').prediction_model.sklearn_model.intercept_)
print(scm.causal_mechanism('Fuel_Consumption_LpKM').prediction_model.sklearn_model.coef_)

let's discuss this before diving into the other points and suggestions you made above