How to assess the validity of a linear model based on the data

[LorenzoCiampiconi]

Hey Everyone,

I would like to open a discussion on how to evaluate the effectiveness and validity of a linear model in estimating causal effects.

Currently I'm working on a project and our model is passing the refutation test proposed in the documentation of this library. The problem is defined with time series of continuous values for treatments, confounders and outcome. I am wondering if there are any other approach to assess if using a linear model is a good idea. In particular, I tried to apply the standard way of verify the assumption of linearity by looking at the residuals of the underlying linear model and performing traditional test such as homoscedasticity test.

We checked the residuals for predicting the outcome (not the estimand) and they didn't look great, we know that the model is fit in order to estimate the ATE, so we are wondering if this can give us any kind of qualitative feedback.

Does this makes any sense considering your experience? Is there any suggestion on top of this topic?

Thank you

[amit-sharma]

@LorenzoCiampiconi A linear model should be used only if you have good reason to believe that the effects of all variables are linear.

If you are unsure, then it is better to use more advanced methods. The reason is that it is hard to validate whether a model has captured the effect of confounders correctly. In such a situation, if you have enough data, it is better to rely on machine learning models to capture the confounding effect and then compute the causal effect. Two methods I'd suggest:

1. If treatment is binary: consider any of the propensity score based methods. Here the propensity score is computed using a ML model to predict the treatment given the confounders. here you can plugin any predictive model and do cross-validation to select a model with the best fit.
2. If treatment is continuous: I recommend linear double-ml method from EconML, which can be called using the dowhy API. This method creates two ML models that predict outcome and treatment respectively from the confounding variables, and then uses a simple linear model to estimate the effect. You can find more on the docs.

[GladysKao]

Hi I’m new to this. I really want to know how to get the residuals. I dont' know where to find any relative function