Reopen - Formula Validation

[f-allian]

Reopening an issue for the formula validation for the following PR: #235.

Problem:

The formula validation doesn't work with direct effects, and returns errors for adjustment sets when they should work in practice (externally validated by Dagitty). This also raises a LinAlgError if the data quality is poor.

Temporary fix:

Roll back formula validation commits until we can thoroughly understand the statistical details.

[jmafoster1]

Steps to reproduce

1. Download and extract the mwe.zip.
2. cd into the directory.
3. Activate a conda environment with CTF v5.3.0.
4. Execute python run_causal_tests.py --json_path causal_tests.json --dag_path dag.dot --data_path data.csv
5. Observe error Formula covariates do not satisfy the constructive back-door criterion.

The problem lies in the specified linear regression formula num_shapes_unit ~ num_lines_abs + I(num_shapes_abs/(width*height)) on line 98 of causal_tests.json. This has treatment variable num_lines_abs, outcome variable num_shapes_unit, and three covariates {num_shapes_abs, width, height}. This fails validation, despite being a perfectly valid adjustment set on Dagitty.