Simplified_PCA_Simulation.ipynb Discussion

[paul-opheim]

Todo:

• [x] Correct the main DGP function

[paul-opheim]

• since there is no particular reason the PCA values should have the same sign as the values they are coming from, i get that the PCA regression coefficient is as likely to be negative as it is positive (when the true value is 1)
• there seems to be less attenuation bias with the pca method than with a single mismeasured value, once you take the absolute value of the coefficients

[nicomarto]

I would not worry about the sign, there are two things we have to keep in mind in classical measurement error:

1. Attenuation bias shrinkages the coefficient towards zero, then we should care about absolute values
2. This also means that the true coefficient and the biased one have the same sign. So I would just calculate the mean of the absolute value of coefficients estimated according to our proposed method, and then impute the sign find in the biased coefficient

[ijyliu]

No, the sign is a real problem because Paul and I have been setting the beta to 1 in our simulations.

If we are going to do that absolute value procedure it has to be justified...

[ijyliu]

Doing PCA on covariates now, issue no longer applies