Finding out whether a variable is really collinear #95
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sergiocorreia
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Apr 17, 2017
Issues resolved: 1) qrsolve(XX, XY) suffers from numerical inaccuracies on some cases, so we fix to qrsolve(X, Y) if we don't have weights (Note: this might be a bit slower as the XX and XY are already precomputed. It could also be optimized but for now let's leave it as it is. 2) The methods used to find out omitted variables were different in different points. When demeaning, we looked if the regressors were close to zero, but used absolute values (1e-8) which doesn't work if there is a huge scaling difference between Y and X. Now we will assumme the var has been absorbed by the absvars if the ratio z'z/w'w < (1e-9) where z=old variable and w= demeaned variable. This 1e-9 will also increase with tolerance() as it's just tolerance*1e-1 We also use invsym() as the main driver for whether to drop or not, as that is what it's used on the built-in tools. Then the inputs of qrsolve() will exclude the omitted variables, to prevent any issue.
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A variable is omitted if:
a) After partialling-out, it is zero (or within EPS of zero, where EPS is usually 1e-10)
b) The regression gives a beta of zero for a coef. , or invsym() detects it is collinear and drops it. (2nd approach is probably better). An extra issue is that the error in step a) gets carried to step b).
Not sure if there is an easy way around this, but in any case the tolerance used to detect omitted should be linked to the tolerance used to partial out the variables.
Also, if both Y and X are completely absorbed, their residuals will be very low but within the same magnitude of each other, giving a spurious result.
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