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When I normalize the weights I use for fitting a line with weighted least squares, the parameters of the fitted line and the 'normal' standard errors stay exactly the same, as I would expect. The HC3 standard error estimates, however, change completely.

I get the feeling that I am missing something quite important here, but... well, I am missing it...

Here is some test code in Python:

import statsmodels.api as sm
import numpy as np

myData = np.array([1, 1, 2, 2, 3, 3, 4, 4], dtype=float)
myIndex = sm.add_constant(range(len(myData)))

myWeights = np.array([100,10,100,10,100,10,100,10], dtype=float)

fit1 = sm.WLS(myData, myIndex, weights=myWeights).fit()

print "Parameters: %s" % fit1.params
print "Normal standard errors: %s" % fit1.bse
print "HC3 estimates: %s" % fit1.HC3_se

# Normalise the weights
myWeights /= myWeights.sum()

fit2 = sm.WLS(myData, myIndex, weights=myWeights).fit()

print "Parameters: %s" % fit2.params
print "Normal standard errors: %s" % fit2.bse
print "HC3 estimates: %s" % fit2.HC3_se

Which produces:

Parameters: [ 0.9796748   0.49186992]
Normal standard errors: [ 0.09876738  0.02581648]
HC3 estimates: [ 0.00976334  0.00314918]
Parameters: [ 0.9796748   0.49186992]
Normal standard errors: [ 0.09876738  0.02581648]
HC3 estimates: [ 44.54587593   0.75750668]
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  • $\begingroup$ This looks strange to me. Have you tried with some other data or software? I don't read python but I've tried to reproduce this result in R and cannot do so. $\endgroup$
    – KOE
    Jan 27, 2014 at 20:58
  • $\begingroup$ Stackoverflow won't let me post as an answer for some reason, but I cannot reproduce this with current master. What version of statsmodels are you using? $\endgroup$
    – jseabold
    Jan 28, 2014 at 13:30
  • $\begingroup$ This is not supported in statsmodels 0.5. HCCM matrices are only appropriate for OLS documentation for HCxxx statsmodels.sourceforge.net/stable/generated/… $\endgroup$
    – Josef
    Jan 28, 2014 at 15:31

1 Answer 1

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Different browser let's me post an answer now...

What version are you using? I can't reproduce this with current master. Probably best to post these kinds of issues to github in the future.

https://github.com/statsmodels/statsmodels/issues

Parameters: [ 0.9796748   0.49186992]
Normal standard errors: [ 0.09876738  0.02581648]
HC3 estimates: [ 0.06187963  0.02651504]                                        
Parameters: [ 0.9796748   0.49186992]                                           
Normal standard errors: [ 0.09876738  0.02581648]                               
HC3 estimates: [ 0.06187963  0.02651504]

Version

[~/]
[3]: sm.version.full_version
[3]: '0.6.0.dev-3396b98'
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  • $\begingroup$ OK, thanks! I've got version 0.5.0. Seems like quite a serious bug if this is really it. Anyway, thanks again, I'll check! $\endgroup$
    – Tom
    Jan 28, 2014 at 14:56
  • $\begingroup$ Indeed, upgrading to '0.6.0.dev-c65f584' solves it. $\endgroup$
    – Tom
    Jan 28, 2014 at 15:26
  • $\begingroup$ From the docs "HCCM matrices are only appropriate for OLS." Granted, we should've at least raised a warning for use after WLS. We need to update the docs now that they're right for weights. $\endgroup$
    – jseabold
    Jan 28, 2014 at 15:32
  • $\begingroup$ Do you mean that HCx estimates actually do not work at all for WLS? Or just not in statsmodels 0.5.0? As in: the ones returned for the WLS fit in 0.6.0 do make sense?? $\endgroup$
    – Tom
    Jan 28, 2014 at 17:41
  • $\begingroup$ Just in statsmodels 0.5.0. The ones in the development branch should be correct, but I'd double-check yourself until there's an official release. They're almost certainly correct, but we need to do a bit more testing before the next release. $\endgroup$
    – jseabold
    Jan 29, 2014 at 15:47

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