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st: RE: Insignificant coefficient in prediction


From   Nick Cox <n.j.cox@durham.ac.uk>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Insignificant coefficient in prediction
Date   Wed, 1 Dec 2010 18:12:25 +0000

You get what you ask for. If you fit a model and then follow with -predict-, then Stata fits that model. 

You have scope to hunt for models in which every coefficient is significant at conventional levels and then -predict- with those. 

Stata lets you do that, but it remains agnostic about your prejudices about how to work with data. 

My own view is that insisting that every coefficient be significant is a dogma that admits many exceptions. For example, 

1. Often the search for such a model involves a trawl through many possible models and makes the usual interpretation of significance level problematic. Is a project a fishing expedition or does it have a clear focus on scientific research questions? 

2. Not every researcher feels compelled to use thresholds such as .05 or .01. My attitude to 0.049 is not distinguishable from my attitude to 0.051. 

3. Often there are scientific and/or statistical grounds for including bundles of predictors, even if some or all don't qualify individually as significant. A perhaps esoteric example is that a sine and a cosine term usually belong together, even if one is not significant. A more common example, for many readers of this list, is that a bunch of indicators usually belong together, ditto. 

4. Often much of the point of a project is to use the same model, meaning here specifically the same predictors, in different circumstances. Finding out how far results are similar or different is more straightforward than if researchers just fit a ragbag of different models and insist on everything being significant. 

5. Significance is usually overemphasised in any case. Often the P-value is the dodgiest part of the results, especially if there is doubt about how far the underlying assumptions are satisfied, as there is usually is. 

I imagine that any others whose prejudices overlap with mine could easily extend my list. 

Nick 
n.j.cox@durham.ac.uk 

Mike Kim

I have a question about prediction. Linear predictions in Stata (probably in
all software) after any regression seem to use all estimated coefficients
regardless their statistical significance. How can I understand that we use
insignificant coefficients in forecasting?

sysuse auto, clear
reg mpg weight length  // length is not significant
predict mpgh, xb

The predicted values use all coefficients including the coefficient of
'length' even if it is not significant.

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