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Re: st: significance of the variables based on t-test or f-test


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: significance of the variables based on t-test or f-test
Date   Fri, 31 Aug 2012 09:53:26 +0100

Paul is absolutely right to underline the correlation between linear
and quadratic terms, but I would stress with Maarten that plotting of
the data is surely and sorely needed to get a qualitative
understanding of whether some kind of curvature is needed or
justified.

It is my frequent practice to compare a quadratic fit with a
fractional polynomial (default) fit and a restricted cubic spline fit.

sysuse auto
scatter mpg weight || lfit mpg weight || qfit mpg weight || fpfit mpg
weight, ///
legend(order(1 "data"  2 "linear" 3 "quadratic" 4 "fracpoly"))

For a restricted cubic spline fit, -rcspline- (SSC) is a convenience
wrapper. My suggestions are that

1. If qfit, fpfit, rcspline agree, then quadratic is a good model. It
is not only simple but matches more flexible smoothers. But separate
testing of linear and quadratic terms makes no sense.

2. If any two of qfit, fpfit, rcspline disagree strongly, you need to
think more about what is going on.

Nick

On Fri, Aug 31, 2012 at 9:32 AM, Seed, Paul <paul.seed@kcl.ac.uk> wrote:

> In László's present model, it is likely that the linear and
> quadratic terms are highly correlated, and the tests
> do not make sense taken separately.  Hence the need to rely on the
> F-test for the whole model.  It's weakness suggests nothing much
> (compared to the size & power of the data set) is going on.
>
> Maarten's main conclusion notwithstanding,
> anyone facing a similar problem to László may wish to
> look at using orthogonal polynomials (Stata command -orthog-).
> Reference: Golub, G. H., and C. F. Van Loan. 1996.  Matrix
> Computations. 3rd ed.  Baltimore: Johns Hopkins University Press.
> László might also want to do this if cleaning and transforming
> the data improves the overall F test.
>
> A sequence such as the following might show something.
> Higher degrees can also be used.
>         orthog xi, poly(xi_) degree(2)
>         regress y xi_1 xi_2

2012/8/30 Maarten Buis <maartenlbuis@gmail.com>:

>> The main conclusion is that you cannot reject the hypothesis that
>> screening intensity is neither linearly nor quadraticly related to
>> risk adjusted performance.
>>
>> I would look at a scatter plot of performance against screening
>> intensity and look if you can see any anomalies. If that does not
>> work, than you'll just have to live with the fact that your data tells
>> you that the two are unrelated.

On Wed, Aug 29, 2012 at 6:59 PM, László Németh wrote:

>>> I would like to analyze the relationship between the risk-adjusted
>>> performance (DV) and the screening intensity of the SRI funds (IV). In
>>> the first model I assume a linear relationship between these two
>>> variables:
>>> y = B0 + B1*xi+ui
>>> The t-statistic of screening intensity is here 0.84
>>>
>>> Then I use a second model, where I add the square of screening
>>> intensity (Xi2) as a second independent variable: y=B0 +
>>> B1*xi+B2*xi2+ui
>>> The t-statistic of Xi is 2.02, whereas the t-statistic of Xi2 -2.17
>>> is. Based on this results I assume that there is a quadratic
>>> relationship between the risk-adjusted performance and the screening
>>> intensity of the funds. However, if I run an F-test with the two
>>> independent variables I got a p-value of 0.1008.
>>>
>>> Now, I am not sure how I should interpret these results. Based on the
>>> t-statistic, I think that there is a quadratic relationship, but the
>>> results of the F-test make me uncertain. That is why I would like to
>>> ask for your help in the interpretation of these results.

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