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From |
László Németh <pitlak6@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Mon, 3 Sep 2012 06:07:45 +0200 |

Dear Paul and Nick, thank you very much for your answers. They really helped me a lot in the interpretation of my results. Best regards, László 2012/8/31 Nick Cox <njcoxstata@gmail.com>: > 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. > > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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