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From |
Steven Samuels <sjsamuels@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: FW: Model SS/R-square in nl |

Date |
Thu, 30 Jun 2011 22:03:54 -0400 |

One consequence of the fact that the mean-only model is not nested in the no-constant model is that it is possible that SSE > SST, so that s R-square = 1 - SSE/SST <0 In this example y is constant so the SST = 0, whereas SSE>0. Thus I believe that Gordon is incorrect and that the traditional approach is correct. ********************** clear scalar drop _all range x 0 10 11 gen y = 10 sum x sum y scalar n = r(N) scalar var = r(Var) scalar sstot = (n-1)*var scalar list sstot reg y x, nocons ****************** Steve Some people agree with you, e.g. H. A. Gordon. Errors in Computer Packages. Least Squares Regression Through the Origin Journal of the Royal Statistical Society. Series D (The Statistician) Vol. 30, No. 1 (Mar., 1981), pp. 23-29 But others don't, and the "error" is well-established. If you take your point of view, you have to justify an ANOVA table with the following d.f., taking p = 1 regressor. SS d.f. Model 1 Error n - 1 Total n - 1 ? This problem arises because the mean-only model is _not_ nested in the no-constant model as standard LS theory requires. You can achieve a "nesting" by fitting no mean, getting: Model 1 Error n - 1 Total n The main benefit to the "SST must be the same for all models" approach, I think, is that one can compare R2 consistently for the same data set as R2 = 1 - SSE/SST. Steve sjsamuels@gmail.com On Jun 30, 2011, at 4:24 PM, CJ Lan wrote: If you look at the residual SS, i.e., sum of (yi-yhat)^2, the 1st model renders 28315 and the 2nd model renders 28427, which sounds reasonable because one parameter is eliminated. My point is the Total SS, i.e., sum of (yi-mean(y))^2, should not be changed (=39434). Therefore, in the 2nd model, the Model SS = (Total SS)-(residual SS) = 39434-28427 = 11007 and the R2 should have been 0.2791, which is the answer I got from Matlab. The curve will not be forced through the origin. The curve of the 1st model starts at (b0+b1=45.6) and decreases at an exponential rate. Similarly the curve of the 2nd model starts at (b1=44.5) and decreases at a similar exponential rate. -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox Sent: Thursday, June 30, 2011 4:05 PM To: statalist@hsphsun2.harvard.edu Subject: Re: st: FW: Model SS/R-square in nl No, it is not a bug. Your constant may not be significant by itself, but the model is different. R-squares for different models are often difficult to compare effectively. Plot the fitted curves and the data to see what it is going on. In my experience, especially with nonlinear models, it is far better to rely on physical, biological, economic or other scientific understanding to choose the better model and to compare fitted curves with the data, rather than to rely blindly on a significance test. Does it make sense to force the curve through the origin? Nick On Thu, Jun 30, 2011 at 6:06 PM, CJ Lan <CJ@jupiter.fl.us> wrote: > I was using nl to run a 3-parameter NLS model estimation and got R2=0.28 > (see the first output). Since the parameter b0 is insignificant, I drop > it and re-estimate it again. This time, I got the wrong R2 (=0.86 in > the 2nd output). It is apparent that either the "Model SS" or "Total > SS" is wrongly calculated. Is this bug? Thank you for help. > > (1) > . nl exp3 : passby A in 1/152 > (obs =152) > Iteration 0: residual SS =3D 29741.65 > Iteration 1: residual SS =3D 28448.53 > Iteration 2: residual SS =3D 28316.37 > Iteration 3: residual SS =3D 28315.61 > Iteration 4: residual SS =3D 28315.6 > Iteration 5: residual SS =3D 28315.6 > Iteration 6: residual SS =3D 28315.6 > Iteration 7: residual SS =3D 28315.6 > Source | SS df MS Number of obs =152 > -------------+------------------------------ F( 2, 149) =29.25 > Model | 11118.3472 2 5559.1736 Prob > F =0.0000 > Residual | 28315.6009 149 190.03759 R-squared =0.2819 > -------------+------------------------------ Adj R-squared =0.2723 > Total | 39433.9482 151 261.151975 Root MSE =13.78541 > Res. dev. =1225.905 > 3-parameter asymptotic regression, passby = b0 + b1*b2^A > ------------------------------------------------------------------------ > passby | Coef. Std. Err. t P>|t| 95% Conf.Interval] > -------------+---------------------------------------------------------- > b0 | 11.59292 10.68695 1.08 0.280 -9.52 32.71048 > b1 | 34.10476 9.433555 3.62 0.000 15.4 52.74559 > b2 | .998132 .0011685 854.19 0.000 .995 1.000441 > ------------------------------------------------------------------------ > * Parameter b0 taken as constant term in model & ANOVA table > (SEs, P values, CIs, and correlations are asymptotic approximations) > > (2) > . nl exp2 : passby A in 1/152 > (obs =3D 152) > Iteration 0: residual SS =3D 29510.02 > Iteration 1: residual SS =3D 28427.14 > Iteration 2: residual SS =3D 28426.97 > Iteration 3: residual SS =3D 28426.97 > Source | SS df MS Number of obs =152 > -------------+------------------------------ F( 2, 150) =468.32 > Model | 177506.602 2 88753.3012 Prob > F =0.0000 > Residual | 28426.9672 150 189.513115 R-squared =0.8620 > -------------+------------------------------ Adj R-squared =0.8601 > Total | 205933.57 152 1354.82612 Root MSE =13.76638 > Res. dev. =1226.502 > 2-parameter exp. growth curve, passby =3D b1*b2^A > ------------------------------------------------------------------------ > passby | Coef. Std. Err. t P>|t|[95% Conf.interval] > -------------+---------------------------------------------------------- > b1 | 44.54536 2.038308 21.85 0.000 40.51785 48.57286 > b2 | .9988862 .0001727 5783.22 0.000 .9985449 .9992275 > ------------------------------------------------------------------------ > (SEs, P values, CIs, and correlations are asymptotic approximations) > * * 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/ PLEASE NOTE: Florida has a very broad public records law. Most written communications to or from the Town of Jupiter officials and employees regarding public business are public records available to the public and media upon request. Your e-mail communications may be subject to public disclosure. Under Florida law, e-mail addresses are public records. If you do not want your e-mail address released in response to a public records request, do not send electronic mail to this entity. Instead, contact this office by phone or in writing. The views expressed in this message may not necessarily reflect those of the Town of Jupiter. If you have received this message in error, please notify us immediately by replying to this message, and please delete it from your computer. Thank you. * * 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/

**References**:**st: FW: Model SS/R-square in nl***From:*"CJ Lan" <CJ@jupiter.fl.us>

**Re: st: FW: Model SS/R-square in nl***From:*Nick Cox <njcoxstata@gmail.com>

**RE: st: FW: Model SS/R-square in nl***From:*"CJ Lan" <CJ@jupiter.fl.us>

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