I just realized I used Robust in my Stata 9.2 analysis. When I remove this, the Chi-sq values are much closer to the values I get in R (but negative, as the consistent model must be listed first in a chi-sq calculation). However, with my own data I do get this positive definite error in Stata. Is this a result of unbalanced data? R doesn't give an error, so I am inclined to ignore it in Stata. I am posting my own results from R and Stata, and attaching the data as a csv.<br>
<br>Thanks, hope I am not wasting too much of your time here.<br><br>-Steve<br><br>###R-Output###<br>> library("plm")<br>> <br>> fdi <- read.csv("C:/data/mydata.csv", na.strings=".")<br>
> fdiplm<-plm.data(fdi, index = c("id_code_id", "year"))<br>series are constants and have been removed<br>> <br>> fdi_test<-(lfdi_2000~ lagdlfdi+ laglnstock2000+ lagtradegdp +lagdlgdp)<br>
> <br>> fdi_test_fe <- plm(fdi_test, data=fdiplm, model="within")<br>> fdi_test_re <- plm(fdi_test, data=fdiplm, model="random")<br>> <br>> summary (fdi_test_fe)<br>Oneway (individual) effect Within Model<br>
<br>Call:<br>plm(formula = fdi_test, data = fdiplm, model = "within")<br><br>Unbalanced Panel: n=149, T=3-27, N=2697<br><br>Residuals :<br> Min. 1st Qu. Median 3rd Qu. Max. <br>-8.2100 -0.4760 0.0452 0.5670 4.8700 <br>
<br>Coefficients :<br> Estimate Std. Error t-value Pr(>|t|) <br>lagdlfdi 0.1564759 0.0180645 8.6621 < 2.2e-16 ***<br>laglnstock2000 0.7621350 0.0246798 30.8809 < 2.2e-16 ***<br>lagtradegdp 0.0178568 0.0025859 6.9055 5.003e-12 ***<br>
lagdlgdp 0.2601477 0.0427744 6.0818 1.188e-09 ***<br>---<br>Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 <br><br>Total Sum of Squares: 4606.7<br>Residual Sum of Squares: 2938<br>F-statistic: 361.237 on 4 and 2544 DF, p-value: < 2.22e-16<br>
> summary (fdi_test_re)<br>Oneway (individual) effect Random Effect Model <br> (Swamy-Arora's transformation)<br><br>Call:<br>plm(formula = fdi_test, data = fdiplm, model = "random")<br><br>Unbalanced Panel: n=149, T=3-27, N=2697<br>
<br>Effects:<br> var std.dev share<br>idiosyncratic 1.15487 1.07465 0.6617<br>individual 0.59044 0.76840 0.3383<br>theta : <br> Min. 1st Qu. Median Mean 3rd Qu. Max. <br> 0.3718 0.6700 0.7081 0.6955 0.7355 0.7401 <br>
<br>Residuals :<br> Min. 1st Qu. Median Mean 3rd Qu. Max. <br>-9.15000 -0.47900 0.07270 -0.00713 0.59800 3.95000 <br><br>Coefficients :<br> Estimate Std. Error t-value Pr(>|t|) <br>
(Intercept) 16.7744214 0.1552868 108.0222 < 2.2e-16 ***<br>lagdlfdi 0.1632388 0.0181005 9.0185 < 2.2e-16 ***<br>laglnstock2000 0.8314432 0.0196444 42.3247 < 2.2e-16 ***<br>lagtradegdp 0.0119453 0.0020737 5.7605 8.386e-09 ***<br>
lagdlgdp 0.2558009 0.0424599 6.0245 1.696e-09 ***<br>---<br>Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 <br><br>Total Sum of Squares: 9522.3<br>Residual Sum of Squares: 3140.8<br>F-statistic: 1367.42 on 4 and 2692 DF, p-value: < 2.22e-16<br>
> <br>> phtest(fdi_test_re, fdi_test_fe)<br><br> Hausman Test<br><br>data: fdi_test <br>chisq = 23.7021, df = 4, p-value = 9.164e-05<br>alternative hypothesis: one model is inconsistent <br><br><br>###end R output###<br>
<br>###Stata 9.2 Output--canned###<br>xtreg lfdi_2000 lagdlfdi laglnstock2000 lagtradegdp lagdlgdp, fe;<br><br>Fixed-effects (within) regression Number of obs = 2697<br>Group variable (i): id_code_id Number of groups = 149<br>
<br>R-sq: within = 0.3622 Obs per group: min = 3<br> between = 0.8234 avg = 18.1<br> overall = 0.6998 max = 27<br>
<br> F(4,2544) = 361.24<br>corr(u_i, Xb) = 0.3536 Prob > F = 0.0000<br><br>------------------------------------------------------------------------------<br>
lfdi_2000 | Coef. Std. Err. t P>|t| [95% Conf. Interval]<br>-------------+----------------------------------------------------------------<br> lagdlfdi | .1564758 .0180645 8.66 0.000 .1210532 .1918985<br>
laglnst~2000 | .762135 .0246798 30.88 0.000 .7137404 .8105295<br> lagtradegdp | .0178568 .0025859 6.91 0.000 .0127861 .0229274<br> lagdlgdp | .2601478 .0427744 6.08 0.000 .1762716 .3440241<br>
_cons | 17.01131 .1701713 99.97 0.000 16.67762 17.345<br>-------------+----------------------------------------------------------------<br> sigma_u | .93048942<br> sigma_e | 1.0746505<br>
rho | .42847396 (fraction of variance due to u_i)<br>------------------------------------------------------------------------------<br>F test that all u_i=0: F(148, 2544) = 10.73 Prob > F = 0.0000<br>
<br>. estimates store FIX, title(The FE) ;<br><br>. xtreg lfdi_2000 lagdlfdi laglnstock2000 lagtradegdp lagdlgdp, re;<br><br>Random-effects GLS regression Number of obs = 2697<br>Group variable (i): id_code_id Number of groups = 149<br>
<br>R-sq: within = 0.3606 Obs per group: min = 3<br> between = 0.8402 avg = 18.1<br> overall = 0.7128 max = 27<br>
<br>Random effects u_i ~ Gaussian Wald chi2(4) = 2225.46<br>corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000<br><br>------------------------------------------------------------------------------<br>
lfdi_2000 | Coef. Std. Err. z P>|z| [95% Conf. Interval]<br>-------------+----------------------------------------------------------------<br> lagdlfdi | .1631662 .0180937 9.02 0.000 .1277032 .1986291<br>
laglnst~2000 | .830845 .0196843 42.21 0.000 .7922645 .8694255<br> lagtradegdp | .011992 .0020779 5.77 0.000 .0079195 .0160645<br> lagdlgdp | .2558113 .0424486 6.03 0.000 .1726136 .3390091<br>
_cons | 16.77702 .1556693 107.77 0.000 16.47191 17.08212<br>-------------+----------------------------------------------------------------<br> sigma_u | .77431228<br> sigma_e | 1.0746505<br>
rho | .34173973 (fraction of variance due to u_i)<br>------------------------------------------------------------------------------<br><br>. estimates store RAND, title(The RE) ;<br><br>. hausman FIX RAND;<br>
<br> ---- Coefficients ----<br> | (b) (B) (b-B) sqrt(diag(V_b-V_B))<br> | FIX RAND Difference S.E.<br>-------------+----------------------------------------------------------------<br>
lagdlfdi | .1564758 .1631662 -.0066903 .<br>laglnst~2000 | .762135 .830845 -.06871 .014887<br> lagtradegdp | .0178568 .011992 .0058648 .0015393<br>
lagdlgdp | .2601478 .2558113 .0043365 .0052695<br>------------------------------------------------------------------------------<br> b = consistent under Ho and Ha; obtained from xtreg<br>
B = inconsistent under Ha, efficient under Ho; obtained from xtreg<br><br> Test: Ho: difference in coefficients not systematic<br><br> chi2(4) = (b-B)'[(V_b-V_B)^(-1)](b-B)<br> = 22.94<br>
Prob>chi2 = 0.0001<br> (V_b-V_B is not positive definite)<br>###End Stata 9.2####<br><br><br><br><br><br><br><br><div class="gmail_quote">On Mon, May 18, 2009 at 12:26 PM, Steven Archambault <span dir="ltr"><<a href="mailto:archstevej@gmail.com" target="_blank">archstevej@gmail.com</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<div>Giovani,</div>
<div> </div>
<div>Thank you so much for your comments. I am a bit new to R, and to these mailing lists, so I apologize for being sparse on the details and examples. I am using Stata 9.2, which might be the answer to my problem, as you described. I have done quite a bit of internet searching, and did not read anywhere about the use of a different method for calculating the chi-sq value, so thanks for that. </div>
<div> </div>
<div>
<div>One more issue I have been thinking about. I am assuming your Plm package knows that the FE is the consistient model, as the same results arrive if the code is phtest(femod, remod) or phtest(remod, femod). The order does matter in Stata.</div>
<div> </div></div>
<div>For complteness I am going to post my results using the same Grumfeld dataset for both stata 9.2 (by hand calculation and canned procedure) and R. I am using the Plm package version 1 1-2.</div>
<div> </div>
<div>Regards,</div>
<div>Steve</div>
<div> </div>
<div> </div>
<div> </div>
<div><font size="2" face="NimbusRomNo9L-Regu"><font size="2" face="NimbusRomNo9L-Regu"></font></font> ## begin Stata9.2 output##</div>
<div>xtreg inv value capital, robust re;</div>
<p></p><div>Random-effects GLS regression Number of obs = 200<br></div>Group variable (i): firmid Number of groups = 10<div>
<p>R-sq: within = 0.7668 Obs per group: min = 20<br> between = 0.8196 avg = 20.0<br> overall = 0.8061 max = 20</p>
</div><p>Random effects u_i ~ Gaussian Wald chi2(3) = 77.70</p><div><br>corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000</div>
<p>------------------------------------------------------------------------------<br> | Robust<br> invest | Coef. Std. Err. z P>|z| [95% Conf. Interval]<br>-------------+----------------------------------------------------------------<br>
value | .1097811 .0197587 5.56 0.000 .0710547 .1485076<br> capital | .308113 .0418387 7.36 0.000 .2261107 .3901153<br> _cons | -57.83441 24.67795 -2.34 0.019 -106.2023 -9.466507<br>
-------------+----------------------------------------------------------------</p><div><br> sigma_u | 84.20095<br> sigma_e | 52.767964<br> rho | .71800838 (fraction of variance due to u_i)<br>
------------------------------------------------------------------------------</div>
<p>. matrix bfe=e(b);</p>
<p>. matrix vfe=e(V);</p>
<p>. estimates store remod;</p>
<p>. xtreg inv value capital, robust fe;</p>
<p></p><div>Fixed-effects (within) regression Number of obs = 200<br></div>Group variable (i): firmid Number of groups = 10<div>
<p>R-sq: within = 0.7668 Obs per group: min = 20<br> between = 0.8194 avg = 20.0<br> overall = 0.8060 max = 20</p>
</div><p> F(2,188) = 40.23</p><div><br>corr(u_i, Xb) = -0.1517 Prob > F = 0.0000</div>
<div>------------------------------------------------------------------------------<br> | Robust<br> invest | Coef. Std. Err. t P>|t| [95% Conf. Interval]<br>-------------+----------------------------------------------------------------<br>
value | .1101238 .019378 5.68 0.000 .0718975 .1483501<br> capital | .3100653 .042795 7.25 0.000 .2256452 .3944854<br> _cons | -58.74393 23.37422 -2.51 0.013 -104.8534 -12.63449<br>
-------------+----------------------------------------------------------------<div><br> sigma_u | 85.732501<br> sigma_e | 52.767964<br> rho | .72525012 (fraction of variance due to u_i)<br>
------------------------------------------------------------------------------</div></div>
<div> </div>
<div> ###Hausman by hand### </div>
<p>. estimates store femod;</p>
<p>. matrix vre=e(V);</p>
<p>. matrix bre=e(b);</p>
<p>. matrix bdif=bfe-bre;</p>
<p>. matrix list bdif;</p>
<p>bdif[1,3]<br> value capital _cons<br>y1 -.00034265 -.00195236 .90952273</p>
<p>. matrix bdifp=bdif';</p>
<p>. matrix dv=vfe-vre;</p>
<p>. matrix dvi=inv(dv);</p>
<p>. matrix list bdif;</p>
<p>bdif[1,3]<br> value capital _cons<br>y1 -.00034265 -.00195236 .90952273</p>
<p>. matrix list bdifp;</p>
<p>bdifp[3,1]<br> y1<br> value -.00034265<br>capital -.00195236<br> _cons .90952273</p>
<p>. matrix list dvi;</p>
<p>symmetric dvi[3,3]<br> value capital _cons<br> value -7739.3615<br>capital 5808.2905 -5305.811<br> _cons 3.6641311 .98569198 -.00051157</p>
<p>. matrix chisq=bdif*dvi*bdifp;</p>
<p>. matrix list chisq;</p>
<p>symmetric chisq[1,1]<br> y1<br>y1 -.01956929</p>
<div>###Hausman canned###</div>
<div>. hausman femod remod;</div>
<p></p><div> ---- Coefficients ----<br> | (b) (B) (b-B) sqrt(diag(V_b-V_B))<br> | femod remod Difference S.E.<br>
-------------+----------------------------------------------------------------<br>
value | .1101238 .1097811 .0003427 .<br></div> capital | .3100653 .308113 .0019524 .0089965<br>------------------------------------------------------------------------------<div>
<br>
b = consistent under Ho and Ha; obtained from xtreg<br> B = inconsistent under Ha, efficient under Ho; obtained from xtreg</div><div>
<p> Test: Ho: difference in coefficients not systematic</p>
</div><p></p><div> chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)<br></div> = -0.01 chi2<0 ==> model fitted on these<br> data fails to meet the asymptotic<br>
assumptions of the Hausman test;<br> see suest for a generalized test
<div>## end Stata9.2 output ##</div>
<div> </div>
<div>##begin Output R, using PLM 1.1-2###<font size="2" face="NimbusRomNo9L-Regu"><font size="2" face="NimbusRomNo9L-Regu">
<p align="left">> test<-data(Grunfeld, package="Ecdat")<br>> <br>> fm <- inv~value+capital<br>> femod <- plm(fm, Grunfeld, model="within")<br>> summary(femod)<br>Oneway (individual) effect Within Model</p>
<p align="left">Call:<br>plm(formula = fm, data = Grunfeld, model = "within")</p>
<p align="left">Balanced Panel: n=10, T=20, N=200</p>
<p align="left">Residuals :<br> Min. 1st Qu. Median 3rd Qu. Max. <br>-184.000 -17.600 0.563 19.200 251.000 </p>
<p align="left">Coefficients :<br> Estimate Std. Error t-value Pr(>|t|) <br>value 0.110124 0.011857 9.2879 < 2.2e-16 ***<br>capital 0.310065 0.017355 17.8666 < 2.2e-16 ***<br>---<br>Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 </p>
<p align="left">Total Sum of Squares: 2244400<br>Residual Sum of Squares: 523480<br>F-statistic: 309.014 on 2 and 188 DF, p-value: < 2.22e-16</p><div><br>> remod <- plm(fm, Grunfeld, model="random")<br>
</div>> summary(remod)<br>
Oneway (individual) effect Random Effect Model <br> (Swamy-Arora's transformation)
<p align="left">Call:<br>plm(formula = fm, data = Grunfeld, model = "random")</p>
<p align="left">Balanced Panel: n=10, T=20, N=200</p>
<p align="left">Effects:<br> var std.dev share<br>idiosyncratic 2784.458 52.768 0.282<br>individual 7089.800 84.201 0.718<br>theta: 0.86122 </p>
<p align="left">Residuals :<br> Min. 1st Qu. Median 3rd Qu. Max. <br>-178.00 -19.70 4.69 19.50 253.00 </p>
<p align="left">Coefficients :<br> Estimate Std. Error t-value Pr(>|t|) <br>(Intercept) -57.834415 28.898935 -2.0013 0.04536 * <br>value 0.109781 0.010493 10.4627 < 2e-16 ***<br>capital 0.308113 0.017180 17.9339 < 2e-16 ***<br>
---<br>Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 </p>
<p align="left">Total Sum of Squares: 2381400<br>Residual Sum of Squares: 548900<br>F-statistic: 328.837 on 2 and 197 DF, p-value: < 2.22e-16<br>> phtest(femod, remod)</p><div>
<p align="left"> Hausman Test</p>
<p align="left">data: fm <br>chisq = 2.3304, df = 2, p-value = 0.3119<br>alternative hypothesis: one model is inconsistent </p>
</div><p align="left">###end Plm###</p>
<p align="left"> </p></font></font><br><br><br></div><div><div></div><div>
<div class="gmail_quote">On Mon, May 18, 2009 at 6:01 AM, Millo Giovanni <span dir="ltr"><<a href="mailto:Giovanni_Millo@generali.com" target="_blank">Giovanni_Millo@generali.com</a>></span> wrote:<br>
<blockquote style="border-left: 1px solid rgb(204, 204, 204); margin: 0px 0px 0px 0.8ex; padding-left: 1ex;" class="gmail_quote">Dear Steve,<br><br>I got your inquiry courtesy of Christian Kleiber, who brought it to our<br>
attention: please next time you post anything re a given package,<br>
include the maintainer's address. We cannot guarantee to parse all the<br>daily digests of the R system!<br><br>Your problem: can you please provide a reproducible example? Else it is<br>difficult to help, not knowing your data, your results and even the<br>
Stata version you're using.<br><br>In the following I replicate what you might have done on a well-known<br>dataset.<br><br>From Stata10, on the usual Grunfeld data taken from package "Ecdat":<br><br>## begin Stata10 output ##<br>
. xtreg inv value capital<br><br>Random-effects GLS regression Number of obs =<br>200<br>Group variable: firm Number of groups =<br>10<br><br>R-sq: within = 0.7668 Obs per group: min =<br>
20<br> between = 0.8196 avg =<br>20.0<br> overall = 0.8061 max =<br>20<br><br>Random effects u_i ~ Gaussian Wald chi2(2) =<br>
657.67<br>corr(u_i, X) = 0 (assumed) Prob > chi2 =<br>0.0000<br><br>------------------------------------------------------------------------<br>------<br> inv | Coef. Std. Err. z P>|z| [95% Conf.<br>
Interval]<br>-------------+----------------------------------------------------------<br>------<br> value | .1097811 .0104927 10.46 0.000 .0892159<br>.1303464<br> capital | .308113 .0171805 17.93 0.000 .2744399<br>
.3417861<br> _cons | -57.83441 28.89893 -2.00 0.045 -114.4753<br>-1.193537<br>-------------+----------------------------------------------------------<br>------<br> sigma_u | 84.20095<br> sigma_e | 52.767964<br>
rho | .71800838 (fraction of variance due to u_i)<br>------------------------------------------------------------------------<br>------<br><br>. estimates store remod<br><br>. xtreg inv value capital, fe<br><br>
Fixed-effects (within) regression Number of obs =<br>200<br>Group variable: firm Number of groups =<br>10<br><br>R-sq: within = 0.7668 Obs per group: min =<br>
20<br> between = 0.8194 avg =<br>20.0<br> overall = 0.8060 max =<br>20<br><br> F(2,188) =<br>
309.01<br>corr(u_i, Xb) = -0.1517 Prob > F =<br>0.0000<br><br>------------------------------------------------------------------------<br>------<br> inv | Coef. Std. Err. t P>|t| [95% Conf.<br>
Interval]<br>-------------+----------------------------------------------------------<br>------<br> value | .1101238 .0118567 9.29 0.000 .0867345<br>.1335131<br> capital | .3100653 .0173545 17.87 0.000 .2758308<br>
.3442999<br> _cons | -58.74393 12.45369 -4.72 0.000 -83.31086<br>-34.177<br>-------------+----------------------------------------------------------<br>------<br> sigma_u | 85.732501<br> sigma_e | 52.767964<br>
rho | .72525012 (fraction of variance due to u_i)<br>------------------------------------------------------------------------<br>------<br>F test that all u_i=0: F(9, 188) = 49.18 Prob > F =<br>
0.0000<br><br>. estimates store femod<br><br>. hausman femod remod<br><br> ---- Coefficients ----<br> | (b) (B) (b-B)<br>sqrt(diag(V_b-V_B))<br> | femod remod Difference S.E.<br>
-------------+----------------------------------------------------------<br>------<br> value | .1101238 .1097811 .0003427 .0055213<br> capital | .3100653 .308113 .0019524 .0024516<br>
------------------------------------------------------------------------<br>------<br> b = consistent under Ho and Ha; obtained from<br>xtreg<br> B = inconsistent under Ha, efficient under Ho; obtained from<br>
xtreg<br><br> Test: Ho: difference in coefficients not systematic<br><br> chi2(2) = (b-B)'[(V_b-V_B)^(-1)](b-B)<br> = 2.33<br> Prob>chi2 = 0.3119<br>
<br>.<br>## end Stata10 output ##<br><br>while from plm I get<br><br>## begin R putput ##<br>> data(Grunfeld, package="Ecdat")<br>> fm <- inv~value+capital<br>><br>> femod <- plm(fm, Grunfeld)<br>
> remod <- plm(fm, Grunfeld, model="random")<br>><br>> phtest(femod, remod)<br><br> Hausman Test<br><br>data: fm<br>chisq = 2.3304, df = 2, p-value = 0.3119<br>alternative hypothesis: one model is inconsistent<br>
<br>## end R output ##<br><br>which, besides testifying to the goodness and parsimony of an<br>object-oriented approach as far as screen output is concerned, looks<br>rather consistent to me.<br><br>I cannot but guess that the problem might stem from different RE<br>
estimates: previous versions of Stata used the Wallace-Hussein method by<br>default for computing the variance of random effects. Now Stata uses<br>Swamy-Arora, which has been the default of 'plm' since the beginning.<br>
Yet as plm() allows to choose, you can experiment with different values<br>for the 'random.method' argument in order to see if you get the Stata<br>result. I suggest you start by comparing the coefficient estimates you<br>
get from Stata and R: FE should be unambiguous, RE might vary as said<br>above, and for good reason.<br><br>You also didn't tell us whether your by-hand calculation agrees with<br>phtest() output? (I guess it does not)<br>
<br>Please let us know, possibly with a reproducible example and providing<br>all the above info<br>Giovanni<br><br>PS please also make sure you're not using any VEEEEERY old version of<br>'plm' (prior to, say, 0.3): these had a bug in the p-value calculation<br>
which made it depend on the order of models compared (so that in the<br>wrong case you got p.value=1).<br><br>Giovanni Millo<br>Research Dept.,<br>Assicurazioni Generali SpA<br>Via Machiavelli 4,<br>34132 Trieste (Italy)<br>
tel. +39 040 671184<br>fax +39 040 671160<br><br>> ----------------------------------------------------------------------<br>> --<br>><br>> Subject:<br>> [R-SIG-Finance] Chi-sq Hausman test---R vs Stata<br>
> From:<br>> Steven Archambault <<a href="mailto:archstevej@gmail.com" target="_blank">archstevej@gmail.com</a>><br>> Date:<br>> Sun, 17 May 2009 23:14:13 -0600<br>> To:<br>> <a href="mailto:r-sig-finance@stat.math.ethz.ch" target="_blank">r-sig-finance@stat.math.ethz.ch</a><br>
><br>> To:<br>> <a href="mailto:r-sig-finance@stat.math.ethz.ch" target="_blank">r-sig-finance@stat.math.ethz.ch</a><br>><br>><br>> Hi all,<br>><br>> I am running a panel time series regression testing Fixed Effects and<br>
> Random Effects. I decided to calculate the chi-sq value for the<br>> Hausman test in both R (Phtest) and Stata. I get different results.<br>> Even within Stata, calculating the Chi-sq value with the canned<br>
> procedure or by hand (using<br>
> matrices) gives different results. So, the question should come up<br>there as<br>> well.<br>><br>> Does anybody have any insight on how to pick which results to use? I<br>> guess the one that gives the result I want? Having different programs<br>
> give quite different values for the same tests is frustrating me. I'd<br><br>> be interested in any feedback folks have!<br>><br>> Thanks,<br>> Steve<br>><br>> [[alternative HTML version deleted]]<br>
</blockquote></div><br>
</div></div></blockquote></div><br>