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| From | "Roger B. Newson" <r.newson@imperial.ac.uk> |
| To | statalist@hsphsun2.harvard.edu |
| Subject | Re: AW: st: Missing confidence intervals for median after using -bootstrap- or -bpmedian- |
| Date | Wed, 14 Nov 2012 11:17:19 +0000 |
Pr(Y<theta)-Pr(Y>theta)=0so, if there is only one credible solution, then it will be surrounded by a zero-width confidence interval.)
I hope this helps. Best wishes Roger Roger B Newson BSc MSc DPhil Lecturer in Medical Statistics Respiratory Epidemiology and Public Health Group National Heart and Lung Institute Imperial College London Royal Brompton Campus Room 33, Emmanuel Kaye Building 1B Manresa Road London SW3 6LR UNITED KINGDOM Tel: +44 (0)20 7352 8121 ext 3381 Fax: +44 (0)20 7351 8322 Email: r.newson@imperial.ac.uk Web page: http://www.imperial.ac.uk/nhli/r.newson/ Departmental Web page: http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/ Opinions expressed are those of the author, not of the institution. On 13/11/2012 22:55, Vasyl Druchkiv wrote:
Hello Nick and Roger, thank you for your quick reply! Sorry, that I haven't provided background to the data. The variable from the example contains astigmatism of the eyes that describes cornea steepness. This variable is not symmetric. In fact it is extremely skewed to the left. To get an idea of the data here are some descriptive statistics: astigmatism ------------------------------------------------------------- Percentiles Smallest 1% -4.5 -7 5% -3 -6.5 10% -2.3 -6.5 Obs 16872 25% -1.3 -6.5 Sum of Wgt. 16872 50% -.8 Mean -1.005293 Largest Std. Dev. .9449402 75% -.3 0 90% 0 0 Variance .8929119 95% 0 0 Skewness -1.812464 99% 0 0 Kurtosis 7.150496 So, you can see that the variable is not a constant one: there is a variation, although 54% of the eyes had an astigmatism of -.8. I've applied already -parmest- (-bpmedian- and -parmest- I downloaded from SSC) as suggested by Roger and indeed got the confidence intervals that are equal to median. However it is not only the confidence intervals that concern me. In another case I try to run a quantile regression with bootstrap estimation method and the difference between thinnest and central points of the cornea as dependent variable. The dependent variable is also not symmetric and has positive skewness: cct-tpct ------------------------------------------------------------- Percentiles Smallest 1% 3 0 5% 4 0 10% 4 1 Obs 16872 25% 5 1 Sum of Wgt. 16872 50% 8 Mean 9.485479 Largest Std. Dev. 8.423524 75% 11 122 90% 16 124 Variance 70.95575 95% 20 380 Skewness 14.34001 99% 33 380 Kurtosis 487.1662 When I use for instance ocular side (right/left) as a dummy independent variable I get: Median regression, bootstrap(20) SEs Number of obs = 16872 Raw sum of deviations 68401 (about 8) Min sum of deviations 68061 Pseudo R2 = 0.0050 ------------------------------------------------------------------------------ ccttpct | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- eye | -1 . . . . . _cons | 8 . . . . . ------------------------------------------------------------------------------ So, there is a difference between eyes. However there are no statistics to report. Of course I could use for example Wilcoxon signed-rank test to check the differences (and would probably find insignificant results). But my idea is to fit a multivariate model with more independent variables. If you could help me further it would be great. Thank you in advance and sorry, if I was unclear about some points. Best regards, Vasyl -----Ursprüngliche Nachricht----- Von: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] Im Auftrag von Roger B. Newson Gesendet: Tuesday, November 13, 2012 12:50 PM An: statalist@hsphsun2.harvard.edu Betreff: Re: st: Missing confidence intervals for median after using -bootstrap- or -bpmedian- The problem here seems to me to be a zero standard error for the median, caused by a zero variance for the median, caused by a constant variable. For some reason, Stata is displaying the confidence interval as if the standard error was missing. This may possibly have something to do with version control (-bpmedian- is a Stata Version 10 command). For what it's worth, the -parmest- package (also downloadable from SSC) displays the confidence intervals for a Bonett-Price median of a constant variable "correctly", with a zero standard error and upper and lower confidence linits equal to the median. After -bpmedian-, the user may type parmest, list(,) and display the "correct" confidence interval. You might also like to try using the -sccendif- module of the -scsomersd- package, which can also be downloaded from SSC, and which also calculates confidence intervals for medians, allowing the possibility of clustering and/or sampling-probability weights. I hope this helps. Best wishes Roger Roger B Newson BSc MSc DPhil Lecturer in Medical Statistics Respiratory Epidemiology and Public Health Group National Heart and Lung Institute Imperial College London Royal Brompton Campus Room 33, Emmanuel Kaye Building 1B Manresa Road London SW3 6LR UNITED KINGDOM Tel: +44 (0)20 7352 8121 ext 3381 Fax: +44 (0)20 7351 8322 Email: r.newson@imperial.ac.uk Web page: http://www.imperial.ac.uk/nhli/r.newson/ Departmental Web page: http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/ Opinions expressed are those of the author, not of the institution. On 13/11/2012 00:49, Nick Cox wrote:I am not a statistician; in fact many, perhaps most, people on this list wouldn't call themselves statisticians. You are asked to make clear where user-written programs you refer to come from. -bpmedian- is from SSC or Roger Newson's website. You don't tell us anything much about your data, either what it is (the name "var" is not revealing) or any descriptive statistics. But I see you have a large sample size. It seems likely therefore that the confidence interval for anything will be narrow at worst. However, it seems likely also from your results that you have lots of ties. If so, the unusual result of a confidence interval of length 0 is likely to be an artefact of coarseness in data recording. If so, then reporting a confidence interval isn't really possible, as it should be more like .8 +/- smidgen where smidgen is less than the resolution of measurement. By resolution, I mean the minimum difference between reported measurements. If possible data are values like .7, .8, .9 the resolution is 0.1. Conversely, if I were reviewing or examining this research, I would want a report on the fraction of values that were recorded as .8. In fact I would want a graph of the data. Of course, you may intend to do all that. Nick On Mon, Nov 12, 2012 at 9:32 PM, Vasyl Druchkiv <dvv1985@yahoo.de> wrote:Dear statisticians, I try to estimate CI's for the median with -bpmedian- or with -bootstrap- using *--------------------- begin example ------------------ centile var bootstrap median=r(p50): sum var, detail *--------------------- end example -------------------- The problem is that I get empty cells on standard error and confidence intervals either by implementing -bpmediam- or -bootstrap-. *--------------------- begin example ------------------ Bonett-Price confidence interval for median of: var Number of observations: 16872 --------------------------------------------------------------------- ------- -- var | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+------------------------------------------------------- -------------+------- -- _cons | -.8 . . . . . *--------------------- end example ------------------ I looked for the calculation method used in -bpmedian- . This method is described in: Bonett, D. G. and Price, R. M. 2002. Statistical inference for a linear function of medians: Confidence intervals, hypothesis testing, and sample size requirements. Psychological Methods 7(3): 370-383. Furthermore, I tried to estimate CI's with SPSS using bootstrap and got (-0.8;-0.8) for 95% CI's. It means that the problem occurs when both limits coincide with the median. However, the method described in Bonnett-Price uses the formula: sum(cjηj)±Za/2(sum(cj2varηj))^1/2 (pp: 372) So, even if the last term is equal to 0 due to the pointy distribution (var ηj=0), lower and upper limits must be displayed in stata output and be equal to -0.8 in my example. Can I just assume that CI's are equal to median?* * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/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/faqs/resources/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/faqs/resources/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/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/