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Re: AW: st: Missing confidence intervals for median after using -bootstrap- or -bpmedian-
From
"Roger B. Newson" <[email protected]>
To
[email protected]
Subject
Re: AW: st: Missing confidence intervals for median after using -bootstrap- or -bpmedian-
Date
Wed, 14 Nov 2012 11:17:19 +0000
Thanks for the clarification. How many subjects have a value of
-astigmatism- of exactly -0.8? I ask because zero standard errors (and
zero-width confidence intervals) for the median can also occur when a
large number of observations have a value exactly equal to the median.
This is because, in this case, the population median can only really
have that value, because any other candidate value theta clearly has the
property that Pr(Y<theta)-Pr(Y>theta) is nonzero (where Y is the
variable being measured). (Recall that a median is defined as a solution
in theta to the equation
Pr(Y<theta)-Pr(Y>theta)=0
so, 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: [email protected]
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: [email protected] [mailto:[email protected]] Im Auftrag von Roger B. Newson
Gesendet: Tuesday, November 13, 2012 12:50 PM
An: [email protected]
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: [email protected]
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 <[email protected]> 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?
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