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From |
Nick Cox <njcoxstata@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Bootstrapping question |

Date |
Fri, 8 Feb 2013 14:11:24 +0000 |

I agree, but note the bottom line, namely that Henry's problem is about an ordinal variable with several proportions. As a minute point, Jeffreys' procedure has a frequentist interpretation as a continuity-corrected version of the so-called exact (Clopper-Pearson) confidence interval. See -ssc type cij.hlp- and the embedded references. (-cij-, -ciji- and -ciw-, -ciwi- on SSC were superseded when StataCorp added those procedures to official -ci-, -cii- but the help files include some details that never got into -ci- documentation.) Nick On Fri, Feb 8, 2013 at 2:00 PM, JVerkuilen (Gmail) <jvverkuilen@gmail.com> wrote: > I think you might get a lot of benefit out of either a full likelihood > or Bayesian analysis, but these aren't necessarily easy. > > Here's an example if you had binomial data with N = 10, with y = 0 successes. > > L(p) = (1 - p)^10 > > > It turns out that L(p) is maximized at p = 0.0 (as one would expect), > but this is of course a silly estimate for a probability, and the Wald > interval is even sillier. Try > > cii 10 0, wald > > To determine 95% confidence interval from the likelihood function, > find the p such that L(p) = 0.15, which is equivalent to -2 LL(p) = > 3.84, for the .05 cutoff for a chi square(1). This can be done > analytically with the likelihood above, but in general you need to > solve it numerically. If you read off the table of values you find > that the upper limit of the likelihood based confidence interval is > 0.175. > > (One intermediate step is to normalize the likelihood such that the > maximum value is scaled to equal 1. It's not needed here because the > maximum value is 1.) In Stata the easiest way to do this is simply to > generate p and the relevant likelihood (or equivalently -2 > log-likelihood) and plot. > > Example: > > set obs 101 > range temp 1 101 > gen p = (temp - 1)/100 > drop temp > gen L = (1 - p)^10 > quietly sum L > gen L0 = L/r(max) > twoway (connected L0 p, sort) > > > (Try all the other cii options such as wilson, agresti, jeffreys, too. > Jeffreys is a Bayesian method that's very close to what I show.) Your > problem is more complicated because it's multinomial, but this general > approach might help. > > See Yudi Pawitan. (2001), In All Likelihood, Oxford. > http://ukcatalogue.oup.com/product/9780198507659.do#.URR6e1qLzQA * * 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/

**Follow-Ups**:**Re: st: Bootstrapping question***From:*"JVerkuilen (Gmail)" <jvverkuilen@gmail.com>

**References**:**Re: st: Problem with standard errors using eststo***From:*Johan Hellström <johan.hellstrom@pol.umu.se>

**st: Bootstrapping question***From:*"Ilian, Henry (ACS)" <Henry.Ilian@dfa.state.ny.us>

**Re: st: Bootstrapping question***From:*Maarten Buis <maartenlbuis@gmail.com>

**Re: st: Bootstrapping question***From:*Nick Cox <njcoxstata@gmail.com>

**RE: st: Bootstrapping question***From:*"Ilian, Henry (ACS)" <Henry.Ilian@dfa.state.ny.us>

**Re: st: Bootstrapping question***From:*Nick Cox <njcoxstata@gmail.com>

**Re: st: Bootstrapping question***From:*Steve Samuels <sjsamuels@gmail.com>

**Re: st: Bootstrapping question***From:*Nick Cox <njcoxstata@gmail.com>

**RE: st: Bootstrapping question***From:*"Ilian, Henry (ACS)" <Henry.Ilian@dfa.state.ny.us>

**Re: st: Bootstrapping question***From:*Nick Cox <njcoxstata@gmail.com>

**RE: st: Bootstrapping question***From:*"Ilian, Henry (ACS)" <Henry.Ilian@dfa.state.ny.us>

**Re: st: Bootstrapping question***From:*Nick Cox <njcoxstata@gmail.com>

**RE: st: Bootstrapping question***From:*"Ilian, Henry (ACS)" <Henry.Ilian@dfa.state.ny.us>

**Re: st: Bootstrapping question***From:*Nick Cox <njcoxstata@gmail.com>

**Re: st: Bootstrapping question***From:*"JVerkuilen (Gmail)" <jvverkuilen@gmail.com>

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