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From |
"JVerkuilen (Gmail)" <jvverkuilen@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Bootstrapping question |

Date |
Fri, 8 Feb 2013 09:00:20 -0500 |

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:*Nick Cox <njcoxstata@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>

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