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From |
"Joseph Coveney" <jcoveney@bigplanet.com> |

To |
"Statalist" <statalist@hsphsun2.harvard.edu> |

Subject |
Re: st: ttest or xtmelogit? |

Date |
Tue, 11 Mar 2008 13:36:18 +0900 |

David Airey wrote: I have a typical pilot data set. Small. I have 12 mice, 6 from one group, 6 from another. For each mouse I have about 50 yes/no scores. 50 was enough to get precision on a given mouse. I'm interested in the group difference. In the past I used xtgee with mouse as the i(mouse) option, i.e., mouse as the cluster, with family(binomial) and link(logit). But previously, I did this with double the number of mice, so I felt I had enough clusters. Here, I am feeling uncomfortable about the number of clusters (12). The same goes for xtmelogit, new in Stata 10. Given the number of mice, is it better to simply transform the summary statistics for animals (mean of the yes/ no vector by animal), like with an arcsine or logit, and use a ttest? -------------------------------------------------------------------------------- Unless the intraclass correlation is high, the distribution of sums of 50 binary observations per mouse should look quite normal-like, even with expectations in the neighborhood of 10% or 90%. Also, the t test is supposed to be reasonably robust, absent skew. It looks like the t test would work with untransformed sum scores of 50 observations for each of 12 mice within a reasonable range of intraclass correlations (see simulation do-file below). The simulation compares untransformed sum scores to logit-transformed mean scores (with the same fix-up for floors and ceilings as used in the arcsine-of-square-root tranform). As you might expect from the fix-up moving everything toward the middle, untransformed sum scores comes out ahead in power. Both maintain Type I error rate well. It would be interesting to see how Jeff Herrin's -cltest- would fare by comparison, but it doesn't seem to return scalars for -simulate- to grab onto. Joseph Coveney clear * set more off set seed `=date("2008-03-11", "YMD")' set seed0 `=date("2008-03-11", "YMD")' * capture program drop simem program define simem, rclass version 10 syntax [, delta(real 0) s(real 0)] tempname p_t drop _all set obs 12 generate byte mouse = _n generate byte trt = mod(_n, 2) generate double mu = 0.5 + trt * `delta' + /// `s' * _pi / sqrt(3) * invnormal(uniform()) generate byte den = 50 rndbinx mu den generate double pos_prim = bnlx replace pos_prim = 50 - 1 / 2 / 50 if pos_prim == 50 replace pos_prim = 1 / 2 / 50 if !pos_prim generate double logit_pi = logit( pos_prim / den) ttest bnlx, by(trt) scalar define `p_t' = r(p) ttest logit_pi, by(trt) return scalar p_l = r(p) return scalar p_t = `p_t' end * * Test size * forvalues s = 0.1(0.1)0.5 { display in smcl as text _newline(1) "Null hypothesis; s = `s'" quietly simulate t = r(p_t) l = r(p_l), reps(300) nodots: simem , s(`s') foreach var of varlist t l { generate byte pos_`var' = `var' < 0.05 } summarize pos_* } * * Relative power * forvalues s = 0.1(0.1)0.5 { forvalues delta = 0.1(0.05)0.2 { display in smcl as text _newline(1) "Delta = `delta'; s = `s'" quietly simulate t = r(p_t) l = r(p_l), reps(300) nodots: /// simem , s(`s') delta(`delta') foreach var of varlist t l { generate byte pos_`var' = `var' < 0.05 } summarize pos_* } } exit * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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