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From |
"Feiveson, Alan H. (JSC-SK311)" <alan.h.feiveson@nasa.gov> |

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

Subject |
st: RE: Re: RE: re: RM ANOVA, was SPSS vs. Stata |

Date |
Tue, 3 Aug 2010 10:35:13 -0500 |

Phil, and others For larger data sets with high imbalance I don't think there's much doubt that using a mixed model is more flexible and less biased than rpm anova with complete observations only. But for small sample sizes, using infinite degrees of freedom for the denominators (i.e. chi-square statistics rather than F) also creates bias in the inference. What would be nice is to have some way to calculate approximate denominator degrees of freedom after obtaining the pseud0-F statistics with -xtmixed- and -test-. Al Feiveson -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Philip Ender Sent: Tuesday, August 03, 2010 10:24 AM To: statalist@hsphsun2.harvard.edu Subject: st: Re: RE: re: RM ANOVA, was SPSS vs. Stata <robert.ploutz-snyder-1@nasa.gov> had an example of a repeated measures anova in which two of the observations were set to missing. Here are partial results from his Stata output: Between-subjects error term: person Levels: 5 (4 df) Lowest b.s.e. variable: person Repeated variable: drug Huynh-Feldt epsilon = 0.5297 Greenhouse-Geisser epsilon = 0.4228 Box's conservative epsilon = 0.3333 ------------ Prob > F ------------ Source | df F Regular H-F G-G Box -----------+---------------------------------------------------- drug | 3 27.71 0.0000 0.0019 0.0047 0.0102 Residual | 10 ---------------------------------------------------------------- And here are the partial results from his SPSS: IN SPSS (same dataset): Tests of Within-Subjects Effects Source Type III Sum of Squares df Mean Square F Sig. drug Sphericity Assumed 478.333 3 159.444 13.932 .004 Greenhouse-Geisser 478.333 1.268 377.157 13.932 .044 Huynh-Feldt 478.333 2.466 193.938 13.932 .008 Lower-bound 478.333 1.000 478.333 13.932 .065 Error(drug) Sphericity Assume 68.667 6 11.444 Greenhouse-Geisser 68.667 2.537 27.071 Huynh-Feldt 68.667 4.933 13.920 Lower-bound 68.667 2.000 34.333 ---------------------- I prefer using -xtmixed- for repeated measures designs with missing observation. I think that it is far superior to deleting whole cases when only one observation is missing. In this example there are four observations on each subject. Two of them are missing only a single observation. . xtmixed score i.drug || person: Performing EM optimization: Performing gradient-based optimization: Iteration 0: log restricted-likelihood = -43.456003 Iteration 1: log restricted-likelihood = -43.456003 Computing standard errors: Mixed-effects REML regression Number of obs = 18 Group variable: person Number of groups = 5 Obs per group: min = 3 avg = 3.6 max = 4 Wald chi2(3) = 83.43 Log restricted-likelihood = -43.456003 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ score | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- drug | 2 | 1.120543 2.136759 0.52 0.600 -3.067427 5.308514 3 | -10.17271 1.980896 -5.14 0.000 -14.05519 -6.290222 4 | 6.227293 1.980896 3.14 0.002 2.344808 10.10978 | _cons | 25.77271 3.175225 8.12 0.000 19.54938 31.99603 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Random-effects Parameters | Estimate Std. Err. [95% Conf. Interval] -----------------------------+------------------------------------------------ person: Identity | sd(_cons) | 6.26194 2.334319 3.015775 13.00226 -----------------------------+------------------------------------------------ sd(Residual) | 2.901958 .646767 1.874915 4.491595 ------------------------------------------------------------------------------ LR test vs. linear regression: chibar2(01) = 14.32 Prob >= chibar2 = 0.0001 . testparm i.drug ( 1) [score]2.drug = 0 ( 2) [score]3.drug = 0 ( 3) [score]4.drug = 0 chi2( 3) = 83.43 Prob > chi2 = 0.0000 /* rescale chi2 to F */ . display r(chi2)/r(df) 27.808724 The F-ratio given here is actually closer to the F-ratio for the complete data (F=24.76) then the F-ratio produced by SPSS (F=13.932). I this case I have greater trust in -xtmixed- than I do in the SPSS repeated measures. In general, I feel that complete case analysis can lead to greater bias then using a linear mixed model approach. Further, -xtmixed- allows for more covariance structures than repeated measure in SPSS which only allows for compound symmetry (echangable) and unstructured. Phil -- Phil Ender UCLA Statistical Consulting Group * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/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/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: Re: RE: re: RM ANOVA, was SPSS vs. Stata***From:*Philip Ender <ender97@gmail.com>

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