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From |
"Airey, David C" <david.airey@vanderbilt.edu> |

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

Subject |
Re: st: Stumped...xtmixed and ANOVA F-stats not agreeing for balanced design |

Date |
Fri, 6 May 2011 08:47:16 -0500 |

. Math is helpful! I think I remember reading the mixed model routine in JMP 9 allows negative estimates of variance components. I don't quite understand the choice between SAS and StataCorp statisticians on this point. > Except for the residual, mean squares for random effects in ANOVA are functions > of the variance components, but they aren't the same as the variance components. > So, the values for variances for s, a and b from -xtmixed- won't be the same as > the corresponding mean squares in -anova-. > > By setting the mean squares from your ANOVA table against their expectations and > solving for the variance components, I get the following: > > MS_e = 0.00273899 = sigma2_e > MS_s#a = 0.012825848 = sigma2_e + 2 * sigma2_s#a > MS_s#b = 0.014614037 = sigma2_e + 3 * sigma2_s#b > MS_s = 0.02026831 = sigma2_e + 6 * sigma2_s + 2 * sigma2_s#a + 3 * sigma2_s#b > > sigma2_s#a = (0.012825848 - 0.00273899) / 2 = 0.00504343 > sigma2_s#b = (0.014614037 - 0.00273899) / 3 = 0.00395835 > sigma2_s = (0.02026831 - 0.01008686 - 0.01187505) / 6 = -0.00028227 > > You can see that -anova-'s estimate for the variance of s is negative. > Least-squares (ANOVA) allows negative variance components, but -xtmixed- > doesn't. > > So the model fit by -xtmixed- is slightly different from the one fit by -anova- > in this case. That's why the F statistics aren't the same. > > Joseph Coveney > * * 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/

**Follow-Ups**:**Re: st: Stumped...xtmixed and ANOVA F-stats not agreeing for balanced design***From:*"Joseph Coveney" <jcoveney@bigplanet.com>

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