(previous post bounced due to GPG wrapper)
Daniel Ezra Johnson wrote:
Hi, This is from the help file for logLik():
x <- 1:5 lmx <- lm(x ~ 1) logLik(lmx)
log Lik.' -8.82756 (df=2) Two questions: 1) doesn't the model lmx have one degree of freedom, not two?
If you count the implicit variance, it has two.
2) how is this log-likelihood calculated?
see stats:::logLik.lm : the core is
val <- 0.5 * (sum(log(w)) - N * (log(2 * pi) + 1 - log(N) +
log(sum(w * res^2))))
where res are residuals, w are weights, N is the number of points
If I have two nested linear models (say lm models, not worrying about mixed models here), I know how to compare them using an F-test, but I don't understand the difference (if there is one) between using an F-test and using a likelihood-ratio test.
The likelihood ratio test is asymptotic, so you should use an F test if you're in a situation where it's appropriate. x <- rnorm(100) > y <- 1+2*x+rnorm(100,sd=1)
lm2 <- lm(y~x) lm1 <- lm(y~1) anova(lm2,lm1)
Analysis of Variance Table Model 1: y ~ x Model 2: y ~ 1 Res.Df RSS Df Sum of Sq F Pr(>F) 1 98 94.16 2 99 492.44 -1 -398.29 414.54 < 2.2e-16 *** --- Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1 str() shows that the actual p-value is 5.54e-37
pchisq(2*(logLik(lm2)-logLik(lm1)),1,lower.tail=FALSE)
[1] 7.325424e-38 attr(,"nall") [1] 100 attr(,"nobs") [1] 100 attr(,"df") [1] 3 attr(,"class") [1] "logLik"
Ben Bolker Associate professor, Biology Dep't, Univ. of Florida bolker at ufl.edu / www.zoology.ufl.edu/bolker GPG key: www.zoology.ufl.edu/bolker/benbolker-publickey.asc