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anova comparisons
3 messages · Robert Zimbardo, Rolf Turner, Peter Dalgaard
On 02/23/2013 08:55 PM, Robert Zimbardo wrote:
I have several linear models on the same data: m1 <- lm(y ~ poly(x,1)) m2 <- lm(y ~ poly(x,2)) m3 <- lm(y ~ poly(x,3)) What I don't understand is why anova(m1, m2, m3, test="F") - yields the same RSS and SS values, but a different p-value from anova(m1, m2, test="F") - when it also yields the SAME as anova(m2, m3, test="F") What am I missing?
A basic understanding of the theory of linear models. This really has
little
to do with R. Go and read a good intro to linear modelling.
Insofar as your question has anything to do with R:
When you do
anova(m1, m2, m3, test="F")
the mean squared error from m3 is used as the denominator of the F
statistic.
When you do
anova(m1, m2, test="F")
the mean squared error from m2 is used as the denominator of the F
statistic.
cheers,
Rolf Turner
On Feb 23, 2013, at 10:06 , Rolf Turner wrote:
What am I missing?
A basic understanding of the theory of linear models. This really has little to do with R. Go and read a good intro to linear modelling. Insofar as your question has anything to do with R: When you do anova(m1, m2, m3, test="F") the mean squared error from m3 is used as the denominator of the F statistic. When you do anova(m1, m2, test="F") the mean squared error from m2 is used as the denominator of the F statistic.
Maybe a bit quick there. It's actually about (computer) conventions for ANOVA tables; the theory would prefer you to do what the poster expects: Test sequentially and update the denominator MS along the route. However, lazy programmers (and before them lazy practising statisticians) decided that it is easier to use the MS from the biggest model throughout. (There's also a post-hoc argument, that said MS is less susceptible to small departures from the model assumptions, but I'd say that the main reason is convenience.) Even though it is a common convention, you do need exposure to at least one statistical computer program or one traditional analysis of variance textbook to see it.
Peter Dalgaard, Professor, Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd.mes at cbs.dk Priv: PDalgd at gmail.com