I?m confused by the difference in the fit of a gam model (in package mgcv)
when I specify an interaction in different ways. I would appreciate it if
someone could explain the cause of these differences.
For example:
x <- c(105, 124, 124, 124, 144, 144, 150, 176, 178, 178,
206, 206, 212, 215, 215, 227, 229, 229, 229, 234,
234, 254, 254, 290, 290, 303, 334, 334, 334, 344,
345, 345)
y <- c(0.31, 1.41, 2.87, 1.92, 0.31, 0.31, 0.31, 0.31, 0.31, 0.31,
0.31, 0.31, 0.31, 1.92, 0.31, 0.31, 0.31, 0.31, 0.31, 0.31,
0.31, 2.08, 2.28, 1.59, 2.13, 2.77, 3.97, 4.54, 4.35, 3.6,
5.2, 4.6)
loc <- c("S", "N", "S", "S", "N", "N", "S", "S", "N", "N",
"N", "N", "S", "N", "S", "S", "N", "S", "S", "N",
"N", "N", "N", "N", "N", "S", "N", "S", "S", "N",
"S", "S")
locf <- as.factor(loc)
locN <- as.numeric(loc=="N")
locS <- as.numeric(loc=="S")
# fit the model with a separate smooth for loc = N and loc = S
fit1 <- gam(y ~ locf + s(x, by=locN) + s(x, by=locS))
# fit the model with a separate smooth for each level of the factor loc (N
and S)
fit2 <- gam(y ~ locf + s(x, by=locf))
# The shape of the relations are similar, but the vertical locations are
different,
# and the size of the standard errors of the smooth are different
windows()
par(mfrow=c(2, 2), mar=c(4, 4, 2, 1))
plot(fit1)
plot(fit2)
# The R-sq., deviance explained, GCV score, and scale est. are the same,
# but the estimates and degrees of freedom are different
summary(fit1)
summary(fit2)
I'm using R version 2.13.0 (2011-04-13) and mgcv version 1.7-6 on Windows
XP.
Thanks for your help.
Jean
`·.,, ><(((º> `·.,, ><(((º> `·.,, ><(((º>
Jean V. Adams
Statistician
U.S. Geological Survey
Great Lakes Science Center
223 East Steinfest Road
Antigo, WI 54409 USA
http://www.glsc.usgs.gov (GLSC web site)
jvad...@usgs.gov (E-mail)
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