Thanks to all for the very helpful replies & the reference to a chapter in MASS!
Sven On Tue, 2007-08-07 at 12:07 -0400, Gabor Grothendieck wrote: > Also check this post > > https://stat.ethz.ch/pipermail/r-help/2007-May/132866.html > > for a number of formulations. > > On 8/7/07, Ted Harding <[EMAIL PROTECTED]> wrote: > > On 07-Aug-07 15:34:13, Gabor Grothendieck wrote: > > > In the single model all three levels share the same intercept which > > > means that the slope must change to accomodate it > > > whereas in the three separate models they each have their own > > > intercept. > > > > I think this arose because of the formulation of the "model with > > interaction" as: > > > > summary(lm(y~x:f, data=d)) > > > > If it has been formulated as > > > > summary(lm(y~x*f, data=d)) > > > > there would be three separate intercepts, and three different slopes > > (and the differences would be the same as the differences for the > > separate models). > > > > Ted. > > > > > Try looking at it graphically and note how the black dotted lines > > > are all forced to go through the same intercept, i.e. the same point > > > on the y axis, whereas the red dashed lines are each able to > > > fit their portion of the data using both the intercept and the slope. > > > > > > y.lm <- lm(y~x:f, data=d) > > > plot(y ~ x, d, col = as.numeric(d$f), xlim = c(-5, 20)) > > > for(i in 1:3) { > > > abline(a = coef(y.lm)[1], b = coef(y.lm)[1+i], lty = "dotted") > > > abline(lm(y ~ x, d[as.numeric(d$f) == i,]), col = "red", lty = > > > "dashed") > > > } > > > grid() > > > > > > > > > On 8/7/07, Sven Garbade <[EMAIL PROTECTED]> wrote: > > >> Dear list members, > > >> > > >> I have problems to interpret the coefficients from a lm model > > >> involving > > >> the interaction of a numeric and factor variable compared to separate > > >> lm > > >> models for each level of the factor variable. > > >> > > >> ## data: > > >> y1 <- rnorm(20) + 6.8 > > >> y2 <- rnorm(20) + (1:20*1.7 + 1) > > >> y3 <- rnorm(20) + (1:20*6.7 + 3.7) > > >> y <- c(y1,y2,y3) > > >> x <- rep(1:20,3) > > >> f <- gl(3,20, labels=paste("lev", 1:3, sep="")) > > >> d <- data.frame(x=x,y=y, f=f) > > >> > > >> ## plot > > >> # xyplot(y~x|f) > > >> > > >> ## lm model with interaction > > >> summary(lm(y~x:f, data=d)) > > >> > > >> Call: > > >> lm(formula = y ~ x:f, data = d) > > >> > > >> Residuals: > > >> Min 1Q Median 3Q Max > > >> -2.8109 -0.8302 0.2542 0.6737 3.5383 > > >> > > >> Coefficients: > > >> Estimate Std. Error t value Pr(>|t|) > > >> (Intercept) 3.68799 0.41045 8.985 1.91e-12 *** > > >> x:flev1 0.20885 0.04145 5.039 5.21e-06 *** > > >> x:flev2 1.49670 0.04145 36.109 < 2e-16 *** > > >> x:flev3 6.70815 0.04145 161.838 < 2e-16 *** > > >> --- > > >> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 > > >> > > >> Residual standard error: 1.53 on 56 degrees of freedom > > >> Multiple R-Squared: 0.9984, Adjusted R-squared: 0.9984 > > >> F-statistic: 1.191e+04 on 3 and 56 DF, p-value: < 2.2e-16 > > >> > > >> ## separate lm fits > > >> lapply(by(d, d$f, function(x) lm(y ~ x, data=x)), coef) > > >> $lev1 > > >> (Intercept) x > > >> 6.77022860 -0.01667528 > > >> > > >> $lev2 > > >> (Intercept) x > > >> 1.019078 1.691982 > > >> > > >> $lev3 > > >> (Intercept) x > > >> 3.274656 6.738396 > > >> > > >> > > >> Can anybody give me a hint why the coefficients for the slopes > > >> (especially for lev1) are so different and how the coefficients from > > >> the > > >> lm model with interaction are related to the separate fits? > > >> > > >> Thanks, Sven ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.