I am wondering how to interpret the parameter estimates that lm() reports in this sort of situation:
y = round(rnorm(n=24,mean=5,sd=2),2) A = gl(3,2,24,labels=c("one","two","three")) B = gl(4,6,24,labels=c("i","ii","iii","iv")) # Make both observations for A=1, B=4 missing y[19] = NA y[20] = NA data.frame(y,A,B) nonadd = lm(y ~ A * B)
summary(nonadd)
Call: lm(formula = y ~ A * B) Residuals: Min 1Q Median 3Q Max -3.555e+00 -7.675e-01 -6.939e-17 7.675e-01 3.555e+00 Coefficients: (1 not defined because of singularities) Estimate Std. Error t value Pr(>|t|) (Intercept) 3.755 1.667 2.252 0.0457 * Atwo 1.655 2.358 0.702 0.4974 Athree 3.330 2.358 1.412 0.1856 Bii 1.435 2.358 0.609 0.5552 Biii 2.055 2.358 0.871 0.4021 Biv -1.635 2.358 -0.693 0.5025 Atwo:Bii -1.145 3.335 -0.343 0.7378 Athree:Bii -4.535 3.335 -1.360 0.2011 Atwo:Biii -3.230 3.335 -0.969 0.3536 Athree:Biii -2.105 3.335 -0.631 0.5408 Atwo:Biv 1.655 3.335 0.496 0.6295 Athree:Biv NA NA NA NA --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 2.358 on 11 degrees of freedom (2 observations deleted due to missingness) Multiple R-squared: 0.2797, Adjusted R-squared: -0.3752 F-statistic: 0.4271 on 10 and 11 DF, p-value: 0.9044
fitted(nonadd)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 21 3.755 3.755 5.410 5.410 7.085 7.085 5.190 5.190 5.700 5.700 3.985 3.985 5.810 5.810 4.235 4.235 7.035 7.035 5.430 22 23 24 5.430 5.450 5.450
t(model.matrix(nonadd)%*%coef(nonadd))
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 21 22 23 24 [1,] NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA I guess that the parameter estimates reported are linear combinations of the cell means, but which linear combinations and how does lm() decide what parameters to report? Cheers, Murray -- Dr Murray Jorgensen http://www.stats.waikato.ac.nz/Staff/maj.html Department of Statistics, University of Waikato, Hamilton, New Zealand Email: m...@waikato.ac.nz Fax 7 838 4155 Phone +64 7 838 4773 wk Home +64 7 825 0441 Mobile 021 0200 8350 ______________________________________________ R-help@r-project.org 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.