[R] two-factor linear models with missing cells
David Winsemius
dwinsemius at comcast.net
Mon Aug 3 00:59:18 CEST 2009
Does this help at all?
<after your code...>
> contrasts(A)
two three
one 0 0
two 1 0
three 0 1
> contrasts(B)
ii iii iv
i 0 0 0
ii 1 0 0
iii 0 1 0
iv 0 0 1
> contrasts(A:B)
one:ii one:iii one:iv two:i two:ii two:iii two:iv three:i
three:ii three:iii three:iv
one:i 0 0 0 0 0 0 0
0 0 0 0
one:ii 1 0 0 0 0 0 0
0 0 0 0
one:iii 0 1 0 0 0 0 0
0 0 0 0
one:iv 0 0 1 0 0 0 0
0 0 0 0
two:i 0 0 0 1 0 0 0
0 0 0 0
two:ii 0 0 0 0 1 0 0
0 0 0 0
two:iii 0 0 0 0 0 1 0
0 0 0 0
two:iv 0 0 0 0 0 0 1
0 0 0 0
three:i 0 0 0 0 0 0 0
1 0 0 0
three:ii 0 0 0 0 0 0 0
0 1 0 0
three:iii 0 0 0 0 0 0 0
0 0 1 0
three:iv 0 0 0 0 0 0 0
0 0 0 1
--
David
On Aug 2, 2009, at 6:40 PM, Murray Jorgensen wrote:
> 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
David Winsemius, MD
Heritage Laboratories
West Hartford, CT
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