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R version 2.13.0 Under development (unstable) (2011-03-07 r54691)
Copyright (C) 2011 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
Platform: x86_64-unknown-linux-gnu (64-bit)
R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.
R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.
Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.
> ### lmrob() with "real data"
>
> library(robustbase)
>
> set.seed(0)
> data(salinity)
> summary(m0.sali <- lmrob(Y ~ . , data = salinity))
Call:
lmrob(formula = Y ~ ., data = salinity)
Weighted Residuals:
Min 1Q Median 3Q Max
-2.4326 -0.4018 0.1741 0.5272 5.8751
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 18.39327 4.01996 4.575 0.000122 ***
X1 0.71048 0.04938 14.388 2.68e-13 ***
X2 -0.17770 0.14762 -1.204 0.240397
X3 -0.62733 0.15845 -3.959 0.000584 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Robust residual standard error: 1
Convergence in 11 IRWLS iterations
Robustness weights:
observation 16 is an outlier with |weight| = 0 ( < 0.0036);
2 weights are ~= 1. The remaining 25 ones are summarized as
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.5335 0.8269 0.9760 0.9112 0.9952 0.9989
Algorithmic parameters:
tuning.chi bb tuning.psi refine.tol rel.tol
1.5476400 0.5000000 4.6850610 0.0000001 0.0000001
nResample max.it groups n.group best.r.s k.fast.s k.max
500 50 5 400 2 1 200
trace.lev compute.rd numpoints
0 0 10
psi method cov
"bisquare" "MM" ".vcov.avar1"
seed : int(0)
> (A1 <- anova(m0.sali, Y ~ X1 + X3))
Robust Wald Test Table
Model 1: Y ~ X1 + X2 + X3
Model 2: Y ~ X1 + X3
Largest model fitted by lmrob(), i.e. SM
pseudoDf Test.Stat Df Pr(>chisq)
1 24
2 25 1.4492 1 0.2287
> ## -> X2 is not needed
> (m1.sali <- lmrob(Y ~ X1 + X3, data = salinity))
Call:
lmrob(formula = Y ~ X1 + X3, data = salinity)
Coefficients:
(Intercept) X1 X3
15.8169 0.7210 -0.5415
> (A2 <- anova(m0.sali, m1.sali)) # the same as before
Robust Wald Test Table
Model 1: Y ~ X1 + X2 + X3
Model 2: Y ~ X1 + X3
Largest model fitted by lmrob(), i.e. SM
pseudoDf Test.Stat Df Pr(>chisq)
1 24
2 25 1.4492 1 0.2287
> stopifnot(all.equal(A1$Pr[2], A2$Pr[2], tol=1e-14))
>
> anova(m0.sali, m1.sali, test = "Deviance")
Robust Deviance Table
Model 1: Y ~ X1 + X2 + X3
Model 2: Y ~ X1 + X3
Largest model fitted by lmrob(), i.e. SM
pseudoDf Test.Stat Df Pr(>chisq)
1 24
2 25 1.9567 1 0.1619
> ## whereas 'X3' is highly significant:
> m2 <- update(m0.sali, ~ . -X3)
> (A3 <- anova(m0.sali, m2))
Robust Wald Test Table
Model 1: Y ~ X1 + X2 + X3
Model 2: Y ~ X1 + X2
Largest model fitted by lmrob(), i.e. SM
pseudoDf Test.Stat Df Pr(>chisq)
1 24
2 25 15.675 1 7.521e-05 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> (A4 <- anova(m0.sali, m2, test = "Deviance"))
Robust Deviance Table
Model 1: Y ~ X1 + X2 + X3
Model 2: Y ~ X1 + X2
Largest model fitted by lmrob(), i.e. SM
pseudoDf Test.Stat Df Pr(>chisq)
1 24
2 25 19.65 1 9.302e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
> cX3 <- c(Estimate = -0.627327396, `Std. Error` = 0.15844971,
+ `t value` = -3.9591577, `Pr(>|t|)` = 0.000584156)
> stopifnot(all.equal(cX3, coef(summary(m0.sali))["X3",], tol = 1e-6))
>
>
> ## example(lmrob)
> set.seed(7)
> data(coleman)
> summary( m1 <- lmrob(Y ~ ., data=coleman) )
Call:
lmrob(formula = Y ~ ., data = coleman)
Weighted Residuals:
Min 1Q Median 3Q Max
-4.16181 -0.39226 0.01611 0.55619 7.22766
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 30.50232 6.71260 4.544 0.000459 ***
salaryP -1.66615 0.43129 -3.863 0.001722 **
fatherWc 0.08425 0.01467 5.741 5.10e-05 ***
sstatus 0.66774 0.03385 19.726 1.30e-11 ***
teacherSc 1.16778 0.10983 10.632 4.35e-08 ***
motherLev -4.13657 0.92084 -4.492 0.000507 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Robust residual standard error: 1.134
Convergence in 11 IRWLS iterations
Robustness weights:
observation 18 is an outlier with |weight| = 0 ( < 0.005);
The remaining 19 ones are summarized as
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.1491 0.9412 0.9847 0.9279 0.9947 0.9982
Algorithmic parameters:
tuning.chi bb tuning.psi refine.tol rel.tol
1.5476400 0.5000000 4.6850610 0.0000001 0.0000001
nResample max.it groups n.group best.r.s k.fast.s k.max
500 50 5 400 2 1 200
trace.lev compute.rd numpoints
0 0 10
psi method cov
"bisquare" "MM" ".vcov.avar1"
seed : int(0)
> stopifnot(c(3,18) == which(m1$w < 0.2))
>
> data(starsCYG)
> (RlmST <- lmrob(log.light ~ log.Te, data = starsCYG))
Call:
lmrob(formula = log.light ~ log.Te, data = starsCYG)
Coefficients:
(Intercept) log.Te
-4.969 2.253
> summary(RlmST)
Call:
lmrob(formula = log.light ~ log.Te, data = starsCYG)
Weighted Residuals:
Min 1Q Median 3Q Max
-0.80959 -0.28838 0.00282 0.36668 3.39585
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4.9694 3.4100 -1.457 0.15198
log.Te 2.2532 0.7691 2.930 0.00531 **
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Robust residual standard error: 0.4715
Convergence in 15 IRWLS iterations
Robustness weights:
4 observations c(11,20,30,34) are outliers with |weight| = 0 ( < 0.0021);
4 weights are ~= 1. The remaining 39 ones are summarized as
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.6533 0.9171 0.9593 0.9318 0.9848 0.9986
Algorithmic parameters:
tuning.chi bb tuning.psi refine.tol rel.tol
1.5476400 0.5000000 4.6850610 0.0000001 0.0000001
nResample max.it groups n.group best.r.s k.fast.s k.max
500 50 5 400 2 1 200
trace.lev compute.rd numpoints
0 0 10
psi method cov
"bisquare" "MM" ".vcov.avar1"
seed : int(0)
> stopifnot(c(11,20,30,34) == which(RlmST$w < 0.01))
>
> set.seed(47)
> data(hbk)
> m.hbk <- lmrob(Y ~ ., data = hbk)
> summary(m.hbk)
Call:
lmrob(formula = Y ~ ., data = hbk)
Weighted Residuals:
Min 1Q Median 3Q Max
-0.92731 -0.38663 0.05321 0.71800 10.80005
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.18943 0.11665 -1.624 0.1088
X1 0.08520 0.07316 1.165 0.2481
X2 0.04099 0.02963 1.383 0.1709
X3 -0.05367 0.03199 -1.678 0.0978 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Robust residual standard error: 0.7964
Convergence in 9 IRWLS iterations
Robustness weights:
10 observations c(1,2,3,4,5,6,7,8,9,10)
are outliers with |weight| = 0 ( < 0.0013);
7 weights are ~= 1. The remaining 58 ones are summarized as
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.8549 0.9281 0.9630 0.9540 0.9868 0.9987
Algorithmic parameters:
tuning.chi bb tuning.psi refine.tol rel.tol
1.5476400 0.5000000 4.6850610 0.0000001 0.0000001
nResample max.it groups n.group best.r.s k.fast.s k.max
500 50 5 400 2 1 200
trace.lev compute.rd numpoints
0 0 10
psi method cov
"bisquare" "MM" ".vcov.avar1"
seed : int(0)
> stopifnot(1:10 == which(m.hbk$w < 0.01))
>
> data(heart)
> summary(mhrt <- lmrob(clength ~ ., data = heart))
Call:
lmrob(formula = clength ~ ., data = heart)
Weighted Residuals:
Min 1Q Median 3Q Max
-9.87865 -1.75398 -0.08874 0.81797 5.63933
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 30.2921 62.7390 0.483 0.641
height -0.1368 2.1287 -0.064 0.950
weight 0.3135 0.7360 0.426 0.680
Robust residual standard error: 2.591
Convergence in 36 IRWLS iterations
Robustness weights:
3 weights are ~= 1. The remaining 9 ones are
2 3 4 5 6 7 8 9 11
0.9887 0.9301 0.9608 0.9082 0.9262 0.9963 0.1140 0.9666 0.6149
Algorithmic parameters:
tuning.chi bb tuning.psi refine.tol rel.tol
1.5476400 0.5000000 4.6850610 0.0000001 0.0000001
nResample max.it groups n.group best.r.s k.fast.s k.max
500 50 5 400 2 1 200
trace.lev compute.rd numpoints
0 0 10
psi method cov
"bisquare" "MM" ".vcov.avar1"
seed : int(0)
> stopifnot(8 == which(mhrt$w < 0.15),
+ 11 == which(0.61 < mhrt$w & mhrt$w < 0.62),
+ c(1:7,9:10,12) == which(mhrt$w > 0.90))
>
> data(stackloss)
> mSL <- lmrob(stack.loss ~ ., data = stackloss)
> summary(mSL)
Call:
lmrob(formula = stack.loss ~ ., data = stackloss)
Weighted Residuals:
Min 1Q Median 3Q Max
-10.50974 -1.43819 -0.09134 1.02503 7.23113
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -41.52462 5.29780 -7.838 4.82e-07 ***
Air.Flow 0.93885 0.11743 7.995 3.68e-07 ***
Water.Temp 0.57955 0.26296 2.204 0.0416 *
Acid.Conc. -0.11292 0.06989 -1.616 0.1246
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Robust residual standard error: 1.912
Convergence in 17 IRWLS iterations
Robustness weights:
observation 21 is an outlier with |weight| = 0 ( < 0.0048);
2 weights are ~= 1. The remaining 18 ones are summarized as
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.1215 0.8757 0.9428 0.8721 0.9797 0.9978
Algorithmic parameters:
tuning.chi bb tuning.psi refine.tol rel.tol
1.5476400 0.5000000 4.6850610 0.0000001 0.0000001
nResample max.it groups n.group best.r.s k.fast.s k.max
500 50 5 400 2 1 200
trace.lev compute.rd numpoints
0 0 10
psi method cov
"bisquare" "MM" ".vcov.avar1"
seed : int(0)
>
>
> cat('Time elapsed: ', proc.time(),'\n') # "stats"
Time elapsed: 0.35 0.03 0.375 0 0
>
|
