1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
|
R version 2.11.1 (2010-05-31)
Copyright (C) 2010 The R Foundation for Statistical Computing
ISBN 3-900051-07-0
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.
> ### tests methods argument of lmrob.control
>
> library(robustbase)
>
> data(stackloss)
>
> ## S
> set.seed(0)
> summary(m0 <- lmrob(stack.loss ~ ., data = stackloss, method = "S"))
Length Class Mode
coefficients 4 -none- numeric
scale 1 -none- numeric
k.iter 1 -none- numeric
converged 1 -none- logical
fitted.values 21 -none- numeric
residuals 21 -none- numeric
weights 21 -none- numeric
control 19 -none- list
qr 4 qr list
rank 1 -none- numeric
cov 16 -none- numeric
df.residual 1 -none- numeric
degree.freedom 1 -none- numeric
xlevels 0 -none- list
call 4 -none- call
terms 3 terms call
model 4 data.frame list
x 84 -none- numeric
Warning message:
In lf.cov(init, x) :
:.vcov.w: ignoring cov.resid == final since est != final
> set.seed(0)
> m0a <- lmrob.S(m0$x, stack.loss, lmrob.control())
>
> all.equal(m0[c('coefficients', 'scale', 'weights')],
+ m0a[c('coefficients', 'scale', 'weights')])
[1] TRUE
>
> ## MM
> set.seed(0)
> summary(m1 <- lmrob(stack.loss ~ ., data = stackloss, method = "MM"))
Call:
lmrob(formula = stack.loss ~ ., data = stackloss, method = "MM")
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)
>
> set.seed(0)
> m2 <- update(m1, method = "SM")
>
> all.equal(m1[c('coefficients', 'scale', 'cov')],
+ m2[c('coefficients', 'scale', 'cov')])
[1] TRUE
>
> set.seed(0)
> m3 <- update(m0, method = "SM", cov = '.vcov.w')
>
> ## SMD
> set.seed(0)
> summary(m4 <- lmrob(stack.loss ~ ., data = stackloss, method = "SMD", psi = 'bisquare'))
Call:
lmrob(formula = stack.loss ~ ., data = stackloss, method = "SMD",
psi = "bisquare")
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) -41.5246 8.8552 -4.689 0.000211 ***
Air.Flow 0.9388 0.1162 8.078 3.2e-07 ***
Water.Temp 0.5796 0.3164 1.831 0.084610 .
Acid.Conc. -0.1129 0.1163 -0.971 0.345380
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Robust residual standard error: 2.651
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" "SMD" ".vcov.w"
seed : int(0)
> summary(m4a <- lmrob..D..fit(m3))
Call:
lmrob(formula = stack.loss ~ ., data = stackloss, method = "SMD",
cov = ".vcov.w")
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) -41.5246 8.8552 -4.689 0.000211 ***
Air.Flow 0.9388 0.1162 8.078 3.2e-07 ***
Water.Temp 0.5796 0.3164 1.831 0.084610 .
Acid.Conc. -0.1129 0.1163 -0.971 0.345380
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Robust residual standard error: 2.651
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" "SMD" ".vcov.w"
seed : int(0)
>
> ## rearrange m4a and update call
> m4a <- m4a[names(m4)]
> class(m4a) <- class(m4)
> m4a$call <- m4$call
>
> all.equal(m4, m4a)
[1] TRUE
>
> ## SMDM
> set.seed(0)
> summary(m5 <- lmrob(stack.loss ~ ., data = stackloss, method = "SMDM", psi = 'bisquare'))
Call:
lmrob(formula = stack.loss ~ ., data = stackloss, method = "SMDM",
psi = "bisquare")
Weighted Residuals:
Min 1Q Median 3Q Max
-9.6746 -1.7721 0.1346 1.2041 6.6080
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -41.9398 9.6482 -4.347 0.000438 ***
Air.Flow 0.8747 0.1215 7.198 1.49e-06 ***
Water.Temp 0.8099 0.3320 2.439 0.025977 *
Acid.Conc. -0.1188 0.1268 -0.937 0.361693
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Robust residual standard error: 2.651
Convergence in 17 IRWLS iterations
Robustness weights:
2 weights are ~= 1. The remaining 19 ones are summarized as
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.1546 0.9139 0.9597 0.8874 0.9866 0.9966
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" "SMDM" ".vcov.w"
seed : int(0)
> summary(m5a <- lmrob..M..fit(obj=m4))
Call:
lmrob(formula = stack.loss ~ ., data = stackloss, method = "SMDM",
psi = "bisquare")
Weighted Residuals:
Min 1Q Median 3Q Max
-9.6746 -1.7721 0.1346 1.2041 6.6080
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -41.9398 9.6482 -4.347 0.000438 ***
Air.Flow 0.8747 0.1215 7.198 1.49e-06 ***
Water.Temp 0.8099 0.3320 2.439 0.025977 *
Acid.Conc. -0.1188 0.1268 -0.937 0.361693
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Robust residual standard error: 2.651
Convergence in 17 IRWLS iterations
Robustness weights:
2 weights are ~= 1. The remaining 19 ones are summarized as
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.1546 0.9139 0.9597 0.8874 0.9866 0.9966
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" "SMDM" ".vcov.w"
seed : int(0)
>
> ## rearrange m5a
> m5a <- m5a[names(m5)]
> class(m5a) <- class(m5)
>
> all.equal(m5, m5a)
[1] TRUE
>
|
