R version 2.5.0 Under development (unstable) (2006-12-23 r40295)
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ISBN 3-900051-07-0
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> ###-- Linear Models, basic functionality -- weights included.
>
> ## From John Maindonald :
> roller <- data.frame(
+ weight = c(1.9, 3.1, 3.3, 4.8, 5.3, 6.1, 6.4, 7.6, 9.8, 12.4),
+ depression = c( 2, 1, 5, 5, 20, 20, 23, 10, 30, 25))
>
> roller.lmu <- lm(weight~depression, data=roller)
> roller.lsfu <- lsfit(roller$depression, roller$weight)
>
> roller.lsf <- lsfit(roller$depression, roller$weight, wt = 1:10)
> roller.lsf0 <- lsfit(roller$depression, roller$weight, wt = 0:9)
> roller.lm <- lm(weight~depression, data=roller, weights= 1:10)
> roller.lm0 <- lm(weight~depression, data=roller, weights= 0:9)
> roller.lm9 <- lm(weight~depression, data=roller[-1,],weights= 1:9)
> roller.glm <- glm(weight~depression, data=roller, weights= 1:10)
> roller.glm0<- glm(weight~depression, data=roller, weights= 0:9)
>
> predict(roller.glm0, type="terms")# failed till 2003-03-31
depression
1 -2.6692211
2 -2.8898179
3 -2.0074308
4 -2.0074308
5 1.3015211
6 1.3015211
7 1.9633114
8 -0.9044468
9 3.5074889
10 2.4045050
attr(,"constant")
[1] 6.743646
>
> ## FIXME : glm()$residual [1] is NA, lm()'s is ok.
> ## all.equal(residuals(roller.glm0, type = "partial"),
> ## residuals(roller.lm0, type = "partial") )
>
>
> all.equal(deviance(roller.lm),
+ deviance(roller.glm))
[1] TRUE
> all.equal(weighted.residuals(roller.lm),
+ residuals (roller.glm))
[1] TRUE
>
> all.equal(deviance(roller.lm0),
+ deviance(roller.glm0))
[1] TRUE
> all.equal(weighted.residuals(roller.lm0, drop=FALSE),
+ residuals (roller.glm0))
[1] TRUE
>
> (im.lm0 <- influence.measures(roller.lm0))
Influence measures of
lm(formula = weight ~ depression, data = roller, weights = 0:9) :
dfb.1_ dfb.dprs dffit cov.r cook.d hat inf
2 -0.0530 0.0482 -0.0530 1.551 0.001635 0.1277
3 -0.1769 0.1538 -0.1782 1.569 0.018065 0.1742
4 0.0130 -0.0113 0.0131 1.842 0.000100 0.2613
5 -0.1174 -0.0185 -0.3370 1.049 0.055523 0.0892
6 -0.1031 -0.0162 -0.2960 1.229 0.045771 0.1114
7 -0.0118 -0.1891 -0.5010 1.070 0.119319 0.1555
8 0.7572 -0.5948 0.7972 1.467 0.309976 0.3510
9 0.1225 -0.2067 -0.2664 2.391 0.040794 0.4470 *
10 -0.3348 1.1321 2.0937 0.233 0.895835 0.2826 *
>
> all.equal(unname(im.lm0 $ infmat),
+ unname(cbind( dfbetas (roller.lm0)
+ , dffits (roller.lm0)
+ , covratio (roller.lm0)
+ ,cooks.distance(roller.lm0)
+ ,lm.influence (roller.lm0)$hat)
+ ))
[1] TRUE
>
> all.equal(rstandard(roller.lm9),
+ rstandard(roller.lm0),tol=1e-14)
[1] TRUE
> all.equal(rstudent(roller.lm9),
+ rstudent(roller.lm0),tol=1e-14)
[1] TRUE
> all.equal(rstudent(roller.lm),
+ rstudent(roller.glm))
[1] TRUE
> all.equal(cooks.distance(roller.lm),
+ cooks.distance(roller.glm))
[1] TRUE
>
>
> all.equal(summary(roller.lm0)$coef,
+ summary(roller.lm9)$coef, tol=1e-14)
[1] TRUE
> all.equal(print(anova(roller.lm0), signif.st=FALSE),
+ anova(roller.lm9), tol=1e-14)
Analysis of Variance Table
Response: weight
Df Sum Sq Mean Sq F value Pr(>F)
depression 1 158.408 158.408 5.4302 0.05259
Residuals 7 204.202 29.172
[1] TRUE
>
>
> ### more regression tests for lm(), glm(), etc :
>
> ## moved from ?influence.measures:
> lm.SR <- lm(sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings)
> (IM <- influence.measures(lm.SR))
Influence measures of
lm(formula = sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings) :
dfb.1_ dfb.pp15 dfb.pp75 dfb.dpi dfb.ddpi dffit cov.r
Australia 0.01232 -0.010436 -0.02653 0.04534 -0.000159 0.0627 1.193
Austria -0.01005 0.005944 0.04084 -0.03672 -0.008182 0.0632 1.268
Belgium -0.06416 0.051496 0.12070 -0.03472 -0.007265 0.1878 1.176
Bolivia 0.00578 -0.012703 -0.02253 0.03185 0.040642 -0.0597 1.224
Brazil 0.08973 -0.061626 -0.17907 0.11997 0.068457 0.2646 1.082
Canada 0.00541 -0.006750 0.01021 -0.03531 -0.002649 -0.0390 1.328
Chile -0.19941 0.132652 0.21979 -0.01998 0.120007 -0.4554 0.655
China 0.02112 -0.005726 -0.08311 0.05180 0.110627 0.2008 1.150
Colombia 0.03910 -0.052261 -0.02464 0.00168 0.009084 -0.0960 1.167
Costa Rica -0.23367 0.284279 0.14243 0.05638 -0.032824 0.4049 0.968
Denmark -0.04051 0.020927 0.04653 0.15220 0.048854 0.3845 0.934
Ecuador 0.07176 -0.095239 -0.06067 0.01950 0.047786 -0.1695 1.139
Finland -0.11350 0.111328 0.11695 -0.04364 -0.017132 -0.1464 1.203
France -0.16600 0.147054 0.21900 -0.02942 0.023952 0.2765 1.226
Germany -0.00802 0.008224 0.00835 -0.00697 -0.000293 -0.0152 1.226
Greece -0.14820 0.163938 0.02861 0.15713 -0.059599 -0.2811 1.140
Guatamala 0.01552 -0.054853 0.00614 0.00585 0.097217 -0.2305 1.085
Honduras -0.00226 0.009845 -0.01020 0.00812 -0.001887 0.0482 1.186
Iceland 0.24789 -0.273549 -0.23265 -0.12555 0.184698 -0.4768 0.866
India 0.02105 -0.015769 -0.01439 -0.01374 -0.018958 0.0381 1.202
Ireland -0.31001 0.296238 0.48156 -0.25733 -0.093317 0.5216 1.268
Italy 0.06619 -0.070974 0.00307 -0.06999 -0.028648 0.1388 1.162
Japan 0.63987 -0.656139 -0.67390 0.14610 0.388603 0.8597 1.085
Korea -0.16897 0.135087 0.21895 0.00511 -0.169492 -0.4303 0.870
Luxembourg -0.06827 0.068883 0.04380 -0.02797 0.049134 -0.1401 1.196
Malta 0.03652 -0.048756 0.00791 -0.08659 0.153014 0.2386 1.128
Norway 0.00222 -0.000350 -0.00611 -0.01594 -0.001462 -0.0522 1.168
Netherlands 0.01395 -0.016738 -0.01186 0.00433 0.022591 0.0366 1.229
New Zealand -0.06002 0.065105 0.09412 -0.02638 -0.064740 0.1469 1.134
Nicaragua -0.01209 0.017904 0.00972 -0.00474 -0.010467 0.0397 1.174
Panama 0.02828 -0.053342 0.01446 -0.03467 -0.007889 -0.1775 1.067
Paraguay -0.23227 0.164160 0.15826 0.14361 0.270478 -0.4655 0.873
Peru -0.07182 0.146695 0.09148 -0.08585 -0.287184 0.4811 0.831
Philippines -0.15707 0.226807 0.15743 -0.11140 -0.170674 0.4884 0.818
Portugal -0.02140 0.025514 -0.00380 0.03991 -0.028011 -0.0690 1.233
South Africa 0.02218 -0.020296 -0.00672 -0.02049 -0.016326 0.0343 1.195
South Rhodesia 0.14390 -0.134719 -0.09245 -0.06956 -0.057920 0.1607 1.313
Spain -0.03035 0.031311 0.00394 0.03512 0.005340 -0.0526 1.208
Sweden 0.10098 -0.081623 -0.06166 -0.25528 -0.013316 -0.4526 1.086
Switzerland 0.04323 -0.046492 -0.04364 0.09093 -0.018828 0.1903 1.147
Turkey -0.01092 -0.011985 0.02645 0.00161 0.025138 -0.1445 1.100
Tunisia 0.07377 -0.104998 -0.07727 0.04439 0.103058 -0.2177 1.131
United Kingdom 0.04671 -0.035840 -0.17129 0.12554 0.100314 -0.2722 1.189
United States 0.06910 -0.072886 0.03745 -0.23312 -0.032729 -0.2510 1.655
Venezuela -0.05083 0.100805 -0.03366 0.11366 -0.124486 0.3071 1.095
Zambia 0.16361 -0.079172 -0.33899 0.09406 0.228232 0.7482 0.512
Jamaica 0.10958 -0.100223 -0.05722 -0.00703 -0.295461 -0.3456 1.200
Uruguay -0.13403 0.128805 0.02953 0.13132 0.099591 -0.2051 1.187
Libya 0.55074 -0.483244 -0.37974 -0.01937 -1.024477 -1.1601 2.091
Malaysia 0.03684 -0.061126 0.03235 -0.04956 -0.072294 -0.2126 1.113
cook.d hat inf
Australia 8.04e-04 0.0677
Austria 8.18e-04 0.1204
Belgium 7.15e-03 0.0875
Bolivia 7.28e-04 0.0895
Brazil 1.40e-02 0.0696
Canada 3.11e-04 0.1584
Chile 3.78e-02 0.0373 *
China 8.16e-03 0.0780
Colombia 1.88e-03 0.0573
Costa Rica 3.21e-02 0.0755
Denmark 2.88e-02 0.0627
Ecuador 5.82e-03 0.0637
Finland 4.36e-03 0.0920
France 1.55e-02 0.1362
Germany 4.74e-05 0.0874
Greece 1.59e-02 0.0966
Guatamala 1.07e-02 0.0605
Honduras 4.74e-04 0.0601
Iceland 4.35e-02 0.0705
India 2.97e-04 0.0715
Ireland 5.44e-02 0.2122
Italy 3.92e-03 0.0665
Japan 1.43e-01 0.2233
Korea 3.56e-02 0.0608
Luxembourg 3.99e-03 0.0863
Malta 1.15e-02 0.0794
Norway 5.56e-04 0.0479
Netherlands 2.74e-04 0.0906
New Zealand 4.38e-03 0.0542
Nicaragua 3.23e-04 0.0504
Panama 6.33e-03 0.0390
Paraguay 4.16e-02 0.0694
Peru 4.40e-02 0.0650
Philippines 4.52e-02 0.0643
Portugal 9.73e-04 0.0971
South Africa 2.41e-04 0.0651
South Rhodesia 5.27e-03 0.1608
Spain 5.66e-04 0.0773
Sweden 4.06e-02 0.1240
Switzerland 7.33e-03 0.0736
Turkey 4.22e-03 0.0396
Tunisia 9.56e-03 0.0746
United Kingdom 1.50e-02 0.1165
United States 1.28e-02 0.3337 *
Venezuela 1.89e-02 0.0863
Zambia 9.66e-02 0.0643 *
Jamaica 2.40e-02 0.1408
Uruguay 8.53e-03 0.0979
Libya 2.68e-01 0.5315 *
Malaysia 9.11e-03 0.0652
> summary(IM)
Potentially influential observations of
lm(formula = sr ~ pop15 + pop75 + dpi + ddpi, data = LifeCycleSavings) :
dfb.1_ dfb.pp15 dfb.pp75 dfb.dpi dfb.ddpi dffit cov.r cook.d
Chile -0.20 0.13 0.22 -0.02 0.12 -0.46 0.65_* 0.04
United States 0.07 -0.07 0.04 -0.23 -0.03 -0.25 1.66_* 0.01
Zambia 0.16 -0.08 -0.34 0.09 0.23 0.75 0.51_* 0.10
Libya 0.55 -0.48 -0.38 -0.02 -1.02_* -1.16_* 2.09_* 0.27
hat
Chile 0.04
United States 0.33_*
Zambia 0.06
Libya 0.53_*
> ## colnames will differ in the next line
> all.equal(dfbetas(lm.SR), IM$infmat[, 1:5], check.attributes = FALSE,
+ tol = 1e-12)
[1] TRUE
>
> signif(dfbeta(lm.SR), 3)
(Intercept) pop15 pop75 dpi ddpi
Australia 0.0916 -1.53e-03 -0.02910 4.27e-05 -3.16e-05
Austria -0.0747 8.69e-04 0.04470 -3.46e-05 -1.62e-03
Belgium -0.4750 7.50e-03 0.13200 -3.26e-05 -1.44e-03
Bolivia 0.0429 -1.86e-03 -0.02470 3.00e-05 8.06e-03
Brazil 0.6600 -8.92e-03 -0.19400 1.12e-04 1.34e-02
Canada 0.0402 -9.87e-04 0.01120 -3.32e-05 -5.25e-04
Chile -1.4000 1.83e-02 0.22700 -1.78e-05 2.25e-02
China 0.1560 -8.33e-04 -0.09060 4.85e-05 2.18e-02
Colombia 0.2900 -7.63e-03 -0.02700 1.58e-06 1.80e-03
Costa Rica -1.7000 4.07e-02 0.15300 5.19e-05 -6.37e-03
Denmark -0.2940 2.99e-03 0.04980 1.40e-04 9.46e-03
Ecuador 0.5310 -1.39e-02 -0.06620 1.83e-05 9.44e-03
Finland -0.8420 1.62e-02 0.12800 -4.10e-05 -3.39e-03
France -1.2300 2.14e-02 0.23900 -2.76e-05 4.73e-03
Germany -0.0597 1.20e-03 0.00915 -6.56e-06 -5.82e-05
Greece -1.0900 2.38e-02 0.03110 1.47e-04 -1.17e-02
Guatamala 0.1140 -7.95e-03 0.00667 5.46e-06 1.91e-02
Honduras -0.0168 1.44e-03 -0.01120 7.64e-06 -3.74e-04
Iceland 1.7800 -3.87e-02 -0.24700 -1.14e-04 3.55e-02
India 0.1560 -2.31e-03 -0.01580 -1.29e-05 -3.76e-03
Ireland -2.2800 4.28e-02 0.52200 -2.40e-04 -1.83e-02
Italy 0.4910 -1.04e-02 0.00335 -6.57e-05 -5.67e-03
Japan 4.6300 -9.33e-02 -0.71800 1.34e-04 7.49e-02
Korea -1.2200 1.91e-02 0.23300 4.66e-06 -3.26e-02
Luxembourg -0.5070 1.01e-02 0.04790 -2.63e-05 9.73e-03
Malta 0.2700 -7.08e-03 0.00861 -8.09e-05 3.01e-02
Norway 0.0165 -5.12e-05 -0.00670 -1.50e-05 -2.90e-04
Netherlands 0.1040 -2.45e-03 -0.01300 4.07e-06 4.48e-03
New Zealand -0.4440 9.48e-03 0.10300 -2.47e-05 -1.28e-02
Nicaragua -0.0899 2.62e-03 0.01060 -4.46e-06 -2.08e-03
Panama 0.2080 -7.73e-03 0.01570 -3.24e-05 -1.55e-03
Paraguay -1.6700 2.33e-02 0.16800 1.31e-04 5.20e-02
Peru -0.5150 2.07e-02 0.09670 -7.79e-05 -5.49e-02
Philippines -1.1200 3.19e-02 0.16600 -1.01e-04 -3.26e-02
Portugal -0.1590 3.73e-03 -0.00416 3.76e-05 -5.55e-03
South Africa 0.1650 -2.97e-03 -0.00737 -1.93e-05 -3.24e-03
South Rhodesia 1.0700 -1.97e-02 -0.10100 -6.54e-05 -1.15e-02
Spain -0.2260 4.58e-03 0.00432 3.31e-05 1.06e-03
Sweden 0.7390 -1.17e-02 -0.06650 -2.37e-04 -2.60e-03
Switzerland 0.3200 -6.77e-03 -0.04760 8.52e-05 -3.72e-03
Turkey -0.0807 -1.74e-03 0.02880 1.51e-06 4.96e-03
Tunisia 0.5450 -1.53e-02 -0.08410 4.15e-05 2.03e-02
United Kingdom 0.3450 -5.21e-03 -0.18700 1.17e-04 1.98e-02
United States 0.5130 -1.06e-02 0.04100 -2.19e-04 -6.48e-03
Venezuela -0.3740 1.46e-02 -0.03650 1.06e-04 -2.44e-02
Zambia 1.1200 -1.06e-02 -0.34100 8.14e-05 4.16e-02
Jamaica 0.8080 -1.45e-02 -0.06220 -6.57e-06 -5.81e-02
Uruguay -0.9920 1.88e-02 0.03220 1.23e-04 1.97e-02
Libya 4.0400 -6.98e-02 -0.41100 -1.80e-05 -2.01e-01
Malaysia 0.2720 -8.88e-03 0.03520 -4.63e-05 -1.42e-02
> covratio (lm.SR)
Australia Austria Belgium Bolivia Brazil
1.1928303 1.2678392 1.1761879 1.2238199 1.0823332
Canada Chile China Colombia Costa Rica
1.3283009 0.6547098 1.1498637 1.1666845 0.9681384
Denmark Ecuador Finland France Germany
0.9344047 1.1393880 1.2031561 1.2262654 1.2256855
Greece Guatamala Honduras Iceland India
1.1396174 1.0852720 1.1855450 0.8658808 1.2024438
Ireland Italy Japan Korea Luxembourg
1.2680432 1.1624611 1.0845999 0.8695843 1.1961844
Malta Norway Netherlands New Zealand Nicaragua
1.1282611 1.1680616 1.2285315 1.1336998 1.1742677
Panama Paraguay Peru Philippines Portugal
1.0667255 0.8732040 0.8312741 0.8177726 1.2331038
South Africa South Rhodesia Spain Sweden Switzerland
1.1945449 1.3130954 1.2081541 1.0864869 1.1471125
Turkey Tunisia United Kingdom United States Venezuela
1.1003557 1.1314365 1.1886236 1.6554816 1.0945955
Zambia Jamaica Uruguay Libya Malaysia
0.5116454 1.1995171 1.1872025 2.0905736 1.1126445
>
> ## predict.lm(.)
>
> all.equal(predict(roller.lm, se=TRUE)$se,
+ predict(roller.lm, newdata=roller, se=TRUE)$se, tol= 1e-14)
[1] TRUE
>