[R] Durbin-Watson test in packages "car" and "lmtest"
John Fox
jfox at mcmaster.ca
Sun Apr 21 04:49:41 CEST 2002
Dear Ahmad,
I think that the discrepancy has been cleared up, since durbin.watson, as
has been pointed out, calculates two-sided tests.
Some other relevant points: (1) durbin.watson will calculate dw statistics
and associated p-values for lags greater than 1. (2) I prefer the approach
currently in dwtest, but when durbin.watson was written, dwtest in lmtest
didn't compute p-values. (3) I also agree that it would be useful to allow
one-sided alternatives in durbin.watson and will likely add this if I don't
remove the function from the car package.
I apologize for my slow response to your original posting and the
subsequent exchange -- I was out of town.
John
At 05:05 PM 4/19/2002 -0400, Ahmad Abu Hammour wrote:
>Hi Torsten,
>Here is an example in which P-values have a significant difference. The
>data is a sub sample of a larger one.
>Basically the model I am using is as follows:
>y_{t+2}= y_{t+1} + y_t + I(x_{t+1}-z_{t+1}-w_{t+1}) +e_{t+2}
>
> > ydata
> y z w x
> [1,] 0.0101705342 -5.363636567 0.80677087 -2.425968
> [2,] -0.0040963887 -4.930336567 -0.01515276 -1.852668
> [3,] 0.0007996203 -2.795136567 0.28412361 -0.849268
> [4,] 0.0231375722 -2.523036567 -0.33650002 -0.315968
> [5,] 0.0576658597 -2.925936567 -0.68112365 0.060732
> [6,] 0.0930807057 -2.283836567 -1.59374728 0.214032
> [7,] 0.0904861271 -1.908436567 -3.15057091 0.347332
> [8,] 0.0815802452 -3.063936567 -3.60669454 -0.175968
> [9,] 0.0463679856 -3.947236567 -2.89361816 -1.012668
>[10,] 0.0283314000 -3.528136567 -1.68974179 -1.522668
>[11,] 0.0158693958 -2.890536567 -1.03456542 -1.629268
>[12,] -0.0177988767 -2.165736567 -0.23008905 -1.532668
>[13,] -0.0263232785 -2.400436567 -0.29991268 -1.369268
>[14,] -0.0377695478 -3.243136567 -0.31953631 -0.539268
>[15,] -0.0520095622 -3.241336567 0.22174006 0.120732
>[16,] -0.0773138815 -2.765236567 -0.22328356 1.467332
>[17,] -0.0804307590 -2.833236567 0.09209281 2.107332
>[18,] -0.0446189151 -3.710136567 0.57246918 2.057332
>[19,] -0.0439761920 -4.232636567 0.11764555 2.687332
>[20,] -0.0508314286 -3.445136567 0.91252192 4.874032
>[21,] -0.0373526376 -2.123836567 1.03269829 5.340732
>[22,] -0.0363366045 -4.549336567 1.16137466 3.614032
>[23,] -0.0119795294 -4.660636567 2.10495103 1.744032
>[24,] -0.0271166745 0.940863433 2.73172741 5.450732
>[25,] -0.0319279899 2.972463433 3.93230378 7.954032
>[26,] -0.0285519284 2.601663433 4.25698015 9.447332
>[27,] -0.0362890374 3.900363433 4.49975652 11.397332
>[28,] -0.0193261619 2.440563433 4.24003289 7.057332
>[29,] -0.0211604332 4.133063433 3.62460926 5.907332
>[30,] -0.0393599621 4.764863433 3.78798563 6.740732
>[31,] -0.0368496844 2.967363433 3.09016201 5.137332
>[32,] -0.0111656400 2.374163433 2.32173838 1.820732
>[33,] -0.0049543837 2.858663433 0.59471475 0.570732
>[34,] -0.0085112660 3.900063433 -0.96020888 0.424032
>[35,] 0.0002988086 3.956163433 -1.40353251 0.500732
>[36,] -0.0021387277 2.276463433 -1.99135614 0.720732
>[37,] -0.0143497002 2.857863433 -1.40157977 1.270732
>[38,] -0.0459512047 3.589163433 -1.78060340 2.574032
>[39,] -0.0620556482 4.248163433 -2.43422702 3.537332
>[40,] -0.0665723041 3.225363433 -2.45305065 1.830732
>[41,] -0.0990262190 2.638163433 -2.34577428 1.634032
>[42,] -0.0993943457 2.160963433 -2.00509791 0.780732
>[43,] -0.0896954664 1.651763433 -1.79992154 0.164032
>[44,] -0.1047509912 2.106963433 -1.59274517 0.117332
>[45,] -0.1188326548 3.230463433 -1.40576880 2.007332
>[46,] -0.1012159404 2.484063433 -1.60469242 -0.209268
>[47,] -0.0975617833 2.185163433 -1.23841605 -0.442668
>[48,] -0.0859923186 1.244563433 -0.99983968 -0.495968
>[49,] -0.0467949427 -0.185636567 -1.19776331 -1.649268
>[50,] -0.0351160760 -0.510836567 -0.50778694 -0.569268
>[51,] -0.0233943108 -0.356136567 -0.53781057 0.347332
>[52,] -0.0080094290 0.005063433 -0.71733420 -0.569268
>[53,] 0.0312603960 -0.149336567 -0.69205783 -0.349268
>[54,] 0.0614944090 0.181063433 -0.76188145 0.237332
>[55,] 0.0775709808 0.795863433 -0.58080508 1.110732
>[56,] 0.0952235601 1.131763433 -0.38712871 1.907332
>[57,] 0.1069545973 1.509763433 0.06534766 2.887332
>[58,] 0.1136253179 1.785763433 0.64482403 3.450732
>[59,] 0.1275201332 1.348463433 1.06650040 3.410732
>[60,] 0.1387864450 0.581263433 1.05767677 3.444032
>[61,] 0.1244438565 1.253563433 1.35555315 4.164032
>[62,] 0.1344048716 0.334263433 0.69162952 4.844032
>[63,] 0.1487305153 -0.634036567 0.37670589 4.010732
>[64,] 0.1420063384 -0.159036567 1.22928226 3.190732
>[65,] 0.1469999823 -0.707536567 1.67200000 1.200732
> > library(car)
>Attaching package `car':
>
> The following object(s) are masked from package:base :
> dfbetas rstudent
> > library(lmtest)
> >
> lmy=lm(y[-c(1,2)]~y[-c(1,65)]+y[-c(64,65)]+I(x-z-w)[-c(64,65)]-1,data=as.ts(ydata))
> > dwtest(lmy)
> Durbin-Watson test
>data: lmy
>DW = 2.0077, p-value = 0.4404
> > durbin.watson(lmy)
> lag Autocorrelation D-W Statistic p-value
> 1 -0.01370151 2.007701 0.92
> >
>So, which P-value should I adopt 0.44 or 0.92?
>Thank you for your help.
>Ahmad Abu Hammour
>
>----- Original Message -----
>From: Torsten Hothorn
>Sent: Friday, April 19, 2002 4:51 AM
>To: Ahmad Abu Hammour
>Cc: R-help at stat.math.ethz.ch
>Subject: Re: [R] Durbin-Watson test in packages "car" and "lmtest"
>
> > Hi,
> > P-values in Durbin-Watson test obtained through the use of
> > functions available in packages "lmtest" and "car" are different. The
> > difference is quite significant. function "dwtest" in "lmtest" is much
> > faster than "burbinwatson" in "car". Actually, you can take a nap while
> > the latter trying to calculated Durbin-Watson test. My question is which
> > p-value is better?
>
>The answer is essencially given in ?durbin.watson and ?dwtest. The latter
>states that
>
>The p value is computed
> using a Fortran version of the Applied Statistics Algorithm AS 153
> by Farebrother (1980, 1984). This algorithm is called "pan" or
> "gradsol". For large sample sizes the algorithm might fail to
> compute the p value; in that case a warning is printed and an
> approximate p value will be given; this p value is computed using
> a normal approximation with mean and variance of the Durbin-Watson
> test statistic.
>while ?durbin.watson says
>
> simulate: if `TRUE' p-values will be estimated by bootstrapping.
>
>What is a "quite significant" difference for p-values?
>
>Looking at the example from ?durbin.watson gives:
>
>R> durbin.watson(lm(fconvict ~ tfr + partic + degrees + mconvict,
>data=Hartnagel))
>lag Autocorrelation D-W Statistic p-value
> 1 0.688345 0.6168636 0
>R> dwtest(fconvict ~ tfr + partic + degrees + mconvict, data=Hartnagel)
>
> Durbin-Watson test
>
>data: fconvict ~ tfr + partic + degrees + mconvict
>DW = 0.6169, p-value = 6.96e-09
>
>which is fairly close, so you might give us more details (that is: a
>working example) to see what the "difference" is (that is: a bug in
>either function or a difference due to simulation error / bad
>approximation ...).
>
>Torsten
>
> >
> > Thank you,
> > Ahmad Abu Hammour
> >
-----------------------------------------------------
John Fox
Department of Sociology
McMaster University
Hamilton, Ontario, Canada L8S 4M4
email: jfox at mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox
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