On Wed, 5 Aug 2009, Hardi wrote:
Hi,
I ran an experiment with 3 factors, 2 levels and 200 replications and as
I want to test for residuals independence, I used Durbin-Watson in R.
I found two functions (durbin.watson and dwtest) and while both are
giving the same rho, the p-values are greatly differ:
durbin.watson(mod1)
lag Autocorrelation D-W Statistic p-value
1 -0.04431012 2.088610 0.012
Alternative hypothesis: rho != 0
dwtest(mod1)
Durbin-Watson test
data: mod1
DW = 2.0886, p-value = 0.9964
alternative hypothesis: true autocorrelation is greater than 0
durbin.watson suggests that I should reject the null hypothesis while
dwtest suggests that I should NOT reject Ho.
What do you expect? The default alternative in durbin.watson() is rho != 0
(as displayed above!) and in dwtest() it is rho > 0 (as displayed above!).
For an empirical correlation of -0.044 one would hope that the p-values
are very different.
Beyond that, the approaches for computing the p-value in durbin.watson()
and dwtest() are different. The former uses resampling techniques, the
latter uses either the exact or approximate asymptotic distribution.
If I look it up in the following table:
http://www.stanford.edu/~clint/bench/dw05d.htm, T = 1600 and K = 8 gives
dL = 1.90902 and dU = 1.92659.
Which means I should not reject Ho as DW > dU.
First, this is inferior technology compared to both approaches discussed
above. Second, you are using it wrong! These are upper and lower bounds
for a single critical value for the one-sided alternative rho > 0. So
interpreting it correctly DW > dU means that you can confidently conclude
that DW is _not_ significant. But you didn't need a significance test for
that when the empirical correlation is less than zero and you want to show
that it is greater than zero.
Is there a bug in durbin.watson? should I use dwtest instead? can
somebody help me explain what is happening?
It might help if you read about the theory behind the Durbin-Watson test
and why it is difficult to evaluate its null distributions.
Best,
Z
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