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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