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Re: st: RE: durbin watson


From   Robert A Yaffee <bob.yaffee@nyu.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: RE: durbin watson
Date   Fri, 05 May 2006 11:37:53 -0400

I think that the durbin alternative( durbina)
will give you the p value and that should be
functionally equivalent.

Robert A. Yaffee, Ph.D.
Research Professor
Shirley M. Ehrenkranz
School of Social Work
New York University

home address:
Apt 19-W
2100 Linwood Ave.
Fort Lee, NJ
07024-3171
Phone: 201-242-3824
Fax: 201-242-3825
yaffee@nyu.edu

----- Original Message -----
From: "Steichen, Thomas J." <SteichT@rjrt.com>
Date: Friday, May 5, 2006 10:49 am
Subject: st: RE: durbin watson

> Rudy Fichtenbaum writes:
> > 
> > Does Stata have a way of calculating the p-value for a Durbin-
> Watson 
> > statistic? SAS does this and it is a lot easier for students 
> because 
> > they don't have to rely on a Durbin-Watson table which can 
> > result in the test being inconclusive.
> 
> FORTRAN algorithm AS 153 is available for the p-value (copied 
> below). Are you (or anyone else) brave enough to translate it to Mata
> code?  It is known to be slow, even in compiled code!
> 
> Tom
> 
>      DOUBLE PRECISION FUNCTION GRADSOL(A, M, C, N)
> C
> C     TRANSLATION OF AMENDED VERSION OF APPLIED STATISTICS ALGORITHM
> C     AS 153 (AS R52), VOL. 33, 363-366, 1984.
> C     BY R.W. FAREBROTHER  (ORIGINALLY NAMED GRADSOL OR PAN)
> C
> C     GRADSOL EVALUATES THE PROBABILITY THAT A WEIGHTED SUM OF
> C     SQUARED STANDARD NORMAL VARIATES DIVIDED BY X TIMES THE 
> UNWEIGHTEDC     SUM IS LESS THAN A GIVEN CONSTANT, I.E. THAT
> C     A1.U1**2 + A2.U2**2 + ... + AM.UM**2 <
> C     X*(U1**2 + U2**2 + ... + UM**2) + C
> C     WHERE THE U'S ARE STANDARD NORMAL VARIABLES.
> C     FOR THE DURBIN-WATSON STATISTIC, X = DW, C = 0, AND
> C     A ARE THE NON-ZERO EIGENVALUES OF THE "M*A" MATRIX.
> C
> C     THE ELEMENTS A(I) MUST BE ORDERED.  A(0) = X
> C     N = THE NUMBER OF TERMS IN THE SERIES.   THIS DETERMINES THE
> C     ACCURACY AND ALSO THE SPEED.   NORMALLY N SHOULD BE ABOUT 10-15.
> C     --------------
> C     ORIGINALLY FROM STATLIB.  REVISED 5/3/1996 BY CLINT CUMMINS:
> C     1. DIMENSION A STARTING FROM 0  (FORTRAN 77)
> C        IF THE USER DOES NOT INITIALIZE A(0) = X,
> C        THERE WOULD BE UNPREDICTABLE RESULTS, SINCE A(0) IS ACCESSED
> C        WHEN J2=0 FOR THE FINAL DO 60 LOOP.
> C     2. USE X VARIABLE TO AGREE WITH PUBLISHED CODE
> C     3. FIX BUG 2 LINES BELOW  DO 60 L2 = J2, NU, D
> C        PROD = A(J2)  -->  PROD = A(L2)
> C        (PRIOR TO THIS FIX, ONLY THE TESTS WITH M=3 WORKED CORRECTLY)
> C     4. TRANSLATE TO UPPERCASE AND REMOVE TABS
> C     TESTED SUCCESSFULLY ON THE FOLLOWING BENCHMARKS:
> C     1. FAREBROTHER 1984 TABLE (X=0):
> C        A           C   PROBABILITY
> C        1,3,6       1   .0542
> C        1,3,6       7   .4936
> C        1,3,6      20   .8760
> C        1,3,5,7,9   5   .0544
> C        1,3,5,7,9  20   .4853
> C        1,3,5,7,9  50   .9069
> C        3,4,5,6,7   5   .0405
> C        3,4,5,6,7  20   .4603
> C        3,4,5,6,7  50   .9200
> C     2. DURBIN-WATSON 1951/71 SPIRITS DATASET, FOR 
> X=.2,.3,...,3.8, C=0
> C        COMPARED WITH BETA APPROXIMATION  (M=66), A SORTED IN 
> REVERSE ORDER
> C     3. JUDGE, ET AL 2ND ED. P.399 DATASET, FOR X=.2,.3,...,3.8, C=0
> C        COMPARED WITH BETA APPROXIMATION  (M=8), A SORTED IN 
> EITHER ORDER
> C
>      INTEGER M, N
>      DOUBLE PRECISION A(0:M), C, X
> C
> C     LOCAL VARIABLES
> C
>      INTEGER D, H, I, J1, J2, J3, J4, K, L1, L2, NU, N2
>      DOUBLE PRECISION NUM, PIN, PROD, SGN, SUM, SUM1, U, V, Y
>      DOUBLE PRECISION ZERO, ONE, HALF, TWO
>      DATA ZERO/0.D0/, ONE/1.D0/, HALF/0.5D0/, TWO/2.D0/
> C
> C     SET NU = INDEX OF 1ST A(I) >= X.
> C     ALLOW FOR THE A'S BEING IN REVERSE ORDER.
> C
>      IF (A(1) .GT. A(M)) THEN
>        H = M
>        K = -1
>        I = 1
>      ELSE
>        H = 1
>        K = 1
>        I = M
>      ENDIF
>      X = A(0)
>      DO 10 NU = H, I, K
>        IF (A(NU) .GE. X) GO TO 20
>   10 CONTINUE
> C
> C     IF ALL A'S ARE -VE AND C >= 0, THEN PROBABILITY = 1.
> C
>      IF (C .GE. ZERO) THEN
>        GRADSOL = ONE
>        RETURN
>      ENDIF
> C
> C     SIMILARLY IF ALL THE A'S ARE +VE AND C <= 0, THEN PROBABILITY 
> = 0.
> C
>   20 IF (NU .EQ. H .AND. C .LE. ZERO) THEN
>        GRADSOL = ZERO
>        RETURN
>      ENDIF
> C
>      IF (K .EQ. 1) NU = NU - 1
>      H = M - NU
>      IF (C .EQ. ZERO) THEN
>        Y = H - NU
>      ELSE
>        Y = C * (A(1) - A(M))
>      ENDIF
> C
>      IF (Y .GE. ZERO) THEN
>        D = 2
>        H = NU
>        K = -K
>        J1 = 0
>        J2 = 2
>        J3 = 3
>        J4 = 1
>      ELSE
>        D = -2
>        NU = NU + 1
>        J1 = M - 2
>        J2 = M - 1
>        J3 = M + 1
>        J4 = M
>      ENDIF
>      PIN = TWO * DATAN(ONE) / N
>      SUM = HALF * (K + 1)
>      SGN = K / DBLE(N)
>      N2 = N + N - 1
> C
> C       FIRST INTEGRALS
> C
>      DO 70 L1 = H-2*(H/2), 0, -1
>        DO 60 L2 = J2, NU, D
>          SUM1 = A(J4)
> C         FIX BY CLINT CUMMINS 5/3/96
> C          PROD = A(J2)
>          PROD = A(L2)
>          U = HALF * (SUM1 + PROD)
>          V = HALF * (SUM1 - PROD)
>          SUM1 = ZERO
>          DO 50 I = 1, N2, 2
>            Y = U - V * DCOS(DBLE(I)*PIN)
>            NUM = Y - X
>            PROD = DEXP(-C/NUM)
>            DO 30 K = 1, J1
>              PROD = PROD * NUM / (Y - A(K))
>   30       CONTINUE
>            DO 40 K = J3, M
>              PROD = PROD * NUM / (Y - A(K))
>   40       CONTINUE
>            SUM1 = SUM1 + DSQRT(DABS(PROD))
>   50       CONTINUE
>          SGN = -SGN
>          SUM = SUM + SGN * SUM1
>          J1 = J1 + D
>          J3 = J3 + D
>          J4 = J4 + D
>   60   CONTINUE
> C
> C       SECOND INTEGRAL.
> C
>        IF (D .EQ. 2) THEN
>          J3 = J3 - 1
>        ELSE
>          J1 = J1 + 1
>        ENDIF
>        J2 = 0
>        NU = 0
>   70 CONTINUE
> C
>      GRADSOL = SUM
>      RETURN
>      END
> 
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