SAS Institute Alert Note SN-010047

From: SAS Technical Support (tsdlist@unx.sas.com)
Date: Tue Jun 10 2003 - 12:14:31 EDT

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    SN-010047 ***Alert Note***

    Goodness-of-fit statistics are incorrect for nested logit models

    Product: SAS/ETS
    Component: MDC procedure
    Priority: ALERT

      The goodness-of-fit statistics are incorrect for nested logit models.

      Correct values of the goodness-of-fit measures may be computed in a DATA
      step using the log likelihood value, number of observations, number of
      regressors in the model, and the null model log likelihood value. In
      order to compute the null model log likelihood value, use PROC MDC to
      estimate the null model by restricting the regressor coefficients to 0.0
      and the inclusive value parameters to 1.0, as in the following example:

         proc mdc data=choicedata;
            title 'Null Model';
            model decision = x1 x2 x3 / type=nlogit choice=(mode);
            id id;
            restrict fixedparm=(0.0 0.0 0.0 1.0 1.0); * Release 8.2 syntax *;
            *restrict x1_L1=0.0, x2_L1=0.0, x3_L2G1=0.0, INC_L2G1C1=1.0,
               INC_L2G1C2=1; * SAS System 9 syntax *;
            utility u(1,)=x1-x2, u(2, 1 2 @ 1)=x3;
            nest level(1) = (1 2 3 @ 1, 4 5 @ 2), level(2) = (1 2 @ 1);
         run;

         data GoodnessOfFit;
            LogLo=-611.58641; * null model log likelihood *;
            LogL =-610.23835; * log likelihood *;
            N=380; * number of observations *;
            K=3; * number of regressors *;
            length measure $ 20;
            keep measure Value;
            R=2*(LogL-LogLo);
            U=-2*LogLo;
            measure='LikelihoodRatio';
            value=R;
            output;
            measure='UpperBoundOfR';
            value=U;
            output;
            measure='AldrichNelson';
            value=R/(R+N);
            output;
            measure='CraggUhler1';
            value=1-exp(-R/N);
            output;
            measure='CraggUhler2';
            value=(1-exp(-R/N))/(1-exp(-U/N));
            output;
            measure='Estrella';
            value=1-(1-R/U)**(U/N);
            output;
            measure='AdjustedEstrella';
            value=1-((LogL-K)/LogLo)**(-2/N*LogLo);
            output;
            measure='McFaddenLRI';
            value=R/U;
            output;
            measure='VeallZimmermann';
            value=(R*(U+N))/(U*(R+N));
            output;
         run;

    Keywords:
      nested logit model goodness of fit statistics incorrstat incorrout
      goodness-of-fit statistics are incorrect for nested logit models
      010047 10047

    SAS Note Revised On: Wed, 21 May 2003

    System Version Reported Version Fixed

    AIX 64 bit 8.2 TS2M0 9.1 TS1M0
    AIX 64 bit 9 TSM0 9.1 TS1M0
    AIX/6000 8.2 TS2M0
    VM/ESA (CMS) 8.2 TS2M0
    Compaq Tru64 UNIX 8.2 TS2M0 9.1 TS1M0
    Compaq Tru64 UNIX 9 TSM0 9.1 TS1M0
    HP-UX Operating Systems 8.2 TS2M0
    HP-UX Itanium 9 TSM0 9.1 TS1M0
    HP-UX 64 bit 8.2 TS2M0 9.1 TS1M0
    HP-UX 64 bit 9 TSM0 9.1 TS1M0
    Intel ABI 8.2 TS2M0
    Intel Itanium Processor Family(IPF) 9 TSM0 9.1 TS1M0
    Linux 8.2 TS2M0 9.1 TS1M0
    Linux 9 TSM0 9.1 TS1M0
    MIPS ABI 8.2 TS2M0
    OS/390 (MVS) 8.2 TS2M0 9.1 TS1M0
    OS/390 (MVS) 9 TSM0 9.1 TS1M0
    IBM OS/2 8.2 TS2M0
    Solaris 8.2 TS2M0
    Solaris 64 bit 8.2 TS2M0 9.1 TS1M0
    Solaris 64 bit 9 TSM0 9.1 TS1M0
    OpenVMS VAX 8.2 TS2M0
    OpenVMS Alpha 8.2 TS2M0 9.1 TS1M0
    OpenVMS Alpha 9 TSM0 9.1 TS1M0
    Windows NT 8.2 TS2M0 9.1 TS1M0
    Windows NT 8.2 TS2M0 9.1 TS1M0
    Windows NT 9 TSM0 9.1 TS1M0
    Windows 2000 Datacenter Server 8.2 TS2M0 9.1 TS1M0
    Windows 2000 Datacenter Server 8.2 TS2M0 9.1 TS1M0
    Windows 2000 Datacenter Server 9 TSM0 9.1 TS1M0
    Windows 2000 Professional 8.2 TS2M0 9.1 TS1M0
    Windows 2000 Professional 8.2 TS2M0 9.1 TS1M0
    Windows 2000 Professional 9 TSM0 9.1 TS1M0
    Windows 2000 Server and Advanced Server 8.2 TS2M0 9.1 TS1M0
    Windows 95 8.2 TS2M0
    Windows 98 8.2 TS2M0
    Windows ME 8.2 TS2M0
    Windows XP 8.2 TS2M0 9.1 TS1M0

    No Fixes Available

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