SAS Institute Alert Note SN-010183

From: SAS Technical Support (tsdlist@unx.sas.com)
Date: Wed Jul 02 2003 - 13:58:45 EDT

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    SN-010183 ***Alert Note***

    Incorrect chi-square tests when PARAM, LOESS, or SPLINE is specified

    Product: SAS/STAT
    Component: GAM procedure
    Priority: ALERT

      For models containing a PARAM or LOESS component, all chi-square tests
      in the "Analysis of Deviance" table, even for SPLINE or SPLINE2
      components, are incorrectly computed and are liberal (p-values are too
      small). Use the following formula to compute a correct chi-square
      statistic for each component in this table:

                          (Sum of Squares)
        -----------------------------------------------------
         (Deviance of the Final Estimate) / (N - (Model DF))

      where (Sum of Squares) is the value in the "Analysis of Deviance" table,
      (Deviance of the Final Estimate) is found in the "Iteration Summary and
      Fit Statistics" table, N is the Number of Observations reported in the
      "Summary of Input Data Set" table, and (Model DF) is computed as the sum
      of the DF (degrees of freedom) column in the "Analysis of Deviance"
      table plus one for the intercept plus one for each parameter estimated
      for a PARAM effect. Parameters estimated as zero with missing standard
      error do not contribute to the Model DF, nor do terms labeled
      "Linear(...)".

      The p-value for the above chi-square statistic can be obtained using the
      DATA step function PROBCHI with the chi-square value as computed above
      and DF as reported in the "Analysis of Deviance" table.

      For models containing the SPLINE smoother, the degrees of freedom
      reported in the "Fit Summary for Smoothing Components" table and in the
      "Analysis of Deviance" table for these components should be reduced by
      one. The DF reported for a SPLINE component should be the effective
      number of DF for only the nonlinear part of the SPLINE component, but
      mistakenly includes one DF for the linear part as well. For models
      not involving PARAM or LOESS components, this inflation of the DF makes
      the SPLINE test conservative in large samples, but the test performs
      well for small- and medium-sized samples. A corrected p- value for a
      SPLINE component can be computed by using the PROBCHI function in the
      DATA step. The chi-square argument used in PROBCHI should be the
      reported chi-square if the model does not contain a LOESS or PARAM
      component, or the value computed as above if there is at least one LOESS
      or PARAM component in the model. The DF argument used in PROBCHI should
      be one less than reported. After reduction by one, if the DF are close
      to zero (say, less than 0.5) then this indicates that there is no
      nonlinear part of the SPLINE component and a p-value should not be
      computed.

    Keywords:
      incorrstat incorrout analysis of deviance chisquare linear df degrees of
      freedom model df incorrect inflated too large
      incorrect chi-square tests when param, loess, or spline is specified
      010183 10183

    SAS Note Revised On: Mon, 30 Jun 2003

    System Version Reported Version Fixed

    AIX/6000 8.1 TS1M0
    VM/ESA (CMS) 8.1 TS1M0
    Compaq Tru64 UNIX 8.1 TS1M0 9.1 TS1M0
    HP-UX Operating Systems 8.1 TS1M0
    Intel ABI 8.1 TS1M0
    MIPS ABI 8.1 TS1M0
    OS/390 (MVS) 8.1 TS1M0 9.1 TS1M0
    IBM OS/2 8.1 TS1M0
    Solaris 8.1 TS1M0
    OpenVMS VAX 8.1 TS1M0
    OpenVMS Alpha 8.1 TS1M0 9.1 TS1M0
    Windows NT 8.1 TS1M0 9.1 TS1M0
    Windows 2000 Datacenter Server 8.1 TS1M0 9.1 TS1M0
    Windows 2000 Professional 8.1 TS1M0 9.1 TS1M0
    Windows 2000 Server and Advanced Server 8.1 TS1M0 9.1 TS1M0
    Windows 95 8.1 TS1M0
    Windows 98 8.1 TS1M0

    No Fixes Available

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