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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