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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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