The MULTREG statement performs power and sample size analyses for Type III F tests of sets of predictors in multiple linear regression, assuming either fixed or normally distributed predictors.
Summary of Options
Table 91.9 summarizes the options available in the MULTREG statement.
specifies the level of significance of the statistical test. The default is 0.05, which corresponds to the usual 0.05 100% = 5% level of significance. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.
MODEL=keyword-list
specifies the assumed distribution of the tested predictors. MODEL=FIXED indicates a fixed predictor distribution. MODEL=RANDOM (the default) indicates a joint multivariate normal distribution for the response and tested predictors. You can use the aliases CONDITIONAL for FIXED and UNCONDITIONAL for RANDOM. For information about specifying the keyword-list, see the section Specifying Value Lists in Analysis Statements.
FIXED
fixed predictors
RANDOM
random (multivariate normal) predictors
NFRACTIONAL
NFRAC
enables fractional input and output for sample sizes. See the section Sample Size Adjustment Options for information about the ramifications of the presence (and absence) of the NFRACTIONAL option.
NFULLPREDICTORS=number-list
NFULLPRED=number-list
specifies the number of predictors in the full model, not counting the intercept. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.
NOINT
specifies a no-intercept model (for both full and reduced models). By default, the intercept is included in the model. If you want to test the intercept, you can specify the NOINT option and simply consider the intercept to be one of the predictors being tested. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.
specifies the number of predictors in the reduced model, not counting the intercept. This is the same as the difference between values of the NFULLPREDICTORS= and NTESTPREDICTORS= options. Note that supplying a value of 0 is the same as specifying an F test of a Pearson correlation. This option cannot be used at the same time as the NTESTPREDICTORS= option. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.
specifies the sample size or requests a solution for the sample size by specifying a missing value (NTOTAL=.). The minimum acceptable value for the sample size depends on the MODEL=, NOINT, NFULLPREDICTORS=, NTESTPREDICTORS=, and NREDUCEDPREDICTORS= options. It ranges from p + 1 to p + 3, where p is the value of the NFULLPREDICTORS option. For further information about minimum NTOTAL values, see Table 91.36. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.
OUTPUTORDER=INTERNAL | REVERSE | SYNTAX
controls how the input and default analysis parameters are ordered in the output. OUTPUTORDER=INTERNAL (the default) arranges the parameters in the output according to the following order of their corresponding options:
The OUTPUTORDER=SYNTAX option arranges the parameters in the output in the same order in which their corresponding options are specified in the MULTREG statement. The OUTPUTORDER=REVERSE option arranges the parameters in the output in the reverse of the order in which their corresponding options are specified in the MULTREG statement.
PARTIALCORR=number-list
PCORR=number-list
specifies the partial correlation between the tested predictors and the response, adjusting for any other predictors in the model. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.
POWER=number-list
specifies the desired power of the test or requests a solution for the power by specifying a missing value (POWER=.). The power is expressed as a probability, a number between 0 and 1, rather than as a percentage. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.
RSQUAREDIFF=number-list
RSQDIFF=number-list
specifies the difference in between the full and reduced models. This is equivalent to the proportion of variation explained by the predictors you are testing. It is also equivalent to the squared semipartial correlation of the tested predictors with the response. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.
RSQUAREFULL=number-list
RSQFULL=number-list
specifies the of the full model, where is the proportion of variation explained by the model. For information about specifying the number-list, see the section Specifying Value Lists in Analysis Statements.
This section summarizes the syntax for the common analyses that are supported in the MULTREG statement.
Type III F Test of a Set of Predictors
You can express effects in terms of partial correlation, as in the following statements. Default values of the TEST=, MODEL=, and ALPHA= options specify a Type III F test with a significance level of 0.05, assuming normally distributed predictors.
proc power;
multreg
model = random
nfullpredictors = 7
ntestpredictors = 3
partialcorr = 0.35
ntotal = 100
power = .;
run;