## Example 57.9 Using a TEST statement

This example creates an EST-type data set that contains regression coefficients and their corresponding covariance matrices computed from imputed data sets. These estimates are then combined to generate valid statistical inferences about the regression model. A TEST statement is used to test linear hypotheses about the parameters.

The following statements use the REG procedure to generate regression coefficients:

```proc reg data=outmi outest=outreg covout noprint;
model Oxygen= RunTime RunPulse;
by _Imputation_;
run;
```

The following statements combine the results for the imputed data sets. A TEST statement is used to test linear hypotheses of Intercept=0 and RunTime=RunPulse.

```proc mianalyze data=outreg edf=28;
modeleffects Intercept RunTime RunPulse;
test Intercept, RunTime=RunPulse / mult;
run;
```

The "Test Specification" table in Output 57.9.1 displays the matrix and the vector in a TEST statement. Since there is no label specified for the TEST statement, "Test 1" is used as the label.

Output 57.9.1 Test Specification
The MIANALYZE Procedure
Test: Test 1

Test Specification
Parameter L Matrix C
Intercept RunTime RunPulse
TestPrm1 1.000000 0 0 0
TestPrm2 0 1.000000 -1.000000 0

The "Variance Information" table in Output 57.9.2 displays the between-imputation variance, within-imputation variance, and total variance for each univariate inference. A detailed description of these statistics is provided in the section Combining Inferences from Imputed Data Sets and the section Multiple Imputation Efficiency.

Output 57.9.2 Variance Information
Variance Information
Parameter Variance DF Relative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
Between Within Total
TestPrm1 45.529229 76.543614 131.178689 9.1917 0.713777 0.461277 0.915537
TestPrm2 0.014715 0.114324 0.131983 20.598 0.154459 0.141444 0.972490

The "Parameter Estimates" table in Output 57.9.3 displays the estimated mean and standard error of the linear components. The inferences are based on the t distribution. The table also displays a 95% mean confidence interval and a t test with the associated p-value for the hypothesis that each linear component of is equal to zero.

Output 57.9.3 Parameter Estimates
Parameter Estimates
Parameter Estimate Std Error 95% Confidence Limits DF Minimum Maximum C t for H0:
Parameter=C
Pr > |t|
TestPrm1 90.837440 11.453327 65.01034 116.6645 9.1917 83.020730 100.839807 0 7.93 <.0001
TestPrm2 -2.964292 0.363294 -3.72070 -2.2079 20.598 -3.091586 -2.763582 0 -8.16 <.0001

With the MULT option, the procedure assumes that the between-imputation covariance matrix is proportional to the within-imputation covariance matrix and displays a multivariate inference for all the linear components taken jointly in Output 57.9.4.

Output 57.9.4 Multivariate Inference
Multivariate Inference
Assuming Proportionality of Between/Within Covariance Matrices
Avg Relative
Increase
in Variance
Num DF Den DF F for H0:
Parameter=Theta0
Pr > F
0.419868 2 35.053 60.34 <.0001