This example creates an ordinary SAS data set that contains sample means and standard errors computed from imputed data sets. These estimates are then combined to generate valid univariate inferences about the population means.
The following statements use the UNIVARIATE procedure to generate sample means and standard errors for the variables in each imputed data set:
proc univariate data=outmi noprint; var Oxygen RunTime RunPulse; output out=outuni mean=Oxygen RunTime RunPulse stderr=SOxygen SRunTime SRunPulse; by _Imputation_; run;
The following statements display the output data set from PROC UNIVARIATE shown in Output 58.1.1:
proc print data=outuni; title 'UNIVARIATE Means and Standard Errors'; run;
Output 58.1.1: UNIVARIATE Output Data Set
UNIVARIATE Means and Standard Errors |
Obs | _Imputation_ | Oxygen | RunTime | RunPulse | SOxygen | SRunTime | SRunPulse |
---|---|---|---|---|---|---|---|
1 | 1 | 47.0120 | 10.4441 | 171.216 | 0.95984 | 0.28520 | 1.59910 |
2 | 2 | 47.2407 | 10.5040 | 171.244 | 0.93540 | 0.26661 | 1.75638 |
3 | 3 | 47.4995 | 10.5922 | 171.909 | 1.00766 | 0.26302 | 1.85795 |
4 | 4 | 47.1485 | 10.5279 | 171.146 | 0.95439 | 0.26405 | 1.75011 |
5 | 5 | 47.0042 | 10.4913 | 172.072 | 0.96528 | 0.27275 | 1.84807 |
The following statements combine the means and standard errors from imputed data sets, The EDF= option requests that the adjusted degrees of freedom be used in the analysis. For sample means based on 31 observations, the complete-data error degrees of freedom is 30.
proc mianalyze data=outuni edf=30; modeleffects Oxygen RunTime RunPulse; stderr SOxygen SRunTime SRunPulse; run;
The “Model Information” table in Output 58.1.2 lists the input data set(s) and the number of imputations. The “Variance Information” table in Output 58.1.2 displays the between-imputation variance, within-imputation variance, and total variance for each univariate inference. It also displays the degrees of freedom for the total variance. The relative increase in variance due to missing values, the fraction of missing information, and the relative efficiency for each imputed variable are also displayed. A detailed description of these statistics is provided in the section Combining Inferences from Imputed Data Sets and the section Multiple Imputation Efficiency.
Output 58.1.2: Variance Information
Model Information | |
---|---|
Data Set | WORK.OUTUNI |
Number of Imputations | 5 |
Variance Information | |||||||
---|---|---|---|---|---|---|---|
Parameter | Variance | DF | Relative Increase in Variance |
Fraction Missing Information |
Relative Efficiency |
||
Between | Within | Total | |||||
Oxygen | 0.041478 | 0.930853 | 0.980626 | 26.298 | 0.053471 | 0.051977 | 0.989712 |
RunTime | 0.002948 | 0.073142 | 0.076679 | 26.503 | 0.048365 | 0.047147 | 0.990659 |
RunPulse | 0.191086 | 3.114442 | 3.343744 | 25.463 | 0.073626 | 0.070759 | 0.986046 |
The “Parameter Estimates” table in Output 58.1.3 displays the estimated mean and corresponding standard error for each variable. The table also displays a 95% confidence interval for the mean and a t statistic with the associated p-value for testing the hypothesis that the mean is equal to the value specified. You can use the THETA0= option to specify the value for the null hypothesis, which is zero by default. The table also displays the minimum and maximum parameter estimates from the imputed data sets.
Output 58.1.3: Parameter Estimates
Parameter Estimates | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Parameter | Estimate | Std Error | 95% Confidence Limits | DF | Minimum | Maximum | Theta0 | t for H0: Parameter=Theta0 |
Pr > |t| | |
Oxygen | 47.180993 | 0.990266 | 45.1466 | 49.2154 | 26.298 | 47.004201 | 47.499541 | 0 | 47.64 | <.0001 |
RunTime | 10.511906 | 0.276910 | 9.9432 | 11.0806 | 26.503 | 10.444149 | 10.592244 | 0 | 37.96 | <.0001 |
RunPulse | 171.517500 | 1.828591 | 167.7549 | 175.2801 | 25.463 | 171.146171 | 172.071730 | 0 | 93.80 | <.0001 |
Note that the results in this example could also have been obtained with the MI procedure.