The MIANALYZE Procedure

Getting Started

The Fitness data set has been altered to contain an arbitrary missing pattern:

  
*----------------- Data on Physical Fitness -----------------*
| These measurements were made on men involved in a physical |
| fitness course at N.C. State University.                   |
| Only selected variables of                                 |
| Oxygen (oxygen intake, ml per kg body weight per minute),  |
| Runtime (time to run 1.5 miles in minutes), and            |
| RunPulse (heart rate while running) are used.              |
| Certain values were changed to missing for the analysis.   |
*------------------------------------------------------------*;

  
   data FitMiss;
      input Oxygen RunTime RunPulse @@;
      datalines;
   44.609  11.37  178     45.313  10.07  185  
   54.297   8.65  156     59.571    .      .  
   49.874   9.22    .     44.811  11.63  176  
     .     11.95  176     49.091  10.85    .  
   39.442  13.08  174     60.055   8.63  170  
   50.541    .      .     37.388  14.03  186  
   44.754  11.12  176     47.273    .      .  
   51.855  10.33  166     49.156   8.95  180  
   40.836  10.95  168     46.672  10.00    .  
     .     10.25    .     50.388  10.08  168  
   39.407  12.63  174     46.080  11.17  156  
   45.441   9.63  164       .      8.92  146  
   45.118  11.08    .     39.203  12.88  168  
   45.790  10.47  186     50.545   9.93  148  
   48.673   9.40  186     47.920  11.50  170  
   47.467  10.50  170  
   ;

Assume that the data are multivariate normally distributed and that the missing data are missing at random (see the "Statistical Assumptions for Multiple Imputation" section in "The MI Procedure" chapter for a description of these assumptions). The following statements use the MI procedure to impute missing values for the FitMiss data set.

   proc mi data=FitMiss noprint out=outmi seed=37851;   
      var Oxygen RunTime RunPulse; 
   run;

The MI procedure creates imputed data sets, which are stored in the outmi data set. A variable named _Imputation_ indicates the imputation numbers. Based on m imputations, m different sets of the point and variance estimates for a parameter can be computed. In this example, m=5 is the default.

The following statements generate regression coefficients for each of the five imputed data sets:

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

   proc print data=outreg(obs=8);
      var _Imputation_ _Type_ _Name_
         Intercept RunTime RunPulse;
      title 'Parameter Estimates from Imputed Data Sets';
   run;

Parameter Estimates from Imputed Data Sets

Obs	_Imputation_	_TYPE_	_NAME_	Intercept	RunTime	RunPulse
1	1	PARMS		97.2874	-2.98892	-0.10684
2	1	COV	Intercept	55.7516	-0.73348	-0.27870
3	1	COV	RunTime	-0.7335	0.15167	-0.00509
4	1	COV	RunPulse	-0.2787	-0.00509	0.00194
5	2	PARMS		90.9324	-2.93338	-0.07391
6	2	COV	Intercept	37.5576	-0.25970	-0.20442
7	2	COV	RunTime	-0.2597	0.13978	-0.00722
8	2	COV	RunPulse	-0.2044	-0.00722	0.00166

Figure 10.1: Parameter Estimates

The following statements combine the five sets of regression coefficients:

   proc mianalyze data=outreg;
      var Intercept RunTime RunPulse;
   run;

The MIANALYZE Procedure

Model Information
Data Set	WORK.OUTREG
Number of Imputations	5

Multiple Imputation Variance Information
Parameter	Variance			DF	Relative Increase in Variance	Fraction Missing Information
Parameter	Between	Within	Total	DF	Relative Increase in Variance	Fraction Missing Information
Intercept	74.179857	57.287519	146.303348	10.805	1.553843	0.665161
RunTime	0.034202	0.142151	0.183193	79.694	0.288719	0.242803
RunPulse	0.001533	0.002304	0.004144	20.292	0.798522	0.491731

Figure 10.2: Model Information and Variance Information Tables

The "Model Information" table lists the input data set(s) and the number of imputations. The "Multiple Imputation Variance Information" table displays the between-imputation, within-imputation, and total variances for combining complete-data inferences. It also displays the degrees of freedom for the total variance, the relative increase in variance due to missing values, and the fraction of missing information for each parameter estimate.

The MIANALYZE Procedure

Multiple Imputation Parameter Estimates
Parameter	Estimate	Std Error	95% Confidence Limits		DF	Minimum	Maximum	Theta0	t for H0: Parameter=Theta0	Pr > \|t\|
Intercept	92.156840	12.095592	65.47596	118.8377	10.805	77.939497	99.920480	0	7.62	<.0001
RunTime	-2.955317	0.428011	-3.80714	-2.1035	79.694	-3.159663	-2.660085	0	-6.90	<.0001
RunPulse	-0.079851	0.064376	-0.21401	0.0543	20.292	-0.112277	-0.015111	0	-1.24	0.2290

Figure 10.3: Multiple Imputation Parameter Estimates

The "Multiple Imputation Parameter Estimates" table displays a combined estimate and standard error for each regression coefficient (parameter). Inferences are based on t distributions. The table displays a 95% confidence interval and a t-test with the associated p-value for the hypothesis that the parameter is equal to the value specified with the THETA0= option (in this case, zero by default). The minimum and maximum parameter estimates from the imputed data sets are also displayed.

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