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          .  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    .   46.774  10.25    .     50.388  10.08  168   39.407  12.63  174     46.080  11.17  156   45.441   9.63  164       .      8.92    .   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   ;  

Suppose 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=3237851;   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;  

The following statements display parameter estimates and covariance matrices from the first two imputed data sets in Figure 45.1.

  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                     86.544   2.82231   0.05873   2         1         COV       Intercept      100.145   0.53519   0.55077   3         1         COV       RunTime   0.535      0.10774   0.00345   4         1         COV       RunPulse   0.551   0.00345     0.00343   5         2         PARMS                     83.021   3.00023   0.02491   6         2         COV       Intercept       79.032   0.66765   0.41918   7         2         COV       RunTime   0.668      0.11456   0.00313   8         2         COV       RunPulse   0.419   0.00313     0.00264  

Figure 45.1: Parameter Estimates

The following statements combine the five sets of regression coefficients:

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

  The MIANALYZE Procedure   Model Information   Data Set                  WORK.OUTREG   Number of Imputations     5  

Figure 45.2: Model Information Table

The Model Information table shown in Figure 45.2 lists the input data set(s) and the number of imputations.

  The MIANALYZE Procedure   Multiple Imputation Variance Information   -----------------Variance----------------   Parameter        Between        Within        Total        DF   Intercept      45.529229     76.543614   131.178689    23.059   RunTime         0.019390      0.106220     0.129487    123.88   RunPulse        0.001007      0.002537     0.003746    38.419   Multiple Imputation Variance Information   Relative       Fraction   Increase        Missing        Relative   Parameter     in Variance    Information      Efficiency   Intercept        0.713777       0.461277        0.915537   RunTime          0.219051       0.192620        0.962905   RunPulse         0.476384       0.355376        0.933641  

Figure 45.3: Variance Information Table

The Multiple Imputation Variance Information table shown in Figure 45.3 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, the fraction of missing information, and the relative efficiency for each parameter estimate.

  The MIANALYZE Procedure   Multiple Imputation Parameter Estimates   Parameter        Estimate      Std Error    95% Confidence Limits        DF   Intercept       90.837440      11.453327     67.14779     114.5271   23.059   RunTime   3.032870       0.359844   3.74511   2.3206   123.88   RunPulse   0.068578       0.061204   0.19243       0.0553   38.419   Multiple Imputation Parameter Estimates   Parameter         Minimum        Maximum   Intercept       83.020730     100.839807   RunTime   3.204426   2.822311   RunPulse   0.112840   0.024910   Multiple Imputation Parameter Estimates   t for H0:   Parameter          Theta0   Parameter=Theta0   Pr > t   Intercept               0               7.93     <.0001   RunTime                 0   8.43     <.0001   RunPulse                0   1.12     0.2695  

Figure 45.4: Multiple Imputation Parameter Estimates

The Multiple Imputation Parameter Estimates table shown in Figure 45.4 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.