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The MIANALYZE Procedure

Example 55.7 Reading Logistic Model Results from PARMS= and COVB= Data Sets

This example creates data sets containing parameter estimates and corresponding covariance matrices computed by a logistic regression analysis for a set of imputed data sets. These estimates are then combined to generate valid statistical inferences about the model parameters.

The following statements use PROC LOGISTIC to generate the parameter estimates and covariance matrix for each imputed data set:

proc logistic data=outfish;
   class Species;
   model Species= Height Width Height*Width/ covb;
   by _Imputation_;
   ods output ParameterEstimates=lgsparms
              CovB=lgscovb;
run;

The following statements display (in Output 55.7.1) the output logistic regression coefficients from PROC LOGISTIC for the first two imputed data sets:

proc print data=lgsparms (obs=8);
   title 'LOGISTIC Model Coefficients (First Two Imputations)';
run;

Output 55.7.1 PROC LOGISTIC Model Coefficients
LOGISTIC Model Coefficients (First Two Imputations)

Obs _Imputation_ Variable DF Estimate StdErr WaldChiSq ProbChiSq
1 1 Intercept 1 -22.7507 45.7309 0.2475 0.6188
2 1 Height 1 4.3267 3.7473 1.3332 0.2482
3 1 Width 1 -1.7027 7.8049 0.0476 0.8273
4 1 Height*Width 1 -0.3517 0.5542 0.4028 0.5256
5 2 Intercept 1 -27.2116 26.3744 1.0645 0.3022
6 2 Height 1 4.1833 2.0347 4.2271 0.0398
7 2 Width 1 1.1045 6.1278 0.0325 0.8570
8 2 Height*Width 1 -0.4495 0.3251 1.9116 0.1668

The following statements displays the covariance matrices associated with parameter estimates derived from the first two imputations in Output 55.7.2:

proc print data=lgscovb (obs=8);
   title 'LOGISTIC Model Covariance Matrices (First Two Imputations)';
run;

Output 55.7.2 PROC LOGISTIC Covariance Matrices
LOGISTIC Model Covariance Matrices (First Two Imputations)

Obs _Imputation_ Parameter Intercept Height Width HeightWidth
1 1 Intercept 2091.316 -158.686 -330.408 24.9984
2 1 Height -158.686 14.04241 21.1609 -1.98425
3 1 Width -330.408 21.1609 60.91617 -3.84737
4 1 HeightWidth 24.9984 -1.98425 -3.84737 0.307092
5 2 Intercept 695.6072 -36.8743 -148.034 7.997264
6 2 Height -36.8743 4.139861 4.497508 -0.57405
7 2 Width -148.034 4.497508 37.55025 -1.52686
8 2 HeightWidth 7.997264 -0.57405 -1.52686 0.105678

The following statements use the MIANALYZE procedure with input PARMS= and COVB= data sets:

proc mianalyze parms=lgsparms
               covb(effectvar=stacking)=lgscovb;
   modeleffects Intercept Height Width Height*Width;
run;

The "Variance Information" table in Output 55.7.3 displays the between-imputation, within-imputation, and total variances for combining complete-data inferences.

Output 55.7.3 Variance Information
The MIANALYZE Procedure

Variance Information
Parameter Variance DF Relative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
Between Within Total
Intercept 5.034765 1668.718613 1674.760331 307358 0.003621 0.003614 0.999278
Height 0.024662 11.102796 11.132390 565996 0.002666 0.002662 0.999468
Width 2.258894 53.686948 56.397621 1731.5 0.050490 0.049161 0.990263
Height*Width 0.002655 0.245967 0.249153 24467 0.012952 0.012867 0.997433

The "Parameter Estimates" table in Output 55.7.4 displays the combined parameter estimates with associated standard errors.

Output 55.7.4 Parameter Estimates
Parameter Estimates
Parameter Estimate Std Error 95% Confidence Limits DF Minimum Maximum Theta0 t for H0:
Parameter=Theta0
Pr > |t|
Intercept -25.952920 40.923836 -106.162 54.25664 307358 -28.627325 -22.750660 0 -0.63 0.5260
Height 4.367841 3.336524 -2.172 10.90732 565996 4.183264 4.570938 0 1.31 0.1905
Width -0.321990 7.509835 -15.051 14.40731 1731.5 -1.702651 1.500299 0 -0.04 0.9658
Height*Width -0.408057 0.499152 -1.386 0.57031 24467 -0.473804 -0.351718 0 -0.82 0.4137

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