### Example 58.7 Reading Logistic Model Results from PARMS= and COVB= Data Sets

This example creates data sets that contains 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 58.7.1) 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 58.7.1: PROC LOGISTIC Model Coefficients

 LOGISTIC Model Coefficients (First Two Imputations)

Obs _Imputation_ Variable DF Estimate StdErr WaldChiSq ProbChiSq _ESTTYPE_
1 1 Intercept 1 -28.2353 316.1 0.0080 0.9288 MLE
2 1 Height 1 5.3362 28.1298 0.0360 0.8495 MLE
3 1 Width 1 -1.0812 60.8035 0.0003 0.9858 MLE
4 1 Height*Width 1 -0.4304 5.1312 0.0070 0.9332 MLE
5 2 Intercept 1 -44.0620 262.5 0.0282 0.8667 MLE
6 2 Height 1 7.3887 23.1824 0.1016 0.7499 MLE
7 2 Width 1 1.6950 49.1462 0.0012 0.9725 MLE
8 2 Height*Width 1 -0.7692 4.0205 0.0366 0.8483 MLE

The following statements displays the covariance matrices associated with parameter estimates derived from the first two imputations in Output 58.7.2:

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

Output 58.7.2: PROC LOGISTIC Covariance Matrices

 LOGISTIC Model Covariance Matrices (First Two Imputations)

Obs _Imputation_ Parameter Intercept Height Width HeightWidth
1 1 Intercept 99938.75 -8395.34 -18879.9 1556.383
2 1 Height -8395.34 791.2859 1535.382 -142.121
3 1 Width -18879.9 1535.382 3697.064 -294.815
4 1 HeightWidth 1556.383 -142.121 -294.815 26.32931
5 2 Intercept 68903.42 -5586.74 -12603.5 1000.283
6 2 Height -5586.74 537.4232 958.5588 -91.2266
7 2 Width -12603.5 958.5588 2415.346 -180.394
8 2 HeightWidth 1000.283 -91.2266 -180.394 16.16428

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 58.7.3 displays the between-imputation, within-imputation, and total variances for combining complete-data inferences.

Output 58.7.3: Variance Information

The MIANALYZE Procedure

Variance Information
Parameter Variance DF Relative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
Between Within Total
Intercept 283.306802 93045 93385 301811 0.003654 0.003647 0.999271
Height 4.985634 751.535758 757.518519 64127 0.007961 0.007929 0.998417
Width 6.262249 3331.888954 3339.403653 789905 0.002255 0.002253 0.999550
Height*Width 0.113341 23.797208 23.933217 123858 0.005715 0.005699 0.998862

The Parameter Estimates table in Output 58.7.4 displays the combined parameter estimates with associated standard errors.

Output 58.7.4: Parameter Estimates

Parameter Estimates
Parameter Estimate Std Error 95% Confidence Limits DF Minimum Maximum Theta0 t for H0:
Parameter=Theta0
Pr > |t|
Intercept -45.536682 305.589037 -644.483 553.4092 301811 -73.331892 -28.235273 0 -0.15 0.8815
Height 7.452449 27.523054 -46.493 61.3977 64127 5.336231 11.217552 0 0.27 0.7866
Width 1.548439 57.787574 -111.713 114.8102 789905 -1.081173 5.645810 0 0.03 0.9786
Height*Width -0.754088 4.892159 -10.343 8.8345 123858 -1.313883 -0.430377 0 -0.15 0.8775