# The MIANALYZE Procedure

### Example 64.9 Reading Nominal Logistic Model Results

This example creates data sets to contain parameter estimates that are computed by a nominal 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=outfish3;
class Species;
model Species= Length Width / link=glogit covb;
by _Imputation_;
ods output ParameterEstimates=lgsparms
CovB=lgscovb;
run;
```

The following statements display (in Output 64.9.1) the output logistic regression coefficients from PROC LOGISTIC for the first two imputed data sets:

```proc print data=lgsparms (obs=12);
title 'LOGISTIC Model Coefficients (First Two Imputations)';
run;
```

Output 64.9.1: PROC LOGISTIC Model Coefficients

 LOGISTIC Model Coefficients (First Two Imputations)

Obs _Imputation_ Variable Response DF Estimate StdErr WaldChiSq ProbChiSq _ESTTYPE_
1 1 Intercept Parkki 1 1.7737 1.7712 1.0029 0.3166 MLE
2 1 Intercept Perch 1 1.1036 1.3426 0.6757 0.4111 MLE
3 1 Length Parkki 1 -0.0353 0.2700 0.0171 0.8960 MLE
4 1 Length Perch 1 -0.8560 0.2635 10.5529 0.0012 MLE
5 1 Width Parkki 1 -0.3784 1.6650 0.0517 0.8202 MLE
6 1 Width Perch 1 5.6213 1.6333 11.8455 0.0006 MLE
7 2 Intercept Parkki 1 2.3507 1.7930 1.7188 0.1898 MLE
8 2 Intercept Perch 1 0.6321 1.3370 0.2235 0.6364 MLE
9 2 Length Parkki 1 -0.3479 0.2460 2.0004 0.1573 MLE
10 2 Length Perch 1 -0.6108 0.2130 8.2274 0.0041 MLE
11 2 Width Parkki 1 1.5786 1.5300 1.0645 0.3022 MLE
12 2 Width Perch 1 4.1610 1.3110 10.0734 0.0015 MLE

The following statements display the covariance matrices that are associated with parameter estimates derived from the first two imputations in Output 64.9.2:

```proc print data=lgscovb (obs=12);
title 'LOGISTIC Model Covariance Matrices (First Two Imputations)';
run;
```

Output 64.9.2: PROC LOGISTIC Covariance Matrices

 LOGISTIC Model Covariance Matrices (First Two Imputations)

Obs _Imputation_ Parameter Intercept_Parkki Intercept_Perch Length_Parkki Length_Perch Width_Parkki Width_Perch
1 1 Intercept_Parkki 3.137016 1.150943 -0.25136 -0.11416 0.857307 0.484917
2 1 Intercept_Perch 1.150943 1.80259 -0.12448 -0.16709 0.557913 0.676397
3 1 Length_Parkki -0.25136 -0.12448 0.072903 0.028705 -0.43386 -0.16464
4 1 Length_Perch -0.11416 -0.16709 0.028705 0.069437 -0.16666 -0.42309
5 1 Width_Parkki 0.857307 0.557913 -0.43386 -0.16666 2.77239 1.00217
6 1 Width_Perch 0.484917 0.676397 -0.16464 -0.42309 1.00217 2.66758
7 2 Intercept_Parkki 3.214747 1.25981 -0.19425 -0.10076 0.436385 0.365388
8 2 Intercept_Perch 1.25981 1.787564 -0.11454 -0.13446 0.460885 0.463036
9 2 Length_Parkki -0.19425 -0.11454 0.060501 0.029263 -0.35903 -0.17062
10 2 Length_Perch -0.10076 -0.13446 0.029263 0.04535 -0.17499 -0.27173
11 2 Width_Parkki 0.436385 0.460885 -0.35903 -0.17499 2.34089 1.081586
12 2 Width_Perch 0.365388 0.463036 -0.17062 -0.27173 1.081586 1.718756

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

```proc mianalyze parms(link=glogit)=lgsparms
covb(effectvar=stacking)=lgscovb
mult;
modeleffects Intercept Length Width;
run;
```

The "Variance Information" table in Output 64.9.3 displays the between-imputation, within-imputation, and total variances for combining complete-data inferences.

Output 64.9.3: Variance Information

The MIANALYZE Procedure

Variance Information
Parameter Response Variance DF Relative
Increase
in Variance
Fraction
Missing
Information
Relative
Efficiency
Between Within Total
Intercept Parkki 0.320907 3.413326 3.798414 389.17 0.112819 0.105964 0.979247
Intercept Perch 0.097847 1.581510 1.698927 837.44 0.074243 0.071327 0.985935
Length Parkki 0.104477 0.087087 0.212460 11.487 1.439631 0.646690 0.885474
Length Perch 0.027078 0.049462 0.081956 25.446 0.656949 0.438914 0.919301
Width Parkki 4.400264 3.544989 8.825306 11.174 1.489516 0.654995 0.884174
Width Perch 1.087492 1.846266 3.151257 23.325 0.706827 0.458630 0.915981

The "Parameter Estimates" table in Output 64.9.4 displays the combined parameter estimates and their associated standard errors.

Output 64.9.4: Parameter Estimates

Parameter Estimates
Parameter Response Estimate Std Error 95% Confidence Limits DF Minimum Maximum Theta0 t for H0:
Parameter=Theta0
Pr > |t|
Intercept Parkki 1.524648 1.948952 -2.30714 5.35644 389.17 0.934503 2.350654 0 0.78 0.4345
Intercept Perch 0.608234 1.303429 -1.95014 3.16661 837.44 0.250824 1.103603 0 0.47 0.6409
Length Parkki 0.136487 0.460933 -0.87280 1.14577 11.487 -0.347887 0.420424 0 0.30 0.7724
Length Perch -0.593458 0.286280 -1.18254 -0.00438 25.446 -0.856010 -0.449840 0 -2.07 0.0484
Width Parkki -1.543028 2.970742 -8.06920 4.98315 11.174 -3.363124 1.578570 0 -0.52 0.6136
Width Perch 3.988903 1.775178 0.31949 7.65831 23.325 3.073085 5.621285 0 2.25 0.0344

The "Multivariate Inference" table in Output 64.9.5 displays multivariate inference for the parameters assuming proportionality of the between-imputation and within-imputation covariance matrices.

Output 64.9.5: Multivariate Inference

Multivariate Inference
Assuming Proportionality of Between/Within Covariance Matrices
Avg Relative
Increase
in Variance
Num DF Den DF F for H0:
Parameter=Theta0
Pr > F
0.403144 6 218.35 3.05 0.0069