This example creates data sets that contains parameter estimates 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 for each imputed data set:
proc logistic data=outfish2; class Species; model Species= Length Width / covb; by _Imputation_; ods output ParameterEstimates=lgsparms; run;
The following statements display (in Output 64.7.1) 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 64.7.1: PROC LOGISTIC Model Coefficients
LOGISTIC Model Coefficients (First Two Imputations) |
Obs | _Imputation_ | Variable | DF | Estimate | StdErr | WaldChiSq | ProbChiSq | _ESTTYPE_ |
---|---|---|---|---|---|---|---|---|
1 | 1 | Intercept | 1 | 0.1637 | 1.8405 | 0.0079 | 0.9291 | MLE |
2 | 1 | Length | 1 | 1.4543 | 0.5167 | 7.9231 | 0.0049 | MLE |
3 | 1 | Width | 1 | -10.2950 | 3.4860 | 8.7216 | 0.0031 | MLE |
4 | 2 | Intercept | 1 | 0.6473 | 1.9003 | 0.1160 | 0.7334 | MLE |
5 | 2 | Length | 1 | 1.2831 | 0.4778 | 7.2123 | 0.0072 | MLE |
6 | 2 | Width | 1 | -9.2991 | 3.2187 | 8.3469 | 0.0039 | MLE |
7 | 3 | Intercept | 1 | -0.0408 | 1.8535 | 0.0005 | 0.9824 | MLE |
8 | 3 | Length | 1 | 0.9208 | 0.3978 | 5.3564 | 0.0206 | MLE |
The following statements displays the covariance matrices associated with parameter estimates derived from the first two imputations in Output 64.7.2:
The following statements use the MIANALYZE procedure with input PARMS= data set:
proc mianalyze parms=lgsparms; modeleffects Intercept Length Width; run;
The "Variance Information" table in Output 64.7.2 displays the between-imputation, within-imputation, and total variances for combining complete-data inferences.
Output 64.7.2: Variance Information
Variance Information | |||||||
---|---|---|---|---|---|---|---|
Parameter | Variance | DF | Relative Increase in Variance |
Fraction Missing Information |
Relative Efficiency |
||
Between | Within | Total | |||||
Intercept | 0.125100 | 3.174905 | 3.325025 | 1962.3 | 0.047283 | 0.046120 | 0.990860 |
Length | 0.039992 | 0.201496 | 0.249486 | 108.11 | 0.238169 | 0.206894 | 0.960265 |
Width | 1.895087 | 9.030840 | 11.304945 | 98.85 | 0.251815 | 0.216847 | 0.958433 |
The "Parameter Estimates" table in Output 64.7.3 displays the combined parameter estimates with associated standard errors.
Output 64.7.3: Parameter Estimates
Parameter Estimates | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
Parameter | Estimate | Std Error | 95% Confidence Limits | DF | Minimum | Maximum | Theta0 | t for H0: Parameter=Theta0 |
Pr > |t| | |
Intercept | 0.073984 | 1.823465 | -3.5021 | 3.65012 | 1962.3 | -0.208872 | 0.647303 | 0 | 0.04 | 0.9676 |
Length | 1.191908 | 0.499485 | 0.2019 | 2.18196 | 108.11 | 0.920752 | 1.454324 | 0 | 2.39 | 0.0188 |
Width | -8.499960 | 3.362283 | -15.1716 | -1.82834 | 98.85 | -10.294965 | -6.703819 | 0 | -2.53 | 0.0131 |