This example creates data sets that contains parameter estimates and corresponding covariance matrices with classification variables computed by a mixed regression model 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 MIXED to generate the parameter estimates and covariance matrix for each imputed data set:
ods select none; proc mixed data=outfish2; class Species; model Length= Species Width/ solution; by _Imputation_; ods output SolutionF=mxparms; run; ods select all;
Because of the ODS SELECT statements, no output is displayed. The following statements display (in Output 76.8.1) the output mixed model coefficients from PROC MIXED for the first two imputed data sets:
proc print data=mxparms (obs=8); var _Imputation_ Effect Species Estimate StdErr; title 'MIXED Model Coefficients (First Two Imputations)'; run;
Output 76.8.1: PROC MIXED Model Coefficients
MIXED Model Coefficients (First Two Imputations) |
Obs | _Imputation_ | Effect | Species | Estimate | StdErr |
---|---|---|---|---|---|
1 | 1 | Intercept | 4.5106 | 0.8244 | |
2 | 1 | Species | Parkki | 1.5774 | 0.7020 |
3 | 1 | Species | Perch | 0 | . |
4 | 1 | Width | 5.2585 | 0.1599 | |
5 | 2 | Intercept | 4.5250 | 0.8771 | |
6 | 2 | Species | Parkki | 1.4885 | 0.7693 |
7 | 2 | Species | Perch | 0 | . |
8 | 2 | Width | 5.2389 | 0.1701 |
The following statements use the MIANALYZE procedure with an input PARMS= data set:
proc mianalyze parms(classvar=full)=mxparms; class Species; modeleffects Intercept Species Width; run;
The "Variance Information" table in Output 76.8.2 displays the between-imputation, within-imputation, and total variances for combining complete-data inferences.
Output 76.8.2: Variance Information
Variance Information (25 Imputations) | ||||||||
---|---|---|---|---|---|---|---|---|
Parameter | Species | Variance | DF | Relative Increase in Variance |
Fraction Missing Information |
Relative Efficiency |
||
Between | Within | Total | ||||||
Intercept | 0.065665 | 0.668667 | 0.736959 | 2794.9 | 0.102131 | 0.093316 | 0.996281 | |
Species | Parkki | 0.077291 | 0.525640 | 0.606023 | 1364.1 | 0.152924 | 0.133909 | 0.994672 |
Species | Perch | 0 | . | . | . | . | . | . |
Width | 0.002276 | 0.025876 | 0.028243 | 3416 | 0.091488 | 0.084356 | 0.996637 |
The "Parameter Estimates" table in Output 76.8.3 displays the combined parameter estimates with associated standard errors.
Output 76.8.3: Parameter Estimates
Parameter Estimates (25 Imputations) | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Parameter | Species | Estimate | Std Error | 95% Confidence Limits | DF | Minimum | Maximum | Theta0 | t for H0: Parameter=Theta0 |
Pr > |t| | |
Intercept | 4.519259 | 0.858463 | 2.83597 | 6.202545 | 2794.9 | 4.013624 | 5.162463 | 0 | 5.26 | <.0001 | |
Species | Parkki | 1.277902 | 0.778475 | -0.24924 | 2.805039 | 1364.1 | 0.647898 | 1.710559 | 0 | 1.64 | 0.1009 |
Species | Perch | 0 | . | . | . | . | 0 | 0 | 0 | . | . |
Width | 5.284285 | 0.168056 | 4.95478 | 5.613786 | 3416 | 5.206516 | 5.369231 | 0 | 31.44 | <.0001 |