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:
proc mixed data=outfish; class Species; model Length= Species Height Width/ solution covb; by _Imputation_; ods output SolutionF=mxparms CovB=mxcovb; run;
The following statements display (in Output 58.8.1) the output mixed model coefficients from PROC MIXED for the first two imputed data sets:
proc print data=mxparms (obs=10); var _Imputation_ Effect Species Estimate StdErr; title 'MIXED Model Coefficients (First Two Imputations)'; run;
Output 58.8.1: PROC MIXED Model Coefficients
MIXED Model Coefficients (First Two Imputations) |
Obs | _Imputation_ | Effect | Species | Estimate | StdErr |
---|---|---|---|---|---|
1 | 1 | Intercept | 12.5356 | 2.7808 | |
2 | 1 | Species | Bream | -11.9103 | 3.5386 |
3 | 1 | Species | Pike | 0 | . |
4 | 1 | Height | -0.1605 | 0.5158 | |
5 | 1 | Width | 7.3962 | 1.1365 | |
6 | 2 | Intercept | 13.3607 | 2.7848 | |
7 | 2 | Species | Bream | -10.5204 | 3.0517 |
8 | 2 | Species | Pike | 0 | . |
9 | 2 | Height | -0.3139 | 0.4384 | |
10 | 2 | Width | 7.4861 | 1.0005 |
The following statements use the MIANALYZE procedure with an input PARMS= data set:
proc mianalyze parms(classvar=full)=mxparms; class Species; modeleffects Intercept Species Height Width; run;
The “Variance Information” table in Output 58.8.2 displays the between-imputation, within-imputation, and total variances for combining complete-data inferences.
Output 58.8.2: Variance Information
Variance Information | ||||||||
---|---|---|---|---|---|---|---|---|
Parameter | Species | Variance | DF | Relative Increase in Variance |
Fraction Missing Information |
Relative Efficiency |
||
Between | Within | Total | ||||||
Intercept | 0.325023 | 7.632716 | 8.022743 | 1692.4 | 0.051099 | 0.049738 | 0.990150 | |
Species | Bream | 0.307202 | 10.394843 | 10.763486 | 3410 | 0.035464 | 0.034815 | 0.993085 |
Species | Pike | 0 | . | . | . | . | . | . |
Height | 0.003686 | 0.217662 | 0.222085 | 10085 | 0.020320 | 0.020110 | 0.995994 | |
Width | 0.006488 | 1.097103 | 1.104888 | 80560 | 0.007096 | 0.007071 | 0.998588 |
The “Parameter Estimates” table in Output 58.8.3 displays the combined parameter estimates with associated standard errors.
Output 58.8.3: Parameter Estimates
Parameter Estimates | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Parameter | Species | Estimate | Std Error | 95% Confidence Limits | DF | Minimum | Maximum | Theta0 | t for H0: Parameter=Theta0 |
Pr > |t| | |
Intercept | 12.669835 | 2.832445 | 7.1144 | 18.22530 | 1692.4 | 12.004593 | 13.360690 | 0 | 4.47 | <.0001 | |
Species | Bream | -11.180159 | 3.280775 | -17.6126 | -4.74767 | 3410 | -11.910303 | -10.520395 | 0 | -3.41 | 0.0007 |
Species | Pike | 0 | . | . | . | . | 0 | 0 | 0 | . | . |
Height | -0.246488 | 0.471259 | -1.1702 | 0.67727 | 10085 | -0.313882 | -0.160511 | 0 | -0.52 | 0.6010 | |
Width | 7.511074 | 1.051137 | 5.4509 | 9.57130 | 80560 | 7.396172 | 7.594860 | 0 | 7.15 | <.0001 |