The MIANALYZE Procedure

Example 76.6 Reading GLM Results from PARMS= and XPXI= Data Sets

This example creates data sets that contains parameter estimates and corresponding $(\mb{X}^\prime \mb{X})^{-1}$ matrices computed by a general linear 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 GLM to generate the parameter estimates and $(\mb{X}^\prime \mb{X})^{-1}$ matrix for each imputed data set:

ods select none;
proc glm data=outmi;
   model Oxygen= RunTime RunPulse/inverse;
   by _Imputation_;
   ods output ParameterEstimates=glmparms
              InvXPX=glmxpxi;
quit;
ods select all;

Because of the ODS SELECT statements, no output is displayed. The following statements display (in Output 76.6.1) the output parameter estimates and standard errors from PROC GLM for the first two imputed data sets:

proc print data=glmparms (obs=6);
   var _Imputation_ Parameter Estimate StdErr;
   title 'GLM Model Coefficients (First Two Imputations)';
run;

Output 76.6.1: PROC GLM Model Coefficients

GLM Model Coefficients (First Two Imputations)

Obs	_Imputation_	Parameter	Estimate	StdErr
1	1	Intercept	86.5440339	10.00726811
2	1	RunTime	-2.8223108	0.32824165
3	1	RunPulse	-0.0587292	0.05854109
4	2	Intercept	83.0207303	8.88996885
5	2	RunTime	-3.0002288	0.33847204
6	2	RunPulse	-0.0249103	0.05137859

The following statements display (in Output 76.6.2) $(\mb{X}^\prime \mb{X})^{-1}$ matrices from PROC GLM for the first two imputed data sets:

proc print data=glmxpxi (obs=8);
   var _Imputation_ Parameter Intercept RunTime RunPulse;
   title 'GLM X''X Inverse Matrices (First Two Imputations)';
run;

Output 76.6.2: PROC GLM $(\mb{X}^\prime \mb{X})^{-1}$ Matrices

GLM X'X Inverse Matrices (First Two Imputations)

Obs	_Imputation_	Parameter	Intercept	RunTime	RunPulse
1	1	Intercept	12.696250656	-0.067849956	-0.069826009
2	1	RunTime	-0.067849956	0.0136594055	-0.000436938
3	1	RunPulse	-0.069826009	-0.000436938	0.0004344762
4	1	Oxygen	86.544033929	-2.822310769	-0.058729234
5	2	Intercept	10.784620785	-0.091107072	-0.057201387
6	2	RunTime	-0.091107072	0.0156332765	-0.000426902
7	2	RunPulse	-0.057201387	-0.000426902	0.0003602208
8	2	Oxygen	83.020730343	-3.000228818	-0.024910305

The standard errors for the estimates in the output Glmparms data set are needed to create the covariance matrix from the $(\mb{X}^\prime \mb{X})^{-1}$ matrix. The following statements use the MIANALYZE procedure with input PARMS= and XPXI= data sets to produce the same results as displayed in Output 76.3.2 and Output 76.3.3 in Example 76.3:

proc mianalyze parms=glmparms xpxi=glmxpxi edf=28;
   modeleffects Intercept RunTime RunPulse;
run;