The MIANALYZE Procedure

Example 58.6 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:

proc glm data=outmi;
   model Oxygen= RunTime RunPulse/inverse;
   by _Imputation_;
   ods output ParameterEstimates=glmparms
              InvXPX=glmxpxi;
quit;

The following statements display (in Output 58.6.1) 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 58.6.1: 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 58.6.2) $(\mb {X}^\prime \mb {X})^{-1}$ 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 58.6.2: 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 58.3.2 and Output 58.3.3 in Example 58.3:

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