The MIANALYZE Procedure

This example combines sample correlation coefficients computed from a set of imputed data sets by using Fisher’s z transformation.

Fisher’s z transformation of the sample correlation r is

The statistic z is approximately normally distributed with mean

and variance , where is the population correlation coefficient and n is the number of observations.

The following statements use the CORR procedure to compute the correlation r and its associated Fisher’s z statistic between variables Oxygen and RunTime for each imputed data set. The ODS statement is used to save Fisher’s z statistic in an output data set.

proc corr data=outmi fisher(biasadj=no);
   var Oxygen RunTime;
   by _Imputation_;
   ods output FisherPearsonCorr= outz;
run;

The following statements display the number of observations and Fisher’s z statistic for each imputed data set in Output 58.10.1:

proc print data=outz;
   title 'Fisher''s Correlation Statistics';
   var _Imputation_ NObs ZVal;
run;

The following statements generate the standard error associated with the z statistic, :

data outz;
   set outz;
   StdZ= 1. / sqrt(NObs-3);
run;

The following statements use the MIANALYZE procedure to generate a combined parameter estimate and its variance, as shown in Output 58.10.2. The ODS statement is used to save the parameter estimates in an output data set.

proc mianalyze data=outz;
   ods output ParameterEstimates=parms;
   modeleffects ZVal;
   stderr StdZ;
run;

In addition to the estimate for z, PROC MIANALYZE also generates 95% confidence limits for z, and . The following statements print the estimate and 95% confidence limits for z in Output 58.10.3:

proc print data=parms;
   title 'Parameter Estimates with 95% Confidence Limits';
   var Estimate LCLMean UCLMean;
run;

An estimate of the correlation coefficient with its corresponding 95% confidence limits is then generated from the following inverse transformation as described in the section Correlation Coefficients:

for , , and .

The following statements generate and display an estimate of the correlation coefficient and its 95% confidence limits, as shown in Output 58.10.4:

data corr_ci;
   set parms;
   r=       tanh( Estimate);
   r_lower= tanh( LCLMean);
   r_upper= tanh( UCLMean);
run;
proc print data=corr_ci;
   title 'Estimated Correlation Coefficient'
         ' with 95% Confidence Limits';
   var r r_lower r_upper;
run;