MCMC Statement 
The MCMC statement specifies the details of the MCMC method for imputation.
Table 56.3 summarizes the options available for the MCMC statement.
Option 
Description 

Data Sets 

Inputs parameter estimates for imputations 

Outputs parameter estimates used in imputations 

Outputs parameter estimates used in iterations 

Imputation Details 

Specifies monotone or full imputation 

Specifies single or multiple chain 

Specifies the number of burnin iterations for each chain 

Specifies the number of iterations between imputations in a chain 

Specifies initial parameter estimates for MCMC 

Specifies the prior parameter information 

Specifies starting parameters 

ODS Output Graphics 

Displays trace plots 

Displays autocorrelation plots 

Traditional Graphics 

Displays trace plots 

Displays autocorrelation plots 

Specifies the graphics catalog name for saving graphics output 

Printed Output 

Displays the worst linear function 

Displays initial parameter values for MCMC 
The following options are available for the MCMC statement (in alphabetical order).
displays the traditional autocorrelation function plots of parameters from iterations. The ACFPLOT option is applicable only if ODS Graphics is not enabled.
The available options are as follows.
displays plots of variances for variables in the list and covariances for pairs of variables in the list. When the option COV is specified without variables, variances for all variables and covariances for all pairs of variables are used.
displays plots of means for variables in the list. When the option MEAN is specified without variables, all variables are used.
When the ACFPLOT is specified without the preceding options, the procedure displays plots of means for all variables that are used.
The display options provide additional information for the autocorrelation function plots. The available display options are as follows:
specifies the color of the displayed confidence limits. The default is CCONF=BLACK.
specifies the color for filling the area enclosed by the axes and the frame. By default, this area is not filled.
specifies the color of the vertical line segments (needles) that connect autocorrelations to the reference line. The default is CNEEDLES=BLACK.
specifies the color of the displayed reference line. The default is CREF=BLACK.
specifies the color of the displayed data points. The default is CSYMBOL=BLACK.
specifies the height of data points in percentage screen units. The default is HSYMBOL=1.
specifies the line type for the displayed confidence limits. The default is LCONF=1, a solid line.
requests that the logarithmic transformations of parameters be used to compute the autocorrelations; it is generally used for the variances of variables. When a parameter has values less than or equal to zero, the corresponding plot is not created.
specifies the line type for the displayed reference line. The default is LREF=3, a dashed line.
specifies a descriptive name, up to eight characters, that appears in the name field of the PROC GREPLAY master menu. The default is NAME=’MI’.
specifies the maximum lag of the series. The default is NLAG=20. The autocorrelations at each lag are displayed in the graph.
specifies the symbol for data points in percentage screen units. The default is SYMBOL=STAR.
specifies the title to be displayed in the autocorrelation function plots. The default is TITLE=’Autocorrelation Plot’.
specifies the width of the displayed confidence limits in percentage screen units. If you specify the WCONF=0 option, the confidence limits are not displayed. The default is WCONF=1.
specifies the width of the displayed needles that connect autocorrelations to the reference line, in percentage screen units. If you specify the WNEEDLES=0 option, the needles are not displayed. The default is WNEEDLES=1.
specifies the width of the displayed reference line in percentage screen units. If you specify the WREF=0 option, the reference line is not displayed. The default is WREF=1.
For example, the following statement requests autocorrelation function plots for the means and variances of the variable y1, respectively:
acfplot( mean( y1) cov(y1) /log);
Logarithmic transformations of both the means and variances are used in the plots. For a detailed description of the autocorrelation function plot, see the section Autocorrelation Function Plot; see also Schafer (1997, pp. 120–126) and the SAS/ETS User’s Guide.
specifies whether a single chain is used for all imputations or a separate chain is used for each imputation. The default is CHAIN=SINGLE.
displays initial parameter values in the MCMC method for each imputation.
specifies the graphics catalog for saving graphics output from PROC MI. The default is WORK.GSEG. For more information, see "The GREPLAY Procedure" in SAS/GRAPH Software: Reference.
specifies whether a fulldata imputation is used for all missing values or a monotonedata imputation is used for a subset of missing values to make the imputed data sets have a monotone missing pattern. The default is IMPUTE=FULL. When IMPUTE=MONOTONE is specified, the order in the VAR statement is used to complete the monotone pattern.
names a SAS data set of TYPE=EST that contains parameter estimates for imputations. These estimates are used to impute values for observations in the DATA= data set. A detailed description of the data set is provided in the section Input Data Sets.
specifies the initial mean and covariance estimates for the MCMC method. The default is INITIAL=EM.
You can specify INITIAL=INPUT=SASdataset to read the initial estimates of the mean and covariance matrix for each imputation from a SAS data set. See the section Input Data Sets for a description of this data set.
With INITIAL=EM, PROC MI derives parameter estimates for a posterior mode, the highest observeddata posterior density, from the EM algorithm. The MLE from the EM algorithm is used to start the EM algorithm for the posterior mode, and the resulting EM estimates are used to begin the MCMC method. The prior information specified in the PRIOR= option is also used in the process to compute the posterior mode.
The following four options are available with INITIAL=EM:
requests bootstrap resampling, which uses a simple random sample with replacement from the input data set for the initial estimate. You can explicitly specify the number of observations in the random sample. Alternatively, you can implicitly specify the number of observations in the random sample by specifying the proportion , to request observations in the random sample, where n is the number of observations in the data set and is the integer part of . This produces an overdispersed initial estimate that provides different starting values for the MCMC method. If you specify the BOOTSTRAP option without the number, p=0.75 is used by default.
sets the convergence criterion. The value must be between 0 and 1. The iterations are considered to have converged when the change in the parameter estimates between iteration steps is less than for each parameter—that is, for each of the means and covariances. For each parameter, the change is a relative change if the parameter is greater than 0.01 in absolute value; otherwise, it is an absolute change. By default, CONVERGE=1E4.
prints the iteration history in the EM algorithm for the posterior mode.
specifies the maximum number of iterations used in the EM algorithm. The default is MAXITER=200.
specifies the number of burnin iterations before the first imputation in each chain. The default is NBITER=200.
specifies the number of iterations between imputations in a single chain. The default is NITER=100.
creates an output SAS data set of TYPE=EST. The data set contains parameter estimates used in each imputation. The data set also includes a variable named _Imputation_ to identify the imputation number. See the section Output Data Sets for a description of this data set.
creates an output SAS data set of TYPE=COV that contains parameters used in the imputation step for each iteration. The data set includes variables named _Imputation_ and _Iteration_ to identify the imputation number and iteration number.
The parameters in the output data set depend on the options specified. You can specify the options MEAN, STD, COV, LR, LR_POST, and WLF to output parameters of means, standard deviations, covariances, 2 log LR statistic, 2 log LR statistic of the posterior mode, and the worst linear function, respectively. When no options are specified, the output data set contains the mean parameters used in the imputation step for each iteration. See the section Output Data Sets for a description of this data set.
requests statistical graphics via the Output Delivery System (ODS). To request these graphs, ODS Graphics must be enabled and you must specify options in the MCMC statement. For more information about ODS Graphics, see Chapter 21, Statistical Graphics Using ODS.
The global plot option LOG requests that the logarithmic transformations of parameters be used. The plot request options include the following:
displays plots of the autocorrelation function of parameters from iterations. The default is ACF( MEAN).
produces all appropriate plots.
suppresses all plots.
displays trace plots of parameters from iterations. The default is TRACE( MEAN).
The available acfoptions are as follows:
specifies the maximum lag of the series. The default is NLAG=20. The autocorrelations at each lag are displayed in the graph.
displays plots of variances for variables in the list and covariances for pairs of variables in the list. When the option COV is specified without variables, variances for all variables and covariances for all pairs of variables are used.
displays plots of means for variables in the list. When the option MEAN is specified without variables, all variables are used.
displays the plot for the worst linear function.
The available traceoptions are as follows:
displays plots of variances for variables in the list and covariances for pairs of variables in the list. When the option COV is specified without variables, variances for all variables and covariances for all pairs of variables are used.
displays plots of means for variables in the list. When the option MEAN is specified without variables, all variables are used.
displays the plot of the worst linear function.
specifies the prior information for the means and covariances. Valid values for name are as follows:
specifies a noninformative prior.
specifies a ridge prior.
specifies a data set that contains prior information.
For a detailed description of the prior information, see the section Bayesian Estimation of the Mean Vector and Covariance Matrix and the section Posterior Step. If you do not specify the PRIOR= option, the default is PRIOR=JEFFREYS.
The PRIOR=INPUT= option specifies a TYPE=COV data set from which the prior information of the mean vector and the covariance matrix is read. See the section Input Data Sets for a description of this data set.
specifies that the initial parameter estimates are used either as the starting value (START=VALUE) or as the starting distribution (START=DIST) in the first imputation step of each chain. If the IMPUTE=MONOTONE option is specified, then START=VALUE is used in the procedure. The default is START=VALUE.
displays the traditional trace (time series) plots of parameters from iterations. The TIMEPLOT option is applicable only if ODS Graphics is not enabled.
The available options are as follows:
displays plots of variances for variables in the list and covariances for pairs of variables in the list. When the option COV is specified without variables, variances for all variables and covariances for all pairs of variables are used.
displays plots of means for variables in the list. When the option MEAN is specified without variables, all variables are used.
When the TIMEPLOT is specified without the preceding options, the procedure displays plots of means for all variables that are used.
The display options provide additional information for the trace plots. The available display options are as follows:
specifies the color of the line segments that connect data points in the trace plots. The default is CCONNECT=BLACK.
specifies the color for filling the area enclosed by the axes and the frame. By default, this area is not filled.
specifies the color of the data points to be displayed in the trace plots. The default is CSYMBOL=BLACK.
specifies the height of data points in percentage screen units. The default is HSYMBOL=1.
specifies the line type for the line segments that connect data points in the trace plots. The default is LCONNECT=1, a solid line.
requests that the logarithmic transformations of parameters be used; it is generally used for the variances of variables. When a parameter value is less than or equal to zero, the value is not displayed in the corresponding plot.
specifies a descriptive name, up to eight characters, that appears in the name field of the PROC GREPLAY master menu. The default is NAME=’MI’.
specifies the symbol for data points in percentage screen units. The default is SYMBOL=PLUS.
specifies the title to be displayed in the trace plots. The default is TITLE=’Trace Plot’.
specifies the width of the line segments that connect data points in the trace plots, in percentage screen units. If you specify the WCONNECT=0 option, the data points are not connected. The default is WCONNECT=1.
For a detailed description of the trace plot, see the section Trace Plot and Schafer (1997, pp. 120–126).
displays the worst linear function of parameters. This scalar function of parameters and is "worst" in the sense that its values from iterations converge most slowly among parameters. For a detailed description of this statistic, see the section Worst Linear Function of Parameters.