The BGLIMM Procedure
Autocall Macros for Postprocessing
Although PROC BGLIMM provides a number of convergence diagnostic tests and posterior summary statistics, it performs the calculations only for the default tests and statistics or only if you specify the necessary options. If you want to analyze the posterior draws of unmonitored parameters or functions of the parameters that are calculated in later DATA step calls, you can use the autocall macros that are listed in Table 15.
Table 15: Postprocessing Autocall Macros
| Macro | Description |
|---|---|
| %ESS | Effective sample sizes |
| %GEWEKE* | Geweke diagnostic |
| %HEIDEL* | Heidelberger-Welch diagnostic |
| %MCSE | Monte Carlo standard errors |
| %POSTACF | Autocorrelation |
| %POSTCOR | Correlation matrix |
| %POSTCOV | Covariance matrix |
| %POSTINT | Equal-tail and HPD intervals |
| %POSTSUM | Mean, standard deviation, and various quantiles |
| %RAFTERY | Raftery diagnostic |
| %SUMINT | Mean, standard deviation, and HPD interval |
| %TADPLOT | Trace plot, autocorrelation plot, and density plot |
| *The %GEWEKE and %HEIDEL macros use a different optimization routine than PROC BGLIMM uses. As a result, there might be numerical differences in some cases, especially when the sample size is small. | |
Table 16 lists options that are shared by all postprocessing autocall macros. For macro-specific options, see Table 17.
Table 16: Shared Options
| Option | Description |
|---|---|
| DATA=SAS-data-set | Names the input data set that contains posterior samples |
| OUT=SAS-data-set | Specifies a name for the output SAS data set to contain the results |
| PRINT=YES | NO | Displays the results (the default is YES) |
| VAR=variable-list | Specifies the variables on which to perform the calculation |
Suppose that the data set that contains posterior samples is called Post and the variables of interest are defined in the macro variable &PARMS. The following statement calls the %ESS macro and calculates the effective sample sizes for each variable:
%ESS(data=Post, var=Alpha Beta U_1-U_17)
By default, the ESS estimates are displayed. You can choose not to display the result and instead use the following statement to save the output to a data set:
%ESS(data=Post, var=&parms, print=NO, out=eout)
Some of the macros can take additional options, which are listed in Table 17.
Table 17: Macro-Specific Options
| Macro | Option | Description |
|---|---|---|
| %ESS | AUTOCORLAG=numeric | Specifies the maximum number of autocorrelation lags used in computing the ESS estimates. By default, AUTOCORLAG=MIN(500, NOBS/4), where NOBS is the sample size of the input data set. |
| HIST=YES | NO | Displays a histogram of all ESS estimates. By default, HIST=NO. | |
| %GEWEKE | FRAC1=numeric | Specifies the earlier portion of the Markov chain used in the test. By default, FRAC1=0.1. |
| FRAC2=numeric | Specifies the latter portion of the Markov chain used in the test. By default, FRAC2=0.5. | |
| %HEIDEL | SALPHA=numeric | Specifies the  level for the stationarity test. By default, SALPHA=0.05. |
| HALPHA=numeric | Specifies the level for the halfwidth test. By default, HALPHA=0.05. |
|
| EPS=numeric | Specifies a small positive number  such that if the halfwidth is less than times the sample mean of the remaining iterations, the halfwidth test is passed. By default, EPS=0.1. |
|
| %MCSE | AUTOCORLAG=numeric | Specifies the maximum number of autocorrelation lags used in computing the Monte Carlo standard error estimates. By default, AUTOCORLAG=MIN(500, NOBS/4), where NOBS is the sample size of the input data set. |
| %POSTACF | LAGS=%str(numeric-list) | Specifies which autocorrelation lags to calculate. The default values are 1, 5, 10, and 50. |
| %POSTINT | ALPHA=value | Specifies the level  for the interval estimates. By default, ALPHA=0.05. |
| %RAFTERY | Q=numeric | Specifies the order of the quantile of interest. By default, Q=0.025. |
| R=numeric | Specifies the margin of error for measuring the accuracy of estimation of the quantile. By default, R=0.005. | |
| EPS=numeric | Specifies the tolerance level for the stationary test. By default, EPS=0.001. |
For example, the following statement calculates and displays autocorrelation at lags 1, 6, 11, 50, and 100. Note that the lags in the numeric-list must be separated by commas.
%POSTACF(data=Post, var=&parms, lags=%str(1 to 15 by 5, 50, 100))