Documentation Example 20 for PROC MCMC
/****************************************************************/
/* S A S S A M P L E L I B R A R Y */
/* */
/* NAME: MCMCEX20 */
/* TITLE: Documentation Example 20 for PROC MCMC */
/* Using a Transformation to Improve Mixing */
/* PRODUCT: STAT */
/* SYSTEM: ALL */
/* KEYS: */
/* PROCS: MCMC */
/* DATA: */
/* */
/* SUPPORT: Fang Chen */
/* REF: PROC MCMC, EXAMPLE 20 */
/* MISC: */
/****************************************************************/
data inputdata;
input nobs grp y @@;
ind = _n_;
datalines;
1 1 24.80 2 1 26.90 3 1 26.65
4 1 30.93 5 1 33.77 6 1 63.31
1 2 23.96 2 2 28.92 3 2 28.19
4 2 26.16 5 2 21.34 6 2 29.46
1 3 18.30 2 3 23.67 3 3 14.47
4 3 24.45 5 3 24.89 6 3 28.95
1 4 51.42 2 4 27.97 3 4 24.76
4 4 26.67 5 4 17.58 6 4 24.29
1 5 34.12 2 5 46.87 3 5 58.59
4 5 38.11 5 5 47.59 6 5 44.67
;
ods graphics on;
proc mcmc data=inputdata nmc=50000 thin=10 outpost=m1 seed=17797
plot=trace;
ods select ess tracepanel;
parms p;
parms tau;
parms mu;
prior p ~ uniform(0,1);
prior tau ~ gamma(shape=0.001,iscale=0.001);
prior mu ~ normal(0,prec=0.00000001);
beginnodata;
taub = tau/p;
tauw = taub-tau;
endnodata;
random theta ~ normal(mu, prec=taub) subject=grp monitor=(theta);
model y ~ normal(theta,prec=tauw);
run;
title 'Scatter Plot of Parameters on Original Scales';
proc sgplot data=m1;
yaxis label = 'p';
xaxis label = 'tau' values=(0 to 0.4 by 0.1);
scatter x = tau y = p;
run;
proc mcmc data=inputdata nmc=50000 thin=10 outpost=m2 seed=17
monitor=(p tau mu) plot=trace;
ods select ess tracepanel;
parms ltau lgp mu ;
prior ltau ~ egamma(shape=0.001,iscale=0.001);
prior lgp ~ logistic(0,1);
prior mu ~ normal(0,prec=0.00000001);
beginnodata;
tau = exp(ltau);
p = logistic(lgp);
taub = tau/p;
tauw = taub-tau;
endnodata;
random theta ~ normal(mu, prec=taub) subject=grp monitor=(theta);
model y ~ normal(theta,prec=tauw);
run;
title 'Scatter Plot of Parameters on Transformed Scales';
proc sgplot data=m2;
yaxis label = 'logit(p)';
xaxis label = 'log(tau)';
scatter x = ltau y = lgp;
run;
title 'Scatter Plot of Parameters on Original Scales';
proc sgplot data=m2;
yaxis label = 'p';
xaxis label = 'tau' values=(0 to 5.0 by 1);
scatter x = tau y = p;
run;
ods graphics off;