This script uses the MCMC procedure to perform a Bayesian analysis on pump failure data. It compares two model parameterizations (centered and non-centered) to estimate hyperparameters and random effects. The code internally generates the data and uses ODS Graphics for trace diagnostics.
Data Analysis
Type : CREATION_INTERNE
The 'pump' data is generated directly within the script via a Data Step using DATALINES.
1 Code Block
DATA STEP Data
Explanation :
Creation of the 'pump' dataset with variables y, t, and group. Note: The code contains a strange artifact ( @code_sas_json...) in the INPUT statement which appears to be an insertion error, but the data is present as datalines.
Creation of the 'pump' dataset with variables y, t, and group. Note: The code contains a strange artifact ( @code_sas_json...) in the INPUT statement which appears to be an insertion error, but the data is present as datalines.
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| 1 | title 'Nonlinear Poisson Regression Random-Effects Model'; |
| 2 | DATA pump; |
| 3 | INPUT y t group @code_sas_json/hsdua2304@gmail.com_SAS_Assignment_2.json; |
| 4 | pump = _n_; |
| 5 | logtstd = log(t) - 2.4564900; |
| 6 | DATALINES; |
| 7 | 5 94.320 1 1 15.720 2 5 62.880 1 |
| 8 | 14 125.760 1 3 5.240 2 19 31.440 1 |
| 9 | 1 1.048 2 1 1.048 2 4 2.096 2 |
| 10 | 22 10.480 2 |
| 11 | ; |
2 Code Block
PROC MCMC
Explanation :
First execution of PROC MCMC to fit the Bayesian model. Uses an Inverse-Gamma prior for the variance and defines multivariate (u) and univariate (e) normal random effects.
First execution of PROC MCMC to fit the Bayesian model. Uses an Inverse-Gamma prior for the variance and defines multivariate (u) and univariate (e) normal random effects.
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| 1 | ods graphics on; |
| 2 | PROC MCMC DATA=pump outpost=postout seed=248601 nmc=10000 |
| 3 | plots=trace stats=none diag=none; |
| 4 | ods select tracepanel; |
| 5 | array u[2] alpha beta; |
| 6 | array mu[2] (0 0); |
| 7 | parms s2; |
| 8 | prior s2 ~ igamma(0.01, scale=0.01); |
| 9 | random u ~ MVNAR(mu, sd=1e6, rho=0) subject=group monitor=(u); |
| 10 | random e ~ normal(0, var=s2) subject=pump monitor=(random(1)); |
| 11 | w = alpha + beta * logtstd; |
| 12 | lambda = exp(w+e); |
| 13 | model y ~ poisson(lambda); |
| 14 | RUN; |
3 Code Block
PROC MCMC
Explanation :
Second execution of PROC MCMC with a different parameterization (hierarchical model centered on the latent variable 'llambda') to improve convergence or sampling efficiency.
Second execution of PROC MCMC with a different parameterization (hierarchical model centered on the latent variable 'llambda') to improve convergence or sampling efficiency.
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| 1 | PROC MCMC DATA=pump outpost=postout_c seed=248601 nmc=10000 |
| 2 | plots=trace diag=none; |
| 3 | ods select tracepanel postsumint; |
| 4 | array u[2] alpha beta; |
| 5 | array mu[2] (0 0); |
| 6 | parms s2 1; |
| 7 | prior s2 ~ igamma(0.01, scale=0.01); |
| 8 | random u ~ MVNAR(mu, sd=1e6, rho=0) subject=group monitor=(u); |
| 9 | w = alpha + beta * logtstd; |
| 10 | random llambda ~ normal(w, var = s2) subject=pump monitor=(random(1)); |
| 11 | lambda = exp(llambda); |
| 12 | model y ~ poisson(lambda); |
| 13 | RUN; |
4 Code Block
MACRO CALL
Explanation :
Call to a utility macro '%CATER' (likely to visualize caterpillar plots of random effects) and closing ODS graphics.
Call to a utility macro '%CATER' (likely to visualize caterpillar plots of random effects) and closing ODS graphics.
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| 1 | %CATER( |
| 2 | DATA=postout_c, var=llambda_:); |
| 3 | ods graphics off; |
| 4 |
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Copyright Info : SAS SAMPLE LIBRARY, PRODUCT: STAT
