Results: 05_mcmc_diag_demo.sas

MCMC Diagnostics

The data are taken from Crowder (1978). The Seeds data set is a factorial layout, with two types of seeds, O. aegyptiaca 75 and O. aegyptiaca 73, and two root extracts, bean and cucumber. You observe r, which is the number of germinated seeds, and n, which is the total number of seeds. The independent variables are seed and extract.

The Print Procedure

Data Set WORK.SEEDS


Obs	r	n	seed	extract	ind
1	10	39	0	0	1
2	23	62	0	0	2
3	23	81	0	0	3
4	26	51	0	0	4
5	17	39	0	0	5
6	5	6	0	1	6
7	53	74	0	1	7
8	55	72	0	1	8
9	32	51	0	1	9
10	46	79	0	1	10
11	10	13	0	1	11
12	8	16	1	0	12
13	10	30	1	0	13
14	8	28	1	0	14
15	23	45	1	0	15
16	0	4	1	0	16
17	3	12	1	1	17
18	22	41	1	1	18
19	15	30	1	1	19
20	32	51	1	1	20
21	3	7	1	1	21

The CONTENTS Procedure

The Contents Procedure

WORK.SEEDS

Attributes


Data Set Name	WORK.SEEDS	Observations	21
Member Type	DATA	Variables	5
Engine	V9	Indexes	0
Created	12/05/2018 00:24:23	Observation Length	40
Last Modified	12/05/2018 00:24:23	Deleted Observations	0
Protection		Compressed	CHAR
Data Set Type		Reuse Space	NO
Label		Point to Observations	YES
Data Representation	HP_UX_64, RS_6000_AIX_64, SOLARIS_64, HP_IA64	Sorted	NO
Encoding	latin1 Western (ISO)

Engine/Host Information


Engine/Host Dependent Information
Data Set Page Size	65536
Number of Data Set Pages	2
Number of Data Set Repairs	0
Filename	/saswork/SAS_work8C54000006EE_sp20635/SAS_workEA33000006EE_sp20635/seeds.sas7bdat
Release Created	9.0401M5
Host Created	SunOS
Inode Number	5920
Access Permission	rw-r--r--
Owner Name	t844523
File Size	192KB
File Size (bytes)	196608

Varnum


Variables in Creation Order
#	Variable	Type	Len
1	r	Num	8
2	n	Num	8
3	seed	Num	8
4	extract	Num	8
5	ind	Num	8

The MCMC Procedure

Number of Observations


Number of Observations Read Number of Observations Used	21 21

Parameters


Parameters
Block	Parameter	Sampling Method	Initial Value	Prior Distribution
1	s2	Conjugate	1.0000	igamma(0.01, s=0.01)
2	beta0	N-Metropolis	0	general(0)
	beta1		0	general(0)
	beta2		0	general(0)
	beta3		0	general(0)

Random-Effects Parameters


Random Effect Parameters
Parameter	Sampling Method	Subject	Number of Subjects	Subject Values	Prior Distribution
delta	N-Metropolis	ind	21	1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 ...	normal(w, var=s2)

The MCMC Procedure

Posterior Statistics

Summary and Interval Statistics


Posterior Summaries and Intervals
Parameter	N	Mean	Standard Deviation	95% HPD Interval
beta0	20000	-0.5570	0.1929	-0.9422	-0.1816
beta1	20000	0.0776	0.3276	-0.5690	0.7499
beta2	20000	1.3667	0.2923	0.8463	1.9724
beta3	20000	-0.8469	0.4718	-1.7741	0.0742
s2	20000	0.1171	0.0993	0.00163	0.3045

The MCMC Procedure

Convergence Diagnostics

Monte Carlo Standard Errors


Monte Carlo Standard Errors
Parameter	MCSE	Standard Deviation	MCSE/SD
beta0	0.0101	0.1929	0.0523
beta1	0.0175	0.3276	0.0533
beta2	0.0138	0.2923	0.0472
beta3	0.0269	0.4718	0.0570
s2	0.00417	0.0993	0.0419

Autocorrelations


Posterior Autocorrelations
Parameter	Lag 1	Lag 5	Lag 10	Lag 50
beta0	0.9483	0.7800	0.6236	0.1669
beta1	0.9598	0.8264	0.6929	0.1694
beta2	0.9290	0.7108	0.5312	0.1070
beta3	0.9646	0.8450	0.7234	0.2149
s2	0.7494	0.5823	0.4598	0.0969

Geweke Diagnostics


Geweke Diagnostics
Parameter	z	Pr > \|z\|
beta0	1.1428	0.2531
beta1	-1.2485	0.2118
beta2	0.3081	0.7580
beta3	-0.2146	0.8300
s2	-0.6170	0.5373

Raftery-Lewis Diagnostics


Raftery-Lewis Diagnostics
Quantile=0.025 Accuracy=+/-0.005 Probability=0.95 Epsilon=0.001
Parameter	Number of Samples			Dependence Factor
Parameter	Burn-In	Total	Minimum	Dependence Factor
beta0	35	37938	3746	10.1276
beta1	51	55996	3746	14.9482
beta2	32	33938	3746	9.0598
beta3	44	47893	3746	12.7851
s2	153	162690	3746	43.4303

Heidelberger-Welch Diagnostics


Heidelberger-Welch Diagnostics
Parameter	Stationarity Test				Half-Width Test
Parameter	Cramer-von Mises Stat	p-Value	Test Outcome	Iterations Discarded	Half-Width	Mean	Relative Half-Width	Test Outcome
beta0	0.1114	0.5316	Passed	0	0.0216	-0.5570	-0.0387	Passed
beta1	0.0930	0.6202	Passed	0	0.0352	0.0776	0.4538	Failed
beta2	0.0942	0.6139	Passed	0	0.0298	1.3667	0.0218	Passed
beta3	0.0887	0.6429	Passed	0	0.0561	-0.8469	-0.0662	Passed
s2	0.0536	0.8539	Passed	0	0.00876	0.1171	0.0748	Passed

Effective Sample Sizes


Effective Sample Sizes
Parameter	ESS	Autocorrelation Time	Efficiency
beta0	366.1	54.6309	0.0183
beta1	351.6	56.8820	0.0176
beta2	449.1	44.5309	0.0225
beta3	308.1	64.9051	0.0154
s2	568.5	35.1815	0.0284

The MCMC Procedure

Diagnostic Plots

beta0

beta1

beta2

beta3

s2

Gelman Rubin Diagnostics

The Print Procedure

Data Set WORK.GELMANRUBIN


Obs	Between-chain	Within-chain	Estimate	UpperBound	Parameter
1	0.4864	0.0419	1.0692	1.0595	beta0
2	0.6238	0.1406	1.0352	1.0348	beta1
3	0.2313	0.1101	1.0389	1.0418	beta2
4	1.5103	0.2837	1.0395	1.0380	beta3
5	.	.	.	.

Obs	r	n	seed	extract	ind
1	10	39	0	0	1
2	23	62	0	0	2
3	23	81	0	0	3
4	26	51	0	0	4
5	17	39	0	0	5
6	5	6	0	1	6
7	53	74	0	1	7
8	55	72	0	1	8
9	32	51	0	1	9
10	46	79	0	1	10
11	10	13	0	1	11
12	8	16	1	0	12
13	10	30	1	0	13
14	8	28	1	0	14
15	23	45	1	0	15
16	0	4	1	0	16
17	3	12	1	1	17
18	22	41	1	1	18
19	15	30	1	1	19
20	32	51	1	1	20
21	3	7	1	1	21

Obs	r	n	seed	extract	ind
1	10	39	0	0	1
2	23	62	0	0	2
3	23	81	0	0	3
4	26	51	0	0	4
5	17	39	0	0	5
6	5	6	0	1	6
7	53	74	0	1	7
8	55	72	0	1	8
9	32	51	0	1	9
10	46	79	0	1	10
11	10	13	0	1	11
12	8	16	1	0	12
13	10	30	1	0	13
14	8	28	1	0	14
15	23	45	1	0	15
16	0	4	1	0	16
17	3	12	1	1	17
18	22	41	1	1	18
19	15	30	1	1	19
20	32	51	1	1	20
21	3	7	1	1	21

Obs	r	n	seed	extract	ind
1	10	39	0	0	1
2	23	62	0	0	2
3	23	81	0	0	3
4	26	51	0	0	4
5	17	39	0	0	5
6	5	6	0	1	6
7	53	74	0	1	7
8	55	72	0	1	8
9	32	51	0	1	9
10	46	79	0	1	10
11	10	13	0	1	11
12	8	16	1	0	12
13	10	30	1	0	13
14	8	28	1	0	14
15	23	45	1	0	15
16	0	4	1	0	16
17	3	12	1	1	17
18	22	41	1	1	18
19	15	30	1	1	19
20	32	51	1	1	20
21	3	7	1	1	21