Random Effects Model with PROC MCMC

This SAS^© script illustrates the use of the MCMC procedure to fit a random effects model. It first creates a 'heights' dataset using `datalines` with family, gender, and height information. Then, a new 'input' dataset is created from 'heights' to encode gender into a binary numerical variable ('gf'). PROC MCMC is then used to fit a normal model where height is modeled as a function of gender and a family-specific random effect. Prior distributions are specified for the model parameters (intercept, gender coefficient, variances). The script enables and disables ODS graphics for MCMC trace visualization.

Data Analysis

Type : INTERNAL_CREATION

Raw data is directly integrated into the script via a `datalines` statement, forming the 'heights' dataset. This is then transformed into 'input' for MCMC analysis.

1 Code Block

DATA STEP Data

Explanation :
This DATA STEP block initializes and populates the 'heights' dataset directly from the data provided in the script via the `datalines` statement. It defines three variables: 'Family' (numeric), 'G' (gender, character), and 'Height' (numeric).

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1	DATA heights;
2	INPUT Family G$ Height;
3	DATALINES;
4	1 F 67
5	1 F 66
6	1 F 64
7	1 M 71
8	1 M 72
9	2 F 63
10	2 F 63
11	2 F 67
12	2 M 69
13	2 M 68
14	2 M 70
15	3 F 63
16	3 M 64
17	4 F 67
18	4 F 66
19	4 M 67
20	4 M 67
21	4 M 69
22	;
23

2 Code Block

DATA STEP Data

Explanation :
This DATA STEP block creates a new dataset named 'input' by reading 'heights'. It transforms the categorical variable 'G' (gender) into a numerical indicator variable 'gf' (1 for Female, 0 for Male) and removes the original 'G' variable for subsequent analysis.

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1	DATA INPUT;
2	SET heights;
3	IF g eq 'F' THEN gf = 1;
4	ELSE gf = 0;
5	drop g;
6	RUN;
7

3 Code Block

ODS Statement

Explanation :
Activates the ODS (Output Delivery System) graphics system to allow for the generation of high-resolution graphs by SAS procedures.

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1	ods graphics on;
2

4 Code Block

PROC MCMC

Explanation :
This MCMC (Monte Carlo Markov Chain) procedure fits a random effects model to the 'input' dataset. It generates an output dataset 'postout' containing the post-MCMC samples. Model parameters are initialized, and prior distributions are specified for the intercept (b0), gender coefficient (b1), residual variance (s2), and random effects variance (s2g). A random effect 'gamma' is defined for each 'family'. The model specifies that 'height' follows a normal distribution with a mean 'mu' (a function of fixed and random effects) and a variance 's2'. The number of iterations (nmc) and the random seed are fixed, and trace plots are requested.

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1	PROC MCMC DATA=INPUT outpost=postout nmc=50000 seed=7893 plots=trace;
2	ods select Parameters REparameters PostSumInt tracepanel;
3	parms b0 0 b1 0 s2 1 s2g 1;
4
5	prior b: ~ normal(0, var = 10000);
6	prior s: ~ igamma(0.01, scale = 0.01);
7	random gamma ~ normal(0, var = s2g) subject=family monitor=(gamma);
8	mu = b0 + b1 * gf + gamma;
9	model height ~ normal(mu, var = s2);
10	RUN;
11

5 Code Block

ODS Statement

Explanation :
Deactivates the ODS graphics system, thus stopping the generation of graphics.

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1	ods graphics off;
2

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Copyright Info : S A S S A M P L E L I B R A R Y, NAME: MCMCGS3, TITLE: Getting Started Example 3 for PROC MCMC, PRODUCT: STAT, SYSTEM: ALL, KEYS: random-effects model, PROCS: MCMC, DATA:, REF: PROC MCMC, GETTING STARTED EXAMPLE 3, MISC:

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