Random Effects Logistic Regression Model

The script begins by creating a SAS^© dataset named 'seeds' via a DATA step with embedded data (datalines). This dataset contains information on the number of successes 'r' out of 'n' trials, as well as explanatory factors 'seed' and 'extract'. Then, the MCMC procedure is invoked to perform a Bayesian analysis. The model specifies a logistic regression where the probability of success is influenced by the factors 'seed', 'extract', and their interaction. A random effect 'delta' is introduced at each observation level to capture unobserved variability. Prior distributions are defined for all model parameters (regression coefficients 'beta' and variance of the random effect 's2'). The MCMC simulation is run for 20000 iterations, and the results of the posterior distribution are stored in the 'postout' table.

Data Analysis

Type : CREATION_INTERNE

The data is entirely generated within the script via a 'DATA' step and 'datalines' statement, creating the 'seeds' table.

1 Code Block

DATA STEP Data

Explanation :
This code block creates a SAS dataset named 'seeds'. The data is read directly from the input stream (datalines). A variable 'ind' is added, serving as a unique identifier for each row (observation).

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1	DATA seeds;
2	INPUT r n seed extract;
3	ind = _N_;
4	DATALINES;
5	10 39 0 0
6	23 62 0 0
7	23 81 0 0
8	26 51 0 0
9	17 39 0 0
10	5 6 0 1
11	53 74 0 1
12	55 72 0 1
13	32 51 0 1
14	46 79 0 1
15	10 13 0 1
16	8 16 1 0
17	10 30 1 0
18	8 28 1 0
19	23 45 1 0
20	0 4 1 0
21	3 12 1 1
22	22 41 1 1
23	15 30 1 1
24	32 51 1 1
25	3 7 1 1
26	;
27	RUN;

2 Code Block

PROC MCMC Data

Explanation :
This block performs a Bayesian analysis via the MCMC procedure. It defines the model parameters (beta0, beta1, beta2, beta3, s2) and their prior distributions. A hierarchical model is constructed with a random effect 'delta' following a normal distribution. The probability 'pi' is modeled by a logistic function of this random effect, and the response variable 'r' is assumed to follow a binomial distribution. The simulation generates 20000 samples from the posterior distribution, which are saved in the 'postout' table.

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1	PROC MCMC DATA=seeds outpost=postout seed=332786 nmc=20000;
2	ods select PostSumInt;
3	parms beta0 0 beta1 0 beta2 0 beta3 0 s2 1;
4	prior s2 ~ igamma(0.01, s=0.01);
5	prior beta: ~ general(0);
6	w = beta0 + beta1seed + beta2extract + beta3seedextract;
7	random delta ~ normal(w, var=s2) subject=ind;
8	pi = logistic(delta);
9	model r ~ binomial(n = n, p = pi);
10	RUN;

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