Probit-Normal Model with PROC NLMIXED for Binomial Data

The script begins by creating a SAS^© dataset named 'rats' using a DATA step and internal data (datalines). This data comes from an experiment comparing a treatment group ('t') to a control group ('c'). Indicator variables (x1, x2) are created to differentiate the two groups. Then, the NLMIXED procedure is applied to model the number of successes 'x' out of 'm' trials. The model defines a linear predictor 'eta' which incorporates fixed effects (t1, t2) and a random effect 'alpha' specific to each litter ('litter'). The probability of success 'p' is modeled via the standard normal distribution function (probit model). The script also estimates a composite parameter 'gamma2' and generates an output dataset containing the predicted probabilities.

Data Analysis

Type : CREATION_INTERNE

The data is created directly within the script via a DATA step and a 'datalines' statement. It does not come from SASHELP or an external source.

1 Code Block

DATA STEP Data

Explanation :
This block creates the SAS table 'rats'. It reads the variables 'trt' (treatment), 'm' (number of trials), and 'x' (number of successes) from embedded data (datalines). It generates indicator variables 'x1' and 'x2' for the control and treatment groups respectively. A litter identifier ('litter') is created using the observation number (_n_).

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1	DATA rats;
2	INPUT trt $ m x @;
3	IF (trt='c') THEN DO;
4	x1 = 1;
5	x2 = 0;
6	END;
7	ELSE DO;
8	x1 = 0;
9	x2 = 1;
10	END;
11	litter = _n_;
12	DATALINES;
13	c 13 13 c 12 12 c 9 9 c 9 9 c 8 8 c 8 8 c 13 12 c 12 11
14	c 10 9 c 10 9 c 9 8 c 13 11 c 5 4 c 7 5 c 10 7 c 10 7
15	t 12 12 t 11 11 t 10 10 t 9 9 t 11 10 t 10 9 t 10 9 t 9 8
16	t 9 8 t 5 4 t 9 7 t 7 4 t 10 5 t 6 3 t 10 3 t 7 0
17	;
18

2 Code Block

PROC NLMIXED Data

Explanation :
This block fits a nonlinear mixed model to the 'rats' table. It defines the initial parameters (parms), the linear predictor 'eta', and the probability 'p' via the probit function (probnorm). The model specifies a binomial distribution for the response 'x'. A random effect 'alpha' with a different variance per treatment group is included and grouped by 'litter'. An estimate of a ratio is calculated with 'estimate', and the predicted probabilities are saved in a new table 'p' with 'predict'.

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1	PROC NLMIXED DATA=rats;
2	parms t1=1 t2=1 s1=.05 s2=1;
3	eta = x1t1 + x2t2 + alpha;
4	p = probnorm(eta);
5	model x ~ binomial(m,p);
6	random alpha ~ normal(0,x1s1s1+x2s2s2) subject=litter;
7	estimate 'gamma2' t2/sqrt(1+s2*s2);
8	predict p out=p;
9	RUN;

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