Hi there,
I hope I understood your question correctly.
As far as the PROBIT regression coeffieints go, there is no obvious restriction (-1,1).
To verify and convince you of that, I modified the code available here:
https://blogs.sas.com/content/iml/2014/06/25/simulate-logistic-data.html
The modified code addressing the PROBIT case is below.
It is important to notice that the original coefficients are:
beta = {2, -4, 1};
Indeed, after increasing the sample size to 10000, you will see that the estimates are close:
beta = {2.049585, -4.099663, 1.023898};
*--------------------- PROBIT CODE --------------------------------------;
/* Example from _Simulating Data with SAS_, p. 226--229 */ %let N = 10000; /* N = sample size */ proc iml; call randseed(1); X = j(&N, 3, 1); /* X[,1] is intercept */ /* 1. Read design matrix for X or assign X randomly. For this example, x1 ~ U(0,1) and x2 ~ N(0,2) */ X[,2] = randfun(&N, "Uniform"); X[,3] = randfun(&N, "Normal", 0, 2); /* Logistic model with parameters {2, -4, 1} */ beta = {2, -4, 1}; eta = X*beta; /* 2. linear model */ mu = probnorm(eta); /* 3. transform by inverse */ /* 4. Simulate binary response. Notice that the "probability of success" is a vector (SAS/IML 12.1) */ y = j(&N,1); /* allocate response vector */ call randgen(y, "Bernoulli", mu); /* simulate binary response */ /* 5. Write y and x1-x2 to data set*/ varNames = "y" || ("x1":"x2"); Out = X; Out[,1] = y; /* simulated response in 1st column */ create LogisticData from Out[c=varNames]; /* no data is written yet */ append from Out; /* output this sample */ close LogisticData; quit;
proc qlim data=LogisticData plots=none; model y = x1 x2 / discrete(distribution=probit); run;
*------------------------------------------------------------------------------------------;
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