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# gbnlprobit - Non linear probit regression

 GBNLPROBIT(1) User Commands GBNLPROBIT(1)

## NAME

gbnlprobit - Non linear probit regression

## SYNOPSIS

gbnlprobit [ options] <function definition>

## DESCRIPTION

Non linear probit estimation. Minimize the negative log-likelihood
sum_{i in N_0} log(1-F(g(X_i))) + sum_{i in N_1} log(F(g(X_i)))
where N_0 and N_1 are the sets of 0 and 1 observations, g is a generic function of the independent variables and F is the normal CDF. It is also possible to minimize the score function
w_0 sum_{i in N_0} theta(F(g(X_i))-t) +
w_1 sum_{i in N_1} theta(t-F(g(X_i)))
where theta is the Heaviside function and t a threshold level. Weights w_0 and w_1 scale the contribution of the two subpopulations. The first column of data contains 0/1 entries. Successive columns are independent variables. The model is specified by a function g(x1,x2...) where x1,.. stands for the first,second .. N-th column independent variables.

### options:

-O
type of output (default 0)
0
parameters
1
parameters and errors
2
<variables> and probabilities
3
parameters and variance matrix
4
marginal effects
-V
variance matrix estimation (default 0)
0
1
< J^{-1} >
2
< H^{-1} >
3
< H^{-1} J H^{-1} >
-z
take zscore (not of 0/1 dummies)
-F
input fields separators (default " \t")
-v
verbosity level (default 0)
0
just results
1
2
summary statistics
3
covariance matrix
4
minimization steps (default 10)
5
model definition
-g
set number of point for global optimal threshold identification
-h
this help
-t
set threshold value (default 0)
0
ignore threshold
(0,1)
user provided threshold
1
compute optimal only global
2
compute optimal
-M
estimation method
0
maximum likelihood
1
min. score (w0=w1=1)
2
min. score (w0=1/N0, w1=1/N1)
-A
MLL optimization options (default 0.01,0.1,100,1e-6,1e-6,5) fields are step,tol,iter,eps,msize,algo. Empty fields for default
step
initial step size of the searching algorithm
tol
line search tolerance iter: maximum number of iterations
eps
algo
optimization methods: 0 Fletcher-Reeves, 1 Polak-Ribiere, 2 Broyden-Fletcher-Goldfarb-Shanno, 3 Steepest descent, 4 simplex
-B
score optimization options (default 0.1,100,1e-6) fields are step,iter,msize. Empty fields for default
step
initial step size of the searching algorithm
iter
maximum number of iterations
msize
max size, stopping criteria simplex dim. <max size optimization method is simplex

## AUTHOR

Written by Giulio Bottazzi