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PROGRAM:

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 <gradF gradF^t>

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 comment headers

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 gradient tolerance : stopping criteria ||gradient||<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

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