I have a multivariate probit model with one selection
equation and three other outcome variable across time.
That is,
selection equation: y1*=x*b1
if y1*>0 for a given individual, we also observe the
following over three points in time:
z1*=w1*theta z2*=w2*theta z3*=w3*theta
To compute the multivariate normal probabilities, I am
using Stephen Jenkin's excellent mvnp progrma. My
question is about the restrictions that should be
placed on the 4x4 Cholesky matrix.
The problem: the Cholesky matrix in my case seems to
converge for some specifications and not others. In
particular, convergence is not achieved if even one
variable is included in both stages, even if there are
several exclusion restrictions. When the variables
are totally different, the model converges and the
results make sense.
What is apparently happening is that the sum of the
squares of the cholesky elements (other than the
diagonal) sum to more than 1.
Would you suggest using atanh to transform the
elements of the Cholesky matrix, as heckprob.ado does
to the covariance matrix?
Thank you,
Kam
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