Compute the derivatives of the utility function UTIL(i) with respect t
the estimated parameters BETA, STETA, GTETA, PHI and PMU, and LAMBDA.
USAGE:
This routine is called before computing the derivatives of the proba
function P(i) with respect to the estimated parameters, for predicti
INPUT:
d dependent variable (vector of ndv elements):
If d(i) = 1 , the individual has chosen the available alternat
If d(i) = 0 , he has not chosen the available alternative i;
If d(i) = -1, the alternative i is not available for the indiv
par estimated parameters in the log-likelihood function (vector of
elements).
xx (ndv x niv) matrix containing an observation on "niv" independ
variables (with and without Box-Cox) specified in "ndv" altern
for estimation or prediction.
dxx1 (ndv x niv) matrix containing the first derivatives of the mat
with respect to the estimated Box-Cox parameters LAMBDA.
ev exponential of the representative utility component V (vector
elements): exp(V(i)).
sev sum of the exp(V(i))'s for STANDARD DOGIT only.
evl phi*ev + 1 for LIN-IPT-LOGIT, or ev + pmu for BT-IPT-LOGIT
(vector of ndv elements)
eev exp(exp(V)) if phi = 0, or evl**(1/phi) if phi > 0 for LIN-IPT
(vector of ndv elements)
util utility function corresponding to the numerator of the probabi
function P (vector of ndv elements)
ndv number of alternatives considered in the estimation.
niv number of beta-coefficients in the estimation.
nopt = 1 : LOGIT
= 2 : STANDARD DOGIT
= 3 : GENERALIZED DOGIT
= 4 : LIN-IPT-LOGIT
= 5 : BT-IPT-LOGIT.
npar total number of estimated parameters, namely the estimated BET
coefficients, the estimated extra parameters (STETA or GTETA o
PHI and PMU) and the estimated Box-Cox parameters LAMBDA.
nparext total number of estimated parameters including the estimated B
coefficients and the estimated extra parameters only.
numl vector of "niv" elements, containing the index numbers of the
parameters (fixed or estimated) associated with the "niv" inde
variables. If numl(k) = 0, then no Box-Cox transformation is a
to the k-th variable.
nume vector of "nest" elements, containing the index numbers of the
mated Box-Cox parameters only.
nest number of distinctly estimated Box-Cox parameters.
OUTPUT:
derutil (ndv x npar) matrix of first derivatives of the utility functi
UTIL(i), i=1,ndv, with respect to the estimated BETA, STETA, G
PHI, PMU and LAMBDA. |