Recursively compute the denominator of the individual conditional likelihood function for the pseudo conditional maximum likelihood method proposed by Bartolucci & Nigro (2012) recursively, adapted from Krailo & Pike (1984).
quasi_sym_pseudo(eta,qi,s,y0=NULL)
value of the denominator
first derivative of the recursive function
a component of the score function
second derivative of the recursive function
a component for the Hessian matrix
individual vector of products between covariate and parameters
total score of the individual
Vector of quantities from first step estimation
Individual initial observation for dynamic models
Francesco Bartolucci (University of Perugia), Claudia Pigini (University of Ancona "Politecnica delle Marche"), Francesco Valentini (University of Ancona "Politecnica delle Marche")
Bartolucci, F. and Nigro, V. (2010), A dynamic model for binary panel data with unobserved heterogeneity admitting a root-n consistent conditional estimator, Econometrica, 78, 719-733.
Bartolucci, F. and Nigro, V. (2012), Pseudo conditional maximum likelihood estimation of the dynamic logit model for binary panel data, Journal of Econometrics, 170, 102-116.
Bartolucci, F., Valentini. F., & Pigini, C. (2021), Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data, Computational Economics, https://doi.org/10.1007/s10614-021-10218-2.
Krailo, M. D., & Pike, M. C. (1984). Algorithm AS 196: conditional multivariate logistic analysis of stratified case-control studies, Journal of the Royal Statistical Society. Series C (Applied Statistics), 33(1), 95-103.