A numerically stable quadrature procedure for the one-factor random-component discrete choice model
نویسنده
چکیده
The Gaussian quadrature formula had been popularized by Butler and Mo$tt (1982 Econometrika 50, 761}764) for the estimation of the error component probit panel model. Borjas and Sueyoshi (1994, Journal of Econometrics 64, 164}182) pointed out some numerical and statistical di$culties of applying it to models with group e!ects. With a moderate or large number of individuals in a group, the likelihood function of the model evaluated by the Gaussian quadrature formula can be numerically unstable, and at worst, impossible to evaluate. Statistical inference may also be inaccurate. We point out that some of these di$culties can be overcome with a carefully designed algorithm and the proper selection of the number of quadrature points. However, with a very large number of individuals in a group, the Gaussian quadrature formulation of integral may have large numerical approximation errors. ( 2000 Elsevier Science S.A. All rights reserved.
منابع مشابه
Simulations of transport in one dimension
Advection-dispersion equation is solved in numerically by using combinations of differential quadrature method (DQM) and various time integration techniques covering some explicit or implicit single and multi step methods. Two different initial boundary value problems modeling conservative and nonconservative transports of some substance represented by initial data are chosen as test problems. ...
متن کاملStable Computation of High Order Gauss Quadrature Rules Using Discretization for Measures in Radiation Transfer
The solution of the radiation transfer equation for the Earth's atmosphere needs to account for the re ectivity of the ground. When using the spherical harmonics method, the solution for this term involves an integral with a particular measure that presents numerical challenges. We are interested in computing a high order Gauss quadrature rule for this measure. We show that the two classical al...
متن کاملOn Rank-Ordered Nested Multinomial Logit Model and D-Optimal Design for this Model
In contrast to the classical discrete choice experiment, the respondent in a rank-order discrete choice experiment, is asked to rank a number of alternatives instead of the preferred one. In this paper, we study the information matrix of a rank order nested multinomial logit model (RO.NMNL) and introduce local D-optimality criterion, then we obtain Locally D-optimal design for RO.NMNL models in...
متن کاملMaximum likelihood estimation of limited and discrete dependent variable models with nested random effects
Gauss–Hermite quadrature is often used to evaluate and maximize the likelihood for random component probit models. Unfortunately, the estimates are biased for large cluster sizes and/or intraclass correlations. We show that adaptive quadrature largely overcomes these problems. We then extend the adaptive quadrature approach to general random coefficient models with limited and discrete dependen...
متن کاملA Simple and Systematic Approach for Implementing Boundary Conditions in the Differential Quadrature Free and Forced Vibration Analysis of Beams and Rectangular Plates
This paper presents a simple and systematic way for imposing boundary conditions in the differential quadrature free and forced vibration analysis of beams and rectangular plates. First, the Dirichlet- and Neumann-type boundary conditions of the beam (or plate) are expressed as differential quadrature analog equations at the grid points on or near the boundaries. Then, similar to CBCGE (direct ...
متن کامل