Abstract

OROZCO-ACOSTA, Erick; LLINAS-SOLANO, Humberto  and  FONSECA-RODRIGUEZ, Javier. Convergence Theorems in Multinomial Saturated and Logistic Models. Rev.Colomb.Estad. [online]. 2020, vol.43, n.2, pp.211-231.  Epub Dec 05, 2020. ISSN 0120-1751.  https://doi.org/10.15446/rce.v43n2.79151.

In this paper, we develop a theoretical study about the logistic and saturated multinomial models when the response variable takes one of R ≥ 2 levels. Several theorems on the existence and calculations of the maximum likelihood (ML) estimates of the parameters of both models are presented and demonstrated. Furthermore, properties are identified and, based on an asymptotic theory, convergence theorems are tested for score vectors and information matrices of both models. Finally, an application of this theory is presented and assessed using data from the R statistical program.

Keywords : Multinomial logit model; Saturated model; Logistic regression; Maximum likelihood estimator; Score vector; Fisher information matrix.

        · abstract in Spanish     · text in English     · English ( pdf )