A flexible class of parametric transition regression models based on copulas: application to poliomyelitis incidence

Abstract

This paper presents an extension of a general parametric class of transitional models of order p. In these models, the conditional distribution of the current observation, given the present and past history, is a mixture of conditional distributions, each of them corresponding to the current observation, given each one of the p-lagged observations. Such conditional distributions are constructed using bivariate copula models which allow for a rich range of dependence suitable to model non-Gaussian time series. Fixed and time varying covariates can be included in the models. These models have the advantage of straightforward construction and estimation for the analysis of time series and more general longitudinal data. A poliomyelitis incidence data set is used to illustrate the proposed methods, contrary to other researches' conclusions whose methods are mainly based on linear models, we find significant evidence of a decreasing trend in polio infection after accounting for seasonality.

Review of poliovirus modeling performed from 2000 to 2019 to support global polio eradication

“…Following the search process shown in Figure 1, the systematic literature review and addition of other studies by the three GPEI-supported modeling groups led to the extraction of information from 176 included studies [1][2][3][4]. As noted, during review of the full text of the studies identified by the search, we excluded papers that presented statistical analyses that did not include a mechanistic poliovirus transmission model [180][181][182][183][184][185][186][187]. Table 1 summarizes some attributes of the included studies.…”

Construcción de Distribuciones Multivariadas con Marginales Dependientes Usando Cópulas en R

“…Las cópulas se han convertido en una herramienta popular para la construcción de modelos multivariados en campos donde hay un gran interés por la dependencia multivariada; más específicamente, han sido utilizadas en campos tan variados como en medicina, para modelar el número de casos mensuales de una enfermedad casi erradicada, por ejemplo, la poliomielitis [1]; en ciencias actuariales, para modelar la mortalidad y las pérdidas dependientes [2,3]; en finanzas, para análisis y gestión de riesgos [4,5]; en estudios biomédicos, en el modelado de tiempos de eventos correlacionados y riesgos competitivos [6], y en ingeniería, en el control de procesos multivariados y en el modelado hidrológico [7].…”

“…Ahora bien, al par de números (x, y) se le puede asociar tres números F(x), G(y) y H(x, y), donde cada uno de ellos pertenece al intervalo [0,1], es decir, a cada (x, y) le corresponde un punto (F(x),G(y)) en el espacio producto [ Como se demuestra en [8], esta correspondencia, que asigna el valor de la función de distribución conjunta a cada par ordenado de los valores de las funciones de distribución marginales, es de hecho una función de distribución. Tales funciones son cópu-las [10].…”

“…Tales funciones son cópu-las [10]. Más formalmente, en [11] se describe una cópula como una distribución multivariada cuyas marginales son uniformes en [0,1]. Para un vector p-dimensional sobre el cubo unitario, una cópula es…”

An efficient copula-based method of identifying regression models of non-monotonic relationships in processing plants

“…While not explicitly referring to the regression analysis, in several studies (Leong and Valdez, 2005;Käärik et al, 2011;Mohseni Ahooyi et al, 2014c), similar functions have been derived by calculating the copula conditional independence. A mixture of copulas is used to create more complex non-Gaussian copulas describing the feature-response relationship (Escarela et al, 2006). Constructing the copulas based on the affine generalized hyperbolic distributions is also considered as a way of generating more complicated parametric copulas applicable to the regression models (Schmidt et al, 2006).…”