Composite likelihood estimation for models of spatial ordinal data and spatial proportional data with zero/one values

Feng, Xiaoping; Zhu, Jun; Lin, Pin‐Yao; Steen-Adams, Michelle M.

doi:10.1002/env.2306

Cited by 14 publications

(14 citation statements)

References 45 publications

(62 reference statements)

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“…Forest cover types were derived from the Wisconsin Land Economic Inventory, a land survey that represents land covers in 1930. Here we consider an early successional forest cover, known as the aspen-paper birch (APB) (Fu et al, 2013;Feng et al, 2014). The response variable is the proportion of APB in a quarter section, varying from 0 (no APB) to 1 (all APB).…”

Section: Study Backgroundmentioning

confidence: 99%

“…We also fitted the spatial Tobit model for comparison. The weight radius is set to be r = 5 (Feng et al, 2014). Maximum likelihood estimation assuming independence provided the initial values for composite likelihood estimation.…”

Section: Model Fitting and Selectionmentioning

confidence: 99%

“…For independent data, Ferrari (2010, 2012) described a class of models based on a mixture of continuous and discrete distributions with probability mass at zero/one. For spatial proportional data, Feng et al (2014) proposed a spatial Tobit model, and the distribution of zero/one values are handled by the thresholding parameter and the regression mean. Although the spatial Tobit model is a natural extension of a spatial probit model for spatial binary data (Heagerty and Lele, 1998;De Oliveira , 2000), the Gaussian latent variable restricts the distribution to be unimodal in the open interval (0, 1), which may not be appropriate for some data distributions in practice (Kieschnick and McCullough, 2003).…”

Section: Introductionmentioning

confidence: 99%

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On regression analysis of spatial proportional data with zero/one values

2015

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Section: Study Backgroundmentioning

confidence: 99%

Section: Model Fitting and Selectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On regression analysis of spatial proportional data with zero/one values

2015

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“…Not all the parameters under the MSpO model () are identifiable. Hence, for parameter identification, 15 we set

var (Z_{i s}) = σ^{2} + τ^{2} = 1

α_{0} = - \infty

α_{1} = 0

, and

α_{J} = \infty

. Let

θ = {(α_{2}, \dots, α_{J - 1}, β^{T}, σ^{2}, ϕ)}^{T}

denote the vector of model parameters, where

0 < α_{2} < α_{3} < \dots < α_{J - 1} < + \infty

β \in ℝ^{1 + p + q}

, and

ϕ \in (0, 1)

.…”

Section: Model Fittingmentioning

confidence: 99%

“…Under this framework, the CL function results from multiplying a collection of component likelihoods, with the responses within a component assumed to be dependent, but orthogonal across components 14 . Maximum CL inference and related asymptotics were established 15 for spatial ordinal data. CL‐based Bayesian inference for spatial extremes 16 also exists.…”

Section: Introductionmentioning

confidence: 99%

Composite likelihood inference for ordinal periodontal data with replicated spatial patterns

Wang

Fung

Bandyopadhyay

et al. 2021

Statistics in Medicine

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Spatial ordinal data observed separately for multiple subjects are common in biomedical research, yet statistical methodology for such ordinal data analysis is limited. The existing methodology often assumes a single realization of spatial ordinal data without replications, a commonplace in disease mapping studies, and thus are not directly applicable. Motivated by a dataset evaluating periodontal disease (PD) status, we propose a multisubject spatial ordinal model that assumes a geostatistical spatial structure within a regression framework through an elegant latent variable representation. For achieving computational scalability within a classical inferential framework, we develop a maximum composite likelihood method for parameter estimation, and establish the asymptotic properties of the parameter estimates. Another major contribution is the development of model diagnostic measures for our dependent data scenario using generalized surrogate residuals. A simulation study suggests sound finite sample properties of the proposed methods. We also illustrate our proposed methodology via application to the motivating PD dataset. A companion R package clordr is available for easy implementation.

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A mixture distribution for modelling bivariate ordinal data

Ip,

2024

Stat Papers

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Ordinal responses often arise from surveys which require respondents to rate items on a Likert scale. Since most surveys contain more than one question, the data collected are multivariate in nature, and the associations between different survey items are usually of considerable interest. In this paper, we focus on a mixture distribution, called the combination of uniform and binomial (CUB), under which each response is assumed to originate from either the respondent’s uncertainty or the actual feeling towards the survey item. We extend the CUB model to the bivariate case for modelling two correlated ordinal data without using copula-based approaches. The proposed model allows the associations between the unobserved uncertainty and feeling components of the variables to be estimated, a distinctive feature compared to previous attempts. This article describes the underlying logic and deals with both theoretical and practical aspects of the proposed model. In particular, we will show that the model is identifiable under a wide range of conditions. Practical inferential aspects such as parameter estimation, standard error calculations and hypothesis tests will be discussed through simulations and a real case study.

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Composite likelihood estimation for models of spatial ordinal data and spatial proportional data with zero/one values

Cited by 14 publications

References 45 publications

On regression analysis of spatial proportional data with zero/one values

On regression analysis of spatial proportional data with zero/one values

Composite likelihood inference for ordinal periodontal data with replicated spatial patterns

A mixture distribution for modelling bivariate ordinal data

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