A Bayesian model for longitudinal circular data based on the projected normal distribution

Núñez-Antonio, Gabriel; Gutiérrez‐Peña, Eduardo

doi:10.1016/j.csda.2012.07.025

Cited by 23 publications

(22 citation statements)

References 23 publications

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“…First steps in that direction were taken by Jordan () in a University of Georgia Master's thesis. More recently, a fully Bayesian approach to this class of models has been explored by Nuñez‐Antonio & Gutiérrez‐Peña ().…”

Section: Discussionmentioning

confidence: 99%

“…As noted by Nuñez‐Antonio & Gutiérrez‐Peña (), further work is needed to elucidate the link between correlation structures on the Euclidean and angular scales. Absent a mathematical characterisation of this link, the examples we have explored via simulation suggest that the standard correlation models available for the working correlation matrices in the marginal SPMLM (MSPMLM) imply similar patterns of correlation on the angular scale.…”

Section: Correlation Structuresmentioning

confidence: 99%

“…Although the general mathematical form of the mapping is hard to derive, for any specific case we can estimate the circular correlation by simulation (cf. Nuñez‐Antonio & Gutiérrez‐Peña , section 2.2). We illustrate that approach in Example 6.1 below for the MFA data based on a fitted MSPMLM with AR(1) working correlation structures.…”

Section: Correlation Structuresmentioning

confidence: 99%

“…Because of the binaural nature of human hearing, sound localisations are often bimodal, motivating the use of a mixture model by these authors. More recently, Nuñez‐Antonio & Gutiérrez‐Peña () propose a Bayesian mixed‐effect version of the SPMLM suitable for longitudinal circular data.…”

Section: Introductionmentioning

confidence: 99%

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Marginal Projected Multivariate Linear Models for Clustered Angular Data

Hall

Shen²

2015

Aus NZ J of Statistics

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Among the diverse frameworks that have been proposed for regression analysis of angular data, the projected multivariate linear model provides a particularly appealing and tractable methodology. In this model, the observed directional responses are assumed to correspond to the angles formed by latent bivariate normal random vectors that are assumed to depend upon covariates through a linear model. This implies an angular normal distribution for the observed angles, and incorporates a regression structure through a familiar and convenient relationship. In this paper we extend this methodology to accommodate clustered data (e.g., longitudinal or repeated measures data) by formulating a marginal version of the model and basing estimation on an EM-like algorithm in which correlation among withincluster responses is taken into account by incorporating a working correlation matrix into the M step. A sandwich estimator is used for the parameter estimates' covariance matrix. The methodology is motivated and illustrated using an example involving clustered measurements of microbril angle on loblolly pine (Pinus taeda L.) Simulation studies are presented that evaluate the finite sample properties of the proposed fitting method. In addition, the relationship between within-cluster correlation on the latent Euclidean vectors and the corresponding correlation structure for the observed angles is explored.

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Section: Discussionmentioning

confidence: 99%

Section: Correlation Structuresmentioning

confidence: 99%

Section: Correlation Structuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Marginal Projected Multivariate Linear Models for Clustered Angular Data

Hall

Shen²

2015

Aus NZ J of Statistics

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“…A cluster effect can be introduced in a projected normal model by expressing u j = b j + e j , j = 1,2 where ( b 1 , b 2 ) are independent N (0, ψ ) variables representing a cluster effect while the unit errors ( e 1 , e 2 ) have independent N (0,1 − ψ ) distributions (Nuñez‐Antonio & Gutiérrez‐Peña, ; Hall & Shen, ). Considering Equation , y is approximately equal to a sum featuring a fixed effect, a cluster effect, and an experimental error, with the β ‐parameters appearing in all three terms.…”

Section: Comparisons With Projected Normal Modelsmentioning

confidence: 99%

A random‐effects model for clustered circular data

Rivest

Kato

2019

Can J Statistics

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This article considers a circular regression model for clustered data, where both the cluster effects and the regression errors have von Mises distributions. It involves β, a vector of parameters for the fixed effects, and two concentration parameters for the error distribution. A measure of intra‐cluster circular correlation and a predictor for an unobserved cluster random effect are studied. Preliminary estimators for the vector β and the two concentration parameters are proposed, and their performance is compared with that of the maximum likelihood estimators in a simulation study. A numerical example investigating the factors impacting the orientation taken by a sand hopper when released is presented. The Canadian Journal of Statistics 47: 712–728; 2019 © 2019 Statistical Society of Canada

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Joint regression modelling of intensity and timing of accelerometer counts

Geraci

2022

Statistics in Medicine

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Accelerometers are commonly used in human medical and public health research to measure physical movement, which is relevant in a wide range of studies, from physical activity and sleep behaviours studies, to identification of movement patterns in people affected by diseases of the locomotor system and prediction of risk of injury in high performance sports. The accelerometer output provides the intensity (activity count) and timing (timestamp) of the movement, which can be used to define bouts of activity (periods of sustained movement of a given intensity). In some contexts, it may be important to include both dimensions to obtain a broader and deeper understanding of the phenomenon under study. Such is the case of a large‐scale epidemiological investigation on the daily and weekly physical activity behaviours of school‐aged children enrolled in the UK Millennium Cohort Study, which has motivated the present article. I present a statistical approach to joint modelling of intensity and timing of activity bouts that takes advantage of the circular nature of the timing. The model, which accounts for the longitudinal structure of the observations, is remarkably simple to implement using standard statistical software.

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A Bayesian model for longitudinal circular data based on the projected normal distribution

Cited by 23 publications

References 23 publications

Marginal Projected Multivariate Linear Models for Clustered Angular Data

Marginal Projected Multivariate Linear Models for Clustered Angular Data

A random‐effects model for clustered circular data

Joint regression modelling of intensity and timing of accelerometer counts

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