Projected Multivariate Linear Models for Directional Data

Presnell, Brett; Morrison, Scott P.; Littell, Ramon C.

doi:10.1080/01621459.1998.10473768

Cited by 102 publications

(70 citation statements)

References 10 publications

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“…However, for each person tested there are three replicates at each of 24 equispaced angles around the circle, necessitating either a hierarchical random‐effects specification or a marginal approach to account for correlation within a subject. Presnell et al. (1998) considered a projection approach to model circular outcomes easily via a linear model; this model could conceivably be extended to the mixed model case but is not suitable for the bimodal data that are considered here.…”

Section: Discussionmentioning

confidence: 99%

A Two-Component Circular Regression Model for Repeated Measures Auditory Localization Data

McMillan¹,

Hanson

Saunders³

et al. 2013

Journal of the Royal Statistical Society Series C: Applied Statistics

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Auditory localization experiments are conducted to evaluate human ability to locate the position of a source of sound, and to determine how population characteristics might affect this ability. These experiments generate data that are circular, bimodal and repeated, and have hypothesized symmetry patterns that should be included and tested within the modelling framework. We propose a two-part mixture of wrapped Cauchy densities for these bimodal angular data, with random effects to model correlation between repeated measures.The effects of signal position and types of symmetry in the signal response around the circle are modelled by using circular B-splines. The model is used to investigate the effects of age and hearing impairment on the ability to localize a low frequency signal.

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Section: Discussionmentioning

confidence: 99%

A Two-Component Circular Regression Model for Repeated Measures Auditory Localization Data

McMillan¹,

Hanson

Saunders³

et al. 2013

Journal of the Royal Statistical Society Series C: Applied Statistics

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“…Aside from the use of the asymptotic covariance matrix

\overset{false^}{italicξ}^{- 1} \overset{false^}{italicζ} \overset{false^}{italicξ}^{- 1}

in place of the information matrix, formulas for fitted values and their standard errors in the MSPMLM are the same as those given by Presnell et al . () for ML estimation in the SPMLM.…”

Section: Examplesmentioning

confidence: 99%

“…Building on the work of Gould () and Johnson & Wehrly (), Fisher & Lee () proposed models in which one or both of the mean direction and concentration parameters are related to covariates through a linear predictor and link function which maps the real line (the range of the linear predictor) to the appropriate range of the corresponding von Mises parameter ( i.e ., to (− π , π ) in the case of the mean direction and [0,∞) for the concentration). As pointed out by Presnell, Morrison & Littell (), however, there are serious drawbacks to this approach, including multimodality of the likelihood surface, non‐identifiability, and computational problems. Instead, these authors proposed a class of models based upon the angular normal distribution, which has a latent variable formulation, in which the observed angular response corresponds to the angle formed by an underlying latent multivariate normal random vector.…”

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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“…An alternative approach is to use the offset normal distribution, allowing the mean vector (µ 1 , µ 2 ) of the bivariate normal to be a linear function of the covariates. See Ref 55 for parameter estimation using maximum likelihood. This method seems to have better numerical properties than the method using monotone link functions.…”

Section: Regression and Correlationmentioning

confidence: 99%

Circular data

Lee

2010

WIREs Computational Stats

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The special nature of circular data means that conventional methods suitable for the analysis of linear data do not apply. In this article, we survey a range of methods that have been developed over the last 50 years to handle the special characteristics of data consisting of angular measurements. We discuss summary statistics and graphical methods, methods for the analysis of single and multiple samples of circular data, circular correlation, regression methods, and time series. We discuss the standard probability models on which these analyses are based, and give several examples of the application of these methods. A reasonably comprehensive bibliography is provided .

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Projected Multivariate Linear Models for Directional Data

Cited by 102 publications

References 10 publications

A Two-Component Circular Regression Model for Repeated Measures Auditory Localization Data

A Two-Component Circular Regression Model for Repeated Measures Auditory Localization Data

Marginal Projected Multivariate Linear Models for Clustered Angular Data

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