Analysing circular data in Stata

Circular data are a large class of directional data, which are of interest to scientists in many fields, including biologists (movements of migrating animals), meteorologists (winds), geologists (directions of joints and faults) and geomorphologists (landforms, oriented stones). Such examples are all recordable as compass bearings relative to North. Other examples include phenomena that are periodic in time, including daily and seasonal rhythms. The analysis of circular data is an odd corner of statistical science which many never visit, even though it has a long and curious history. Perhaps for that reason, it seems that no major statistical language provides direct support for circular statistics, although there is a commercially available special-purpose program called Oriana. This paper describes the development and use of some routines which have been written in Stata, primarily to allow graphical and exploratory analyses. They include commands for data management, summary statistics and significance tests, univariate graphics and bivariate relationships. The graphics routines were developed partly with -gph-. (By the time of the meeting, it may be possible to enhance these using new facilities in Stata 7.) Collectively they offer about as many facilities as does Oriana.

A Bayesian model for longitudinal circular data

The analysis of short longitudinal series of circular data may be problematic and to some extent has not been completely developed. In this paper we present a Bayesian analysis of a model for such data. The model is based on a radial projection onto the circle of a particular bivariate normal distribution. Inferences about the parameters of the model are based on samples from the corresponding joint posterior density which are obtained using a Metropolis-within-Gibbs scheme after the introduction of suitable latent variables. The procedure is illustrated both using a simulated data set and a realdata set previously analyzed in the literature.Circular data, Longitudinal data, Gibbs sampler, Latent variables, Mixed-effects linear models, Projected normal distribution

A semi-parametric model for circular data based on mixtures of beta distributions

This paper introduces a new, semi-parametric model for circular data, based on mixtures of shifted, scaled, beta (SSB) densities. This model is more general than the Bernstein polynomial density model which is well known to provide good approximations to any density with finite support and it is shown that, as for the Bernstein polynomial model, the trigonometric moments of the SSB mixture model can all be derived. Two methods of fitting the SSB mixture model are considered. Firstly, a classical, maximum likelihood approach for fitting mixtures of a given number of SSB components is introduced. The Bayesian information criterion is then used for model selection. Secondly, a Bayesian approach using Gibbs sampling is considered. In this case, the number of mixture components is selected via an appropriate deviance information criterion. Both approaches are illustrated with real data sets and the results are compared with those obtained using Bernstein polynomials and mixtures of von Mises distributions

Circular Bernstein polynomial distributions

This paper introduces a new non-parametric approach to the modeling of circular data, based on the use of Bernstein polynomial densities which generalizes the standard Bernstein polynomial model to account for the specific characteristics of circular data. It is shown that the trigonometric moments of the proposed circular Bernstein polynomial distribution can all be derived in closed form. We comment on how to fit the Bernstein polynomial density approximation to a sample of data and illustrate our approach with a real data example.Circular data, Non-parametric modeling, Bernstein polynomials

Logistic regression for circular data

This paper considers the relationship between a binary response and a circular predictor. It develops the logistic regression model by employing the linear-circular regression approach. The maximum likelihood method is used to estimate the parameters. The Newton-Raphson numerical method is used to find the estimated values of the parameters. A data set from weather records of Toowoomba city is analysed by the proposed methods. Moreover, a simulation study is considered. The R software is used for all computations and simulations

Adjusting outliers in univariate circular data

Circular data analysis is a particular branch of statistics that sits somewhere between the analysis of linear data and the analysis of spherical data. Circular data are used in many scientific fields. The efficiency of the statistical methods that are applied depends on the accuracy of the data in the study. However, circular data may have outliers that cannot be deleted. If this is the case, we have two ways to avoid the effect of outliers. First, we can apply robust methods for statistical estimations. Second, we can adjust the outliers using the other clean data points in the dataset. In this paper, we focus on adjusting outliers in circular data using the circular distance between the circular data points and the circular mean direction. The proposed procedure is tested by applying it to a simulation study and to real data sets. The results show that the proposed procedure can adjust outliers according to the measures used in the paper

Nonparametric Regression Estimation for Circular Data

[Abstract] Non-parametric regression with a circular response variable and a unidimensional linear regressor is a topic which was discussed in the literature. In this work, we extend the results to the case of multivariate linear explanatory variables. Nonparametric procedures to estimate the circular regression function are formulated. A simulation study is carried out to study the sample performance of the proposed estimators.Ministerio de Economía y Competitividad; MTM2016-76969-PMinisterio de Economía y Competitividad; MTM2017-82724-RXunta de Galicia; ED481A-2017/361Grupos de Referencia Competitiva; ED431C-2016-015Centro Singular de Investigación de Galicia; ED431G/0