Circular Regression Research Articles

The Comparison Between Maximum Weighted and Trimmed Likelihood Estimator of the Simple Circular Regression Model

The Maximum Likelihood Estimator (MLE) was used to estimate unknown parameters of the simple circular regression model. However, it is very sensitive to outliers in data set. A robust method to estimate model parameters is proposed.

Circular regression models of modern harmonic producing sources

This study presents a novel measurement-based method for modelling harmonic current injections of low-voltage power electronics equipment. The aim of the developed methodology is to accurately represent harmonic current phase angle in response to the applied harmonic background voltage at the terminals of modelled device. In this method, the harmonic angles are analysed with the techniques of circular statistics. The performed study proves the adequacy of representing phase angles as sets of directional data rather than linear. After graphical and quantitative analysis, the regression models with underlying von Mises distribution are derived in the form of algebraic equation. This algebraic equation features sine and cosine terms and explains relationship between independent variable – voltage harmonic angle and dependent variable – current harmonic angle. The subsequent analysis of the residuals allows to conclude that models developed by applying this technique can be used in commercial simulation packages and allow to account on any value of background harmonic voltage angle.

Identifying Outlier Observations in Linear - Circular Regression Model

Identifying Outlier Observations in Linear - Circular Regression Model

Changes in Antecedent Soil Moisture Modulate Flood Seasonality in a Changing Climate

AbstractDue to difficulties in identifying a climate change signal in flood magnitude, it has been suggested that shifts in flood timing, that is, the day of annual streamflow maxima, may be detectable. Here, we use high‐quality streamflow, largely free of snowmelt, from 221 catchments across Australia to investigate the influence of shifts in soil moisture and rainfall timing on annual streamflow maxima timing. In tropical areas we find that flood timing is strongly linked to the timing of both rainfall and soil moisture annual maxima. However, in southern Australia flood timing is more correlated with soil moisture maxima than rainfall maxima. The link between flood, soil moisture, and rainfall timing is confounded by event severity: For less extreme events flood timing is more likely to correspond to soil moisture timing, whereas rainfall timing becomes increasingly important as flood severity increases. Using circular regression to investigate nonstationarity, we find that flood timing is shifting to earlier in the year in the tropics and later in the year in the southwest of the continent, consistent with changes in mean and extreme rainfall and shifts in soil moisture timing due to tropical expansion. In southeast Australia, there is evidence that the mechanisms controlling flood seasonality are changing with a reversal of trends post Millennium Drought. Overall, changes in soil moisture timing, compared to changes in rainfall timing, are found to have a greater influence on changes in annual maxima streamflow flood timing.

A review of detecting outlier in a circular regression model

Circular data is very relevant and important application technique in many fields such as physical science, medical science and others. During the last few years, writers have shown a deep interest of outlier detection in the circular regression model. In this case, authors have a tendency to study and explore in detail about the outlier detection in circular regression model. This paper aims to review the outlier detection methods in circular regression model. Here, we concentrate the attention on the methods of identifying outlier in this model. These survey of circular regression models in which many interesting properties and is good enough to detect the occurrence of outlier. Through the survey may highlight the significant of methods to detect outliers in circular regressions model and provide guideline for future work to look into the research gap.

Outlier detection in circular regression model using minimum spanning tree method

The existence of outliers in circular-circular regression model can lead to many errors, for example in inferences and parameter estimations. Therefore, this study aims to develop new algorithms that can detect outliers by using minimum spanning tree method. The proposed method is examined via simulation study with different number of sample sizes and level of contaminations. Then, the performance of the proposed method was measured using “success” probability, masking effect, and swamping effect. The results revealed that the proposed method were performed well and able to detect all the outliers planted in various conditions.

Diagnostic analysis of a circular-circular regression model using asymmetric or asymmetric bi-modal circular errors

Many circular data sets encountered in practice are asymmetric or asymmetric bi-modal. In this paper, we propose a diagnostic analysis of a parametric circular regression model with a single circular explanatory variable by assuming asymmetric or asymmetric bi-modal circular errors. We develop a new test statistic for detecting outliers both in circular response and explanatory variables. For the case with a circular explanatory variable, we employ a parametric inverse circular-circular regression model. In addition, we provide a goodness of fit test to find whether circular errors are symmetric or not. Our methods are illustrated using a real data set arising from a study of Genomics.

A random‐effects model for clustered circular data

AbstractThis article considers a circular regression model for clustered data, where both the cluster effects and the regression errors have von Mises distributions. It involvesβ, 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 vectorβand 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 Statistics47: 712–728; 2019 © 2019 Statistical Society of Canada

Outlier Detection in Multiple Circular Regression Model using DFFITc Statistic

This paper presents the identification of outliers in multiple circular regression model (MCRM), where the model studies the relationship between two or more circular variables. To date, most of the published papers concentrating on detecting outliers in circular samples and simple circular regression model with one independent circular variable. However, no related studies have been found for more than one independent circular variable. The existence of outliers could alert the sign and change the magnitude of regression coefficients and may lead to inaccurate model development and wrong prediction. Hence, the intention is to develop an outlier detection procedure using DFFITS statistic for circular case. This method has been successfully used in multiple linear regression model. Therefore, the DFFITc statistic for circular variable has been derived. The corresponding critical values and the performance of the procedure are studied via simulations. The results of simulation studies show that the proposed statistic perform well in detecting outliers in MCRM using DFFITc statistic. The proposed statistic was applied to a real data for illustration purposes.

Circular Modelling of Circumplex Measurements for Interpersonal Behavior.

This article describes a new way to analyze data from the interpersonal circumplex (IPC) for interpersonal behavior. Instead of analyzing Agency and Communion separately or analyzing the IPC’s octants, we propose using a circular regression model that allows us to investigate effects on a blend of Agency and Communion. The proposed circular model is called a projected normal (PN) model. We illustrate the use of a PN mixed-effects model on three repeated measures data sets with circumplex measurements from interpersonal and educational psychology. This model allows us to detect different types of patterns in the data and provides a more valid analysis of circumplex data. In addition to being able to investigate the effect on the location (mean) of scores on the IPC, we can also investigate effects on the spread (variance) of scores on the IPC. We also introduce new tools that help interpret the fixed and random effects of PN models.

A new Concentric Circles Detection method for Object Detection applied to Radar Images

In this work, a new concentric circles detection method for object detection is proposed. It has been applied to the images of a commercial radar, captured with a Charge-Coupled Device (CCD) camera. The processing includes the detection of centres and concentric circles in the images and the identification of the radar scale. Several methods found in the literature have been applied and compared with our novel proposal for multiple concentric circles detection, called “Propagation Method based on Circular Regression”. This methodology has been validated with real radar images, proving its efficiency in obtaining the distance of any object to a marine vessel, with high accuracy and low computational cost, in real time. This system can not only be applied to most existing radars in the market by adjusting the parameters of each model but our proposal for concentric circle detection can be also applied to other sensing applications.

Linear‐Circular Statistical Modeling of Lake Ice‐Out Dates

AbstractOver the past few decades, lake ice phenology in northern temperate lakes has exhibited increased interannual variability. The resulting increase in the incidence of unusually early spring lake ice‐out dates has the potential to affect stability, health, and function of the lake ecosystems. Characterizing the dependency of spring lake ice‐out date to winter and/or spring climate variables offers foreknowledge on the annual lake ice cover season, as the spring ice‐out date is an integrated response to prevailing weather/climate conditions during winter and spring. Here a circular regression framework is presented where ice‐out date regression models, conditioned on a suite of predictor winter and/or spring climate variables (i.e., degree days and snowfall), are developed for 12 Maine lakes to determine the relative import of winter and spring meteorological conditions on year‐to‐year variability of ice‐out dates in Maine lakes. In the circular regression models, ice‐out dates are expressed as points on a unit circle instead of real line, as it preserves the periodicity and order of time‐of‐day variables independent of the choice of reference point. Results show that (a) the magnitude and variance of seasonal spring temperatures explain more than half of the total variability in spring ice‐out date for Maine lakes, (b) the modulating efficacy of spring snowfall on the timing of spring ice‐out dates is the strongest in northern interior Maine lakes, (c) the role of winter degree days in determining the ice‐out dates in Maine lakes is significant across all climate regions, and (d) the effect of winter snowfall on ice‐out dates is significant in coastal Maine lakes. Diagnostics suggest that there are other climatic and nonclimatic variables that produce shifts in the lake ice‐out dates.

Assessing a Bayesian Embedding Approach to Circular Regression Models

Abstract. Circular data is different from linear data and its analysis also requires methods different from conventional methods. In this study a Bayesian embedding approach to estimating circular regression models is investigated, by means of simulation studies, in terms of performance, efficiency, and flexibility. A new Markov chain Monte Carlo (MCMC) sampling method is proposed and contrasted to an existing method. An empirical example of a regression model predicting teachers’ scores on the interpersonal circumplex will be used throughout. Performance and efficiency are better for the newly proposed sampler and reasonable to good in most situations. Furthermore, the method in general is deemed very flexible. Additional research should be done that provides an overview of what circular data looks like in practice, investigates the interpretation of the circular effects and examines how we might conduct a way of hypothesis testing or model checking for the embedding approach.

A system for airport weather forecasting based on circular regression trees

This paper describes a suite of tools and a model for improving the accuracy of airport weather forecasts produced by numerical weather prediction (NWP) products, by learning from the relationships between previously modelled and observed data. This is based on a new machine learning methodology that allows circular variables to be naturally incorporated into regression trees, producing more accurate results than linear and previous circular regression tree methodologies.The software has been made publicly available as a Python package, which contains all the necessary tools to extract historical NWP and observed weather data and to generate forecasts for different weather variables for any airport in the world. Several examples are presented where the results of the proposed model significantly improve those produced by NWP and also by previous regression tree models.

Circular Regression in a Dual-Phase Lock-In Amplifier for Coherent Detection of Weak Signal.

Lock-in amplification (LIA) is an effective approach for recovery of weak signal buried in noise. Determination of the input signal amplitude in a classical dual-phase LIA is based on incoherent detection which leads to a biased estimation at low signal-to-noise ratio. This article presents, for the first time to our knowledge, a new architecture of LIA involving phase estimation with a linear-circular regression for coherent detection. The proposed phase delay estimate, between the input signal and a reference, is defined as the maximum-likelihood of a set of observations distributed according to a von Mises distribution. In our implementation this maximum is obtained with a Newton Raphson algorithm. We show that the proposed LIA architecture provides an unbiased estimate of the input signal amplitude. Theoretical simulations with synthetic data demonstrate that the classical LIA estimates are biased for SNR of the input signal lower than −20 dB, while the proposed LIA is able to accurately recover the weak signal amplitude. The novel approach is applied to an optical sensor for accurate measurement of NO concentrations at the sub-ppbv level in the atmosphere. Side-by-side intercomparison measurements with a commercial LIA (SR830, Stanford Research Inc., Sunnyvale, CA, USA ) demonstrate that the proposed LIA has an identical performance in terms of measurement accuracy and precision but with simplified hardware architecture.

Circular interpretation of regression coefficients.

The interpretation of the effect of predictors in projected normal regression models is not straight‐forward. The main aim of this paper is to make this interpretation easier such that these models can be employed more readily by social scientific researchers. We introduce three new measures: the slope at the inflection point (b c), average slope (AS) and slope at mean (SAM) that help us assess the marginal effect of a predictor in a Bayesian projected normal regression model. The SAM or AS are preferably used in situations where the data for a specific predictor do not lie close to the inflection point of a circular regression curve. In this case b c is an unstable and extrapolated effect. In addition, we outline how the projected normal regression model allows us to distinguish between an effect on the mean and spread of a circular outcome variable. We call these types of effects location and accuracy effects, respectively. The performance of the three new measures and of the methods to distinguish between location and accuracy effects is investigated in a simulation study. We conclude that the new measures and methods to distinguish between accuracy and location effects work well in situations with a clear location effect. In situations where the location effect is not clearly distinguishable from an accuracy effect not all measures work equally well and we recommend the use of the SAM.

Detection of different outlier scenarios in circular regression model using single-linkage method

Outliers are the set of data that are significantly deviates or dissimilar from the rest of the data set. In circular regression model, the existence of outliers are well known to give a large effect on the parameter estimates and inferences. In this study, we proposed clustering-based method using single linkage to detect multiple outliers. Single-linkage is one of several clustering methods, where the distance between two clusters is determined by a single pair element that are closest to each other. We examined two outlier scenarios with a certain degree of contamination. The performance of proposed method on different outlier scenarios are compared and the best method for each outlier scenario is chosen.

The multiple outliers detection using agglomerative hierarchical methods in circular regression model

Two agglomerative hierarchical clustering algorithms for identifying multiple outliers in circular regression model have been developed in this study. The agglomerative hierarchical clustering algorithm starts with every single data in a single cluster and it continues to merge with the closest pair of clusters according to some similarity criterion until all the data are grouped in one cluster. The single-linkage method is one of the simplest agglomerative hierarchical methods that is commonly used to detect outlier. In this study, we compared the performance of single-linkage method with another agglomerative hierarchical method, namely average linkage for detecting outlier in circular regression model. The performances of both methods were examined via simulation studies by measuring their “success” probability, masking effect, and swamping effect with different number of sample sizes and level of contaminations. The results show that the single-linkage method performs very well in detecting the multiple outliers with lower masking and swamping effects.

Circular(2)-linear regression analysis with iteration order manipulation

The selection of statistical analysis techniques to be used must be adjusted to the data. Data in the form of time cycle or point position to the angle of possibility is no longer suitable to be analyzed using classical linear statistic method because the direction and the angle influence the position between one data with other data. This paper aims to examine the comparison of Linear Regression Analysis with Circular Regression Analysis. The writing method used is literature review using simulation data. Simulation of data and analysis is done with the help of R program. The results showed that circular data is better in Circular Regression Analysis than Classical Linear Regression Analysis, so the conclusion is Selection of statistical analysis techniques to be used must be adjusted with the data that already held. Data in the form of time cycles or position of the point to the angle of probability is no longer suitable to be analyzed using classical linear statistic method because the direction and the angle influence the position between one data with other data.

Robust Circular Distance and its Application in the Identification of Outliers in the Simple Circular Regression Model

Abstract: Background and Objective: The existence of outliers in any type of data influences the efficiency of an estimator. Few methods for detecting outliers in a simple circular regression model have been proposed in the study but it suspected that they are not very successful in the presence of multiple outliers in a data set. This study aimed to investigate new statistic to identify multiple outliers in the response variable in a simple circular regression model. Materials and Methods: The proposed statistic is based on calculating robust circular distance between circular residuals and circular location parameter. The performance of the proposed statistic is evaluated by the proportion of detected outliers and the rate of masking and swamping. The simulation study is applied for different sample sizes at 10 and 20% ratios of contamination. Results: The results from simulated data showed that the proposed statistic has the highest proportion of outliers and the lowest rate of masking comparing with some existing methods. Conclusion: The proposed statistic is very successful in detecting outliers with negligible amount of masking and swamping rates.