Abstract
Since late thirties, factorial analysis of a response measured on the real line has been well established and documented in the literature. No such analysis, however, is available for a response measured on the circle (or sphere in general), despite the fact that many designed experiments in industry, medicine, psychology and biology could result in an angular response. In this paper a full factorial analysis is presented for a circular response using the Spherical Projected Multivariate Linear model. Main and interaction effects are defined, estimated and tested. Analogy to the linear response case, two new effect plots: Circular-Main Effect and Circular Interaction Effect plots are proposed to visualize main and interaction effects on circular responses.
Highlights
Factorial designs are widely used in experiments involving several factors where it is necessary to investigate the joint effects of the factors on a response variable
The analysis of factorial designs is well established for a response variable that is measured on the real line
Spherically Projected Multivariate Linear (SPML) solved the dilemma of not having a suitable model to complete a factorial analysis for factorial data with a response measured on the circle
Summary
Factorial designs are widely used in experiments involving several factors where it is necessary to investigate the joint effects of the factors on a response variable. Anderson and Wu (1995) proposed a likelihood ratio test statistic for testing the effects from a factorial design on the location of a circular response They used the angular rotations occurring when moving from one level of one factor to its other level at fixed level of the other factor to evaluate the two-factor interaction effect on the location. In the context of regression analysis of circular response on real-line valued independent variables, remarkable link functions were offered to map the real line onto the unit circle (see Gould, 1969, Johnson and Wehrly, 1978, and Fisher and Lee, 1992) All of these models suffer from computational difficulties because of either the existing of a multimodal likelihood or an irregular likelihood where the maximum might occur on a very narrow peak [Presnell et al, 1998]. The following section gives the notations of circular data and briefly reviews the SPML model
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
