Michel van de Velden

Rotation in correspondence analysis

AbstractIn correspondence analysis rows and columns of a nonnegative data matrix are depicted as points in a, usually, two-dimensional plot. Although such a two-dimensional plot often provides a reasonable approximation, the situation can occur that an approximation of higher dimensionality is required. This is especially the case when the data matrix is large. In such instances it may become difficult to interpret the solution. Similar to what is done in principal component analysis and factor analysis the correspondence analysis solution can be rotated to increase the interpretability. However, due to the various scaling options encountered in correspondence analysis, there are several alternative options for rotating the solutions. In this paper we consider two options for rotation in correspondence analysis. An example is provided so that the benefits of rotation become apparent.

Visualization of Differences in Treatment of Safety Inspections across Port State Control Regimes: A Case for Increased Harmonization Efforts

Abstract The topic of harmonizing port state control (PSC) inspections has been on the agenda of the flag state sub‐committee meeting at the International Maritime Organization in recent years. This article is based on a unique combined dataset of 183 819 PSC inspections and uses correspondence analysis to visualize differences in treatment of vessels across several PSC regimes, representing more than 50 individual port states in order to provide better insight into the areas of possible harmonization. The results show that treatment of vessels across the regimes varies, indicating room for harmonization in all inspection areas. We recommend accelerating the harmonization process by putting more emphasis on the harmonization of inspection procedures, combined training of PSC officers and the use of combined datasets across regimes, in particular in the concept of the development of the Global Integrated Ship Information System of the International Maritime Organization.

Generalized canonical correlation analysis of matrices with missing rows: a simulation study

A method is presented for generalized canonical correlation analysis of two or more matrices with missing rows. The method is a combination of Carroll’s (1968) method and the missing data approach of the OVERALS technique (Van der Burg, 1988). In a simulation study we assess the performance of the method and compare it to an existing procedure called GENCOM, proposed by Green and Carroll (1988). We find that the proposed method outperforms the GENCOM algorithm both with respect to model fit and recovery of the true structure.

Oblique rotation in correspondence analysis: A step forward in the search for the simplest interpretation

Correspondence analysis (CA) is a popular method that can be used to analyse relationships between categorical variables. It is closely related to several popular multivariate analysis methods such as canonical correlation analysis and principal component analysis. Like principal component analysis, CA solutions can be rotated orthogonally as well as obliquely into a simple structure without affecting the total amount of explained inertia. However, some specific aspects of CA prevent standard rotation procedures from being applied in a straightforward fashion. In particular, the role played by weights assigned to points and dimensions and the duality of CA solutions are unique to CA. For orthogonal simple structure rotation, procedures recently have been proposed. In this paper, we construct oblique rotation methods for CA that take into account these specific difficulties. We illustrate the benefits of our oblique rotation procedure by means of two illustrative examples.

Seriation by constrained correspondence analysis: A simulation study

One of the many areas in which correspondence analysis (CA) is an effective method, concerns seriation problems. For example, CA is a well-known technique for the seriation of archaeological assemblages. A problem with the CA seriation solution, however, is that only a relative ordering of the assemblages is obtained. To improve the usual CA solution, a constrained CA approach that incorporates additional information in the form of equality and inequality constraints concerning the time points of the assemblages may be considered. Using such constraints, explicit dates can be assigned to the seriation solution. The set of constraints that can be used in CA by introducing interval constraints is extended. That is, constraints that put the CA solution within a specific time frame. Moreover, the quality of the constrained CA solution is studied in a simulation study. In particular, by means of the simulation study we are able to assess how well ordinary, and constrained CA can recover the true time order. Furthermore, for the constrained approach, it is shown that the true dates are retrieved satisfactory. The simulation study is set up in such a way that it mimics the data of a series of ceramic assemblages consisting of the locally produced tableware from Sagalassos (SW Turkey). It is found that the dating of the assemblages on the basis of constraints appears to work quite well.

Optimal Scaling of Paired Comparison Data

In this paper we consider the analysis of paired comparisons using optimal scaling techniques. In particular, we will, inspired by Guttmans approach for quantifying paired comparisons, formulate a new method to obtain optimal scaling values for the subjects. We will compare our results with those obtained using dual scaling and correspondence analysis. This comparison yields interesting new insights into properties of these methods when applied to paired comparison data. In particular, we will show that the optimal scaling values for the subjects are equivalent to the correspondence analysis coordinates for the subjects.

An application of rotation in correspondence analysis

In correspondence analysis rows and columns of a nonnegative data matrix are depicted as points in a, usually, two dimensional plot. It is well known that the correspondence analysis solution is closely related to a biplot. In this paper we will use this close relationship to introduce simple structure rotation in correspondence analysis. By means of an application to cross-citation data we will show that, similar to the situation in principal component and factor analysis, rotation can be an important tool in improving the interpretability of the original correspondence analysis solution.

Psychological positioning of bottled tea products: A comparison between two Kansei profiling techniques

Appropriate psychological positioning of products is important for marketing of foods and beverages. For better product positioning, understanding of how products’ extrinsic and intrinsic properties are perceived by consumers is required. In this study, it was explored a refined one-to-one interview technique, check-all-that-apply (CATA) linked with a repertory grid method (RGM) (CATA/RGM) designed to measure consumer-relevant Kansei — psychological feelings and impressions for products — as applied to 12 commercial bottled tea products. For statistical analyses, 2 multivariate statistical methods for Kansei profiling were compared: CATA/RGM based-structured free choice profiling (FCP) and cued elicitation. Results showed that the CATA/RGM efficiently differentiated between products, and the product differentiation obtained from the 2 Kansei profiling techniques corresponded. These results indicated that the consumers in this study have similar Kansei towards bottled teas, and the cued elicitation method, which employed correspondence analysis (CA), was useful for studying the interactions between consumer-relevant Kansei and product properties for a specific target group of consumers.

Constrained Dual Scaling for Detecting Response Styles in Categorical Data

Dual scaling (DS) is a multivariate exploratory method equivalent to correspondence analysis when analysing contingency tables. However, for the analysis of rating data, different proposals appear in the DS and correspondence analysis literature. It is shown here that a peculiarity of the DS method can be exploited to detect differences in response styles. Response styles occur when respondents use rating scales differently for reasons not related to the questions, often biasing results. A spline-based constrained version of DS is devised which can detect the presence of four prominent types of response styles, and is extended to allow for multiple response styles. An alternating nonnegative least squares algorithm is devised for estimating the parameters. The new method is appraised both by simulation studies and an empirical application.

On joint dimension reduction and clustering of categorical data

There exist several methods for clustering high-dimensional data. One popular approach is to use a two-step procedure. In the first step, a dimension reduction technique is used to reduce the dimensionality of the data. In the second step, cluster analysis is applied to the data in the reduced space. This method may be referred to as the tandem approach. An important drawback of this method is that the dimension reduction may distort or hide the cluster structure. As an alternative, various authors have proposed joint dimension reduction and clustering approaches. In this paper we review some of these existing joint dimension reduction and clustering methods for categorical data in a unified framework that facilitates comparison.