Detecting response styles by using dual scaling of successive categories

A response style denotes a certain mapping of latent preferences toa rating scale that is common among a certain group of individuals.For example, individuals from the same country may assign highratings to the majority of objects regardless of the specificpreferences for the objects. The existence of response styles causesproblems in international and cross-cultural research as it makes ithard to compare findings. Moreover, even within homogeneous samples,response styles make it difficult to expose the underlyingpreference structure. Detecting the existence and influence of aresponse style is typically a difficult issue as the underlyingpreferences are not directly observable. Hence, we can never be sureif the observed ratings are the result of a response style or anadequate representation of the preferences. In this paper, weconsider the use of dual scaling as a tool to detect the existenceof a response style. By means of a simulation study, we assess theperformance of the proposed method.

Generalized canonical correlation analysis with missing values

Two new methods for dealing with missing values in generalized canonicalcorrelation analysis are introduced. The first approach, which does notrequire iterations, is a generalization of the Test Equating method availablefor principal component analysis. In the second approach, missing values areimputed in such a way that the generalized canonical correlation analysisobjective function does not increase in subsequent steps. Convergence isachieved when the value of the objective function remains constant. By meansof a simulation study, we assess the performance of the new methods. Wecompare the results with those of two available methods; the missing-datapassive method, introduced Gifi's homogeneity analysis framework, and theGENCOM algorithm developed by Green and Carroll.generalized canoncial correlation analysis;missing values

Multidimensional scaling

Multidimensional scaling is a statistical technique to visualize dissimilarity data. In multidimensional scaling, objects are represented as points in a usually two dimensional space, such that the distances between the points match the observed dissimilarities as closely as possible. Here, we discuss what kind of data can be used for multidimensional scaling, what the essence of the technique is, how to choose the dimensionality, transformations of the dissimilarities, and some pitfalls to watch out for when using multidimensional scaling.

Seriation by constrained correspondence analysis: a simulation study

One of the many areas in which Correspondence Analysis (CA) is an effectivemethod, concerns ordination problems. For example, CA is a well-knowntechnique for the seriation of archaeological assemblages. A problem withthe CA seriation solution, however, is that only a relative ordering of theassemblages is obtained. To improve the usual CA solution, a constrained CAapproach that incorporates additional information in the form of equalityand inequality constraints concerning the time points of the assemblages maybe considered. Using such constraints, explicit dates can be assigned to theseriation solution. In this paper, we extend the set of constraints that canbe used in CA by introducing interval constraints. That is, constraints thatput the CA\\ solution within a specific time-frame. Moreover, we study thequality of the constrained CA solution in a simulation study. In particular,by means of the simulation study we are able to assess how well ordinary andconstrained CA can recover the true time order. Furthermore, for theconstrained approach, we see how well the true dates are retrieved. Thesimulation study is set up in such a way that it mimics the data of a seriesof ceramic assemblages consisting of the locally produced tableware fromSagalassos (SW Turkey). We find that the dating of the assemblages on thebasis of constraints appears to work quite well.

Area Biplots

Classical multivariate analysis techniques such as principal components analysis and correspondence analysis use inner products to estimate data values. The results of these techniques may be visualized by representing the row and column points jointly in a biplot where the projection of a row point onto a column point vector followed by a multiplication by the length of the column point vector gives the inner-product that estimates the corresponding data element. In this paper, we propose a newvisualization: after a 90 degrees rotation of the row points, the areas spanned by a triangle of a row point, a column point and the origin estimate the data values. In contrast to the projection biplot, the areas spanned by different row and column points can be compared directly. Areas can only be produced for two dimensions at a time, but higher dimensional solutions can be represented by summing areas over subsequent pairs of dimensions. Here, the area biplot is developed for principal components analysis, correspondence analysis, and for interaction biplots but has general applicability.interaction;correspondence analysis;visualization;principal component analysis;biplot

Detecting response styles by using dual scaling of successive categories

A response style denotes a certain mapping of latent preferences to a rating scale that is common among a certain group of individuals. For example, individuals from the same country may assign high ratings to the majority of objects regardless of the specific preferences for the objects. The existence of response styles causes problems in international and cross-cultural research as it makes it hard to compare findings. Moreover, even within homogeneous samples, response styles make it difficult to expose the underlying preference structure. Detecting the existence and influence of a response style is typically a difficult issue as the underlying preferences are not directly observable. Hence, we can never be sure if the observed ratings are the result of a response style or an adequate representation of the preferences. In this paper, we consider the use of dual scaling as a tool to detect the existence of a response style. By means of a simulation study, we assess the performance of the proposed method

Inverse correspondence analysis

AbstractIn correspondence analysis (CA), rows and columns of a data matrix are depicted as points in low-dimensional space. The row and column profiles are approximated by minimizing the so-called weighted chi-squared distance between the original profiles and their approximations, see for example, [Theory and applications of correspondence analysis, Academic Press, New York, 1984]. In this paper, we will study the inverse CA problem, that is, the possibilities for retrieving one or more data matrices from a low-dimensional CA solution. We will show that there exists a nonempty closed and bounded polyhedron of such matrices. We also present two algorithms to find the vertices of the polyhedron: an exact algorithm that finds all vertices and a heuristic approach for larger sized problems that will find some of the vertices. A proof that the maximum of the Pearson chi-squared statistic is attained at one of the vertices is given. In addition, it is discussed how extra equality constraints on some elements of the data matrix can be imposed on the inverse CA problem. As a special case, we present a method for imposing integer restrictions on the data matrix as well. The approach to inverse CA followed here is similar to the one employed by De Leeuw and Groenen [J. Classification 14 (1997) 3] in their inverse multidimensional scaling problem

Generalized canonical correlation analysis with missing values

Generalized canonical correlation analysis is a versatile technique that allows the joint analysis of several sets of data matrices. The generalized canonical correlation analysis solution can be obtained through an eigenequation and distributional assumptions are not required. When dealing with multiple set data, the situation frequently occurs that some values are missing. In this paper, two new methods for dealing with missing values in generalized canonical correlation analysis are introduced. The first approach, which does not require iterations, is a generalization of the Test Equating method available for principal component analysis. In the second approach, missing values are imputed in such a way that the generalized canonical correlation analysis objective function does not increase in subsequent steps. Convergence is achieved when the value of the objective function remains constant. By means of a simulation study, we assess the performance of the new methods. We compare the results with those of two available methods; the missing-data passive method, introduced in Gifi's homogeneity analysis framework, and the GENCOM algorithm developed by Green and Carroll. An application using world bank data is used to illustrate the proposed methods

Generalized canonical correlation analysis with missing values

Two new methods for dealing with missing values in generalized canonical correlation analysis are introduced. The first approach, which does not require iterations, is a generalization of the Test Equating method available for principal component analysis. In the second approach, missing values are imputed in such a way that the generalized canonical correlation analysis objective function does not increase in subsequent steps. Convergence is achieved when the value of the objective function remains constant. By means of a simulation study, we assess the performance of the new methods. We compare the results with those of two available methods; the missing-data passive method, introduced Gifi's homogeneity analysis framework, and the GENCOM algorithm developed by Green and Carroll

Multidimensional scaling

Multidimensional scaling is a statistical technique to visualize dissimilarity data. In multidimensional scaling, objects are represented as points in a usually two dimensional space, such that the distances between the points match the observed dissimilarities as closely as possible. Here, we discuss what kind of data can be used for multidimensional scaling, what the essence of the technique is, how to choose the dimensionality, transformations of the dissimilarities, and some pitfalls to watch out for when using multidimensional scaling