An adaptation of correspondence analysis for square tables

The application of correspondence analysis to square asymmetrictables is often unsuccessful because of the strong role played by thediagonal entries of the matrix, obscuring the data off the diagonal. A simplemodification of the centering of the matrix, coupled with the correspondingchange in row and column masses and row and column metrics, allows the tableto be decomposed into symmetric and skew--symmetric components, which canthen be analyzed separately. The symmetric and skew--symmetric analyses canbe performed using a simple correspondence analysis program if the data areset up in a special block format.

Correspondence analysis of raw data

Correspondence analysis has found extensive use in ecology, archeology, linguisticsand the social sciences as a method for visualizing the patterns of association in a table offrequencies or nonnegative ratio-scale data. Inherent to the method is the expression of the datain each row or each column relative to their respective totals, and it is these sets of relativevalues (called profiles) that are visualized. This relativization of the data makes perfect sensewhen the margins of the table represent samples from sub-populations of inherently differentsizes. But in some ecological applications sampling is performed on equal areas or equalvolumes so that the absolute levels of the observed occurrences may be of relevance, in whichcase relativization may not be required. In this paper we define the correspondence analysis ofthe raw unrelativized data and discuss its properties, comparing this new method to regularcorrespondence analysis and to a related variant of non-symmetric correspondence analysis.

Computation of multiple correspondence analysis, with code in R

The generalization of simple correspondence analysis, for two categorical variables, to multiple correspondence analysis where they may be three or more variables, is not straighforward, both from a mathematical and computational point of view. In this paper we detail the exact computational steps involved in performing a multiple correspondence analysis, including the special aspects of adjusting the principal inertias to correct the percentages of inertia, supplementary points and subset analysis. Furthermore, we give the algorithm for joint correspondence analysis where the cross-tabulations of all unique pairs of variables are analysed jointly. The code in the R language for every step of the computations is given, as well as the results of each computation.

Multiple correspondence analysis of a subset of response categories

In the analysis of multivariate categorical data, typically the analysis of questionnaire data, it is often advantageous, for substantive and technical reasons, to analyse a subset of response categories. In multiple correspondence analysis, where each category is coded as a column of an indicator matrix or row and column of Burt matrix, it is not correct to simply analyse the corresponding submatrix of data, since the whole geometric structure is different for the submatrix . A simple modification of the correspondence analysis algorithm allows the overall geometric structure of the complete data set to be retained while calculating the solution for the selected subset of points. This strategy is useful for analysing patterns of response amongst any subset of categories and relating these patterns to demographic factors, especially for studying patterns of particular responses such as missing and neutral responses. The methodology is illustrated using data from the International Social Survey Program on Family and Changing Gender Roles in 1994.

Forest fires: Evaluation of government intervention measures

The purpose of this paper is to examine the relation between government measures, volunteer participation, climate variables and forest fires. A number of studies have related forest fires to causes of ignition, to fire history in one area, to the type of vegetation and weathercharacteristics or to community institutions, but there is little research on the relation between fire production and government prevention and extinction measures from a policy evaluation perspective.An observational approach is first applied to select forest fires in the north east of Spain. Taking a selection of fires with a certain size, a multiple regression analysis is conducted to find significant relations between policy instruments under the control of the government and the number of hectares burn in each case, controlling at the same time the effect of weather conditions and other context variables. The paper brings evidence on the effects of simultaneity and the relevance of recurring to army soldiers in specific days with extraordinary high simultaneity. The analysis also brings light on the effectiveness of twopreventive policies and of helicopters for extinction tasks.

Measuring asymmetries in brand associations using correspondence analysis

Correspondence analysis is introduced in the brand associationliterature as an alternative tool to measure dominance, for theparticular case of free choice data. The method is also used to analysedifferences, or asymmetries, between brand-attribute associations whereattributes are associated with evoked brands, and brand-attributeassociations where brands are associated with the attributes. Anapplication to a sample of deodorants is used to illustrate the proposedmethodology.

From correspondence analysis to multiple and joint correspondence analysis

The generalization of simple (two-variable) correspondence analysis to more than two categorical variables, commonly referred to as multiple correspondence analysis, is neither obvious nor well-defined. We present two alternative ways of generalizing correspondence analysis, one based on the quantification of the variables and intercorrelation relationships, and the other based on the geometric ideas of simple correspondence analysis. We propose a version of multiple correspondence analysis, with adjusted principal inertias, as the method of choice for the geometric definition, since it contains simple correspondence analysis as an exact special case, which is not the situation of the standard generalizations. We also clarify the issue of supplementary point representation and the properties of joint correspondence analysis, a method that visualizes all two-way relationships between the variables. The methodology is illustrated using data on attitudes to science from the International Social Survey Program on Environment in 1993.

Correspondence analysis of two transition tables

The case of two transition tables is considered, that is two squareasymmetric matrices of frequencies where the rows and columns of thematrices are the same objects observed at three different timepoints. Different ways of visualizing the tables, either separatelyor jointly, are examined. We generalize an existing idea where asquare matrix is descomposed into symmetric and skew-symmetric partsto two matrices, leading to a decomposition into four components: (1)average symmetric, (2) average skew-symmetric, (3) symmetricdifference from average, and (4) skew-symmetric difference fromaverage. The method is illustrated with an artificial example and anexample using real data from a study of changing values over threegenerations.

A note on the dual scaling of dominance data and its relationship to correspondence analysis

Dual scaling of a subjects-by-objects table of dominance data (preferences,paired comparisons and successive categories data) has been contrasted with correspondence analysis, as if the two techniques were somehow different. In this note we show that dual scaling of dominance data is equivalent to the correspondence analysis of a table which is doubled with respect to subjects. We also show that the results of both methods can be recovered from a principal components analysis of the undoubled dominance table which is centred with respect to subject means.

Perceptual mapping of practical ethics along the value chain: A multiple correspondence analysis with industry and cultural indices as supplementary variables

This paper presents findings from a study investigating a firm s ethical practices along the value chain. In so doing we attempt to better understand potential relationships between a firm s ethical stance with its customers and those of its suppliers within a supply chain and identify particular sectoral and cultural influences that might impinge on this. Drawing upon a database comprising of 667 industrial firms from 27 different countries, we found that ethical practices begin with the firm s relationship with its customers, the characteristics of which then influence the ethical stance with the firm s suppliers within the supply chain. Importantly, market structure along with some key cultural characteristics were also found to exert significant influence on the implementation of ethical policies in these firms.

Tying up the loose ends in simple correspondence analysis

Although correspondence analysis is now widely available in statistical software packages and applied in a variety of contexts, notably the social and environmental sciences, there are still some misconceptions about this method as well as unresolved issues which remain controversial to this day. In this paper we hope to settle these matters, namely (i) the way CA measures variance in a two-way table and how to compare variances between tables of different sizes, (ii) the influence, or rather lack of influence, of outliers in the usual CA maps, (iii) the scaling issue and the biplot interpretation of maps,(iv) whether or not to rotate a solution, and (v) statistical significance of results.

Subset correspondence analysis: Visualizing relationships among a selected set of response categories from a questionnaire survey

It is shown how correspondence analysis may be applied to a subset of response categories from a questionnaire survey, for example the subset of undecided responses or the subset of responses for a particular category. The idea is to maintain the original relative frequencies of the categories and not re-express them relative to totals within the subset, as would normally be done in a regular correspondence analysis of the subset. Furthermore, the masses and chi-square metric assigned to the data subset are the same as those in the correspondence analysis of the whole data set. This variant of the method, called Subset Correspondence Analysis, is illustrated on data from the ISSP survey on Family and Changing Gender Roles.

Correspondence analysis and categorical conjoint measurement

We show the equivalence between the use of correspondence analysis (CA)of concadenated tables and the application of a particular version ofconjoint analysis called categorical conjoint measurement (CCM). Theconnection is established using canonical correlation (CC). The second part introduces the interaction e¤ects in all three variants of theanalysis and shows how to pass between the results of each analysis.

Community pharmacist intervention in depressed primary care patients (PRODEFAR study): randomized controlled trial protocol.

Background: Treatment of depression, the most prevalent and costly mental disorder, needs to be improved. Non-concordance with clinical guidelines and non-adherence can limit the efficacy of pharmacological treatment of depression. Through pharmaceutical care, pharmacists can improve patients' compliance and wellbeing. The aim of this study is to evaluate the effectiveness and costeffectiveness of a community pharmacist intervention developed to improve adherence and outcomes of primary care patients with depression. Methods/design: A randomized controlled trial, with 6-month follow-up, comparing patients receiving a pharmaceutical care support programme in primary care with patients receiving usual care. The total sample comprises 194 patients (aged between 18 and 75) diagnosed with depressive disorder in a primary care health centre in the province of Barcelona (Spain). Subjects will be asked for written informed consent in order to participate in the study. Diagnosis will be confirmed using the SCID-I. The intervention consists of an educational programme focused on improving knowledge about medication, making patients aware of the importance of compliance, reducing stigma, reassuring patients about side-effects and stressing the importance of carrying out general practitioners' advice. Measurements will take place at baseline, and after 3 and 6 months. Main outcome measure is compliance with antidepressants. Secondary outcomes include; clinical severity of depression (PHQ-9), anxiety (STAI-S), health-related quality of life (EuroQol-5D), satisfaction with the treatment received, side-effects, chronic physical conditions and sociodemographics. The use of healthcare and social care services will be assessed with an adapted version of the Client Service Receipt Inventory (CSRI). Discussion: This trial will provide valuable information for health professionals and policy makers on the effectiveness and cost-effectiveness of a pharmaceutical intervention programme in the context of primary care. Trial registration: NCT00794196