Biplots of fuzzy coded data

A biplot, which is the multivariate generalization of the two-variable scatterplot, can be used to visualize the results of many multivariate techniques, especially those that are based on the singular value decomposition. We consider data sets consisting of continuous-scale measurements, their fuzzy coding and the biplots that visualize them, using a fuzzy version of multiple correspondence analysis. Of special interest is the way quality of fit of the biplot is measured, since it is well-known that regular (i.e., crisp) multiple correspondence analysis seriously under-estimates this measure. We show how the results of fuzzy multiple correspondence analysis can be defuzzified to obtain estimated values of the original data, and prove that this implies an orthogonal decomposition of variance. This permits a measure of fit to be calculated in the familiar form of a percentage of explained variance, which is directly comparable to the corresponding fit measure used in principal component analysis of the original data. The approach is motivated initially by its application to a simulated data set, showing how the fuzzy approach can lead to diagnosing nonlinear relationships, and finally it is applied to a real set of meteorological data.defuzzification, fuzzy coding, indicator matrix, measure of fit, multivariate data, multiple correspondence analysis, principal component analysis.

Learning by doing as a human capital factor: Case of Eskisehir furniture manufacturing sector

This study seeks to determine the impacts of learning by doing, human capital and R&D factors on firm’s output by using simultaneous equations system. In this study, medium and large-sized companies from furniture manufacturing sector in Eskisehir, Turkey are selected as the research domain and a database is generated based on the information collected through face-to-face interviews with company executives (or with officials designated by them), the financial statements of researched companies, and the records of Eskisehir Chamber of Industry. According to the estimation results obtained, the human capital stock, learning by practice phenomenon and the research and development expenditures have a linear impact on the company's total output. It is understood that, fixed capital stock and size of company become prominent in terms of their impact on the human capital, and the mentioned variables demonstrate a positive relation with the output. Likewise, the linear relationship between learning by practice and company size as well as wage level; and between research & development expenditures and company size are the factors that come forth in the explanation of the dependent variables

Biplots of fuzzy coded data

A biplot, which is the multivariate generalization of the two-variable scatterplot, can be used to visualize the results of many multivariate techniques, especially those that are based on the singular value decomposition. We consider data sets consisting of continuous-scale measurements, their fuzzy coding and the biplots that visualize them, using a fuzzy version of multiple correspondence analysis. Of special interest is the way quality of fit of the biplot is measured, since it is well-known that regular (i.e., crisp) multiple correspondence analysis seriously under-estimates this measure. We show how the results of fuzzy multiple correspondence analysis can be defuzzified to obtain estimated values of the original data, and prove that this implies an orthogonal decomposition of variance. This permits a measure of fit to be calculated in the familiar form of a percentage of explained variance, which is directly comparable to the corresponding fit measure used in principal component analysis of the original data. The approach is motivated initially by its application to a simulated data set, showing how the fuzzy approach can lead to diagnosing nonlinear relationships, and finally it is applied to a real set of meteorological data

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A biplot, which is the multivariate generalization of the two-variable scatterplot, can be used to visualize the results of many multivariate techniques, especially those that are based on the singular value decomposition. We consider data sets consisting of continuous-scale measurements, their fuzzy coding and the biplots that visualize them, using a fuzzy version of multiple correspondence analysis. Of special interest is the way quality of fit of the biplot is measured, since it is well-known that regular (i.e., crisp) multiple correspondence analysis seriously under-estimates this measure. We show how the results of fuzzy multiple correspondence analysis can be defuzzified to obtain estimated values of the original data, and prove that this implies an orthogonal decomposition of variance. This permits a measure of fit to be calculated in the familiar form of a percentage of explained variance, which is directly comparable to the corresponding fit measure used in principal component analysis of the original data. The approach is motivated initially by its application to a simulated data set, showing how the fuzzy approach can lead to diagnosing nonlinear relationships, and finally it is applied to a real set of meteorological data

Sampling frame coverage and domain adjustment procedures for internet surveys

The objective of this paper is to define and compare alternative sampling frames for the representative population coverage as a basis for sample selection in internet surveys. The study aims to provide a methodology for domain weighting and adjustment procedures for free access web surveys that are based on the restricted access surveys. Some basic variables can be proposed for the data adjustment, namely gender breakdown, age groups, and education groups. The application of our work consists of a first stage based on a web survey by an e-mail invitation (restricted access) and a second stage based on a voluntary participation web survey (free access). An advertising company's registered customer list was taken as the sampling frame population for the first stage. This frame was an electronic e-mail list of the population of registered customers. Two different types of questionnaire were loaded on the company's internet web site for a month each, for two independent rounds, for testing the visual aspects of the questionnaire design. The restricted access internet survey design relies on probability selection procedures in this study. These results are used with the provided algorithms for the adjustment procedures of free access web surveys. A new methodology is also proposed for the estimation and allocation of the population frame characteristics of adult internet users by gender and age groups. The proposed alternative methodologies will be beneficial tools for future web survey users