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19 Introduccin a los procedimientos de escalamiento ptimo de datos categricos de SPSS
Lecturas recomendadas
Si desea obtener informacin general sobre las tcnicas de escalamiento ptimo consulte los siguientes textos: Barlow, R. E., D. J. Bartholomew, D. J. Bremner, y H. D. Brunk. 1972. Statistical inference under order restrictions. Nueva York: John Wiley and Sons. Benzcri, J. P. 1969. Statistical analysis as a tool to make patterns emerge from data. En: Methodologies of Pattern Recognition, S. Watanabe, ed. Nueva York: Academic Press, 3574. Bishop, Y. M., S. E. Feinberg, y P. W. Holland. 1975. Discrete multivariate analysis. Cambridge (Mass.): MIT Press. De Leeuw, J. 1984. The Gifi system of nonlinear multivariate analysis. En: Data Analysis and Informatics III, E. Diday, et al., ed., 415424. De Leeuw, J. 1990. Multivariate analysis with optimal scaling. En: Progress in Multivariate Analysis, S. Das Gupta, y J. Sethuraman, Editores. Calcuta: Indian Statistical Institute. De Leeuw, J., y J. Van Rijckevorsel. 1980. HOMALS and PRINCALSSome generalizations of principal components analysis. En: Data Analysis and Informatics, E. Diday, et al., ed. msterdam: North-Holland, 231242. De Leeuw, J., F. W. Young, y Y. Takane. 1976. Additive structure in qualitative data: An alternating least squares method with optimal scaling features. Psychometrika, 41, 471503. Gifi, A. 1990. Nonlinear multivariate analysis. Chichester: John Wiley and Sons. Heiser, W. J., y J. J. Meulman. 1995. Nonlinear methods for the analysis of homogeneity and heterogeneity. En: Recent Advances in Descriptive Multivariate Analysis, W. J. Krzanowski, ed. Oxford: Oxford University Press, 5189. Israels, A. 1987. Eigenvalue techniques for qualitative data. Leiden: DSWO Press. Krzanowski, W. J., y F. H. C. Marriott. 1994. Multivariate analysis: Part I, distributions, ordination and inference. Londres: Edward Arnold. Lebart, L., A. Morineau, y K. M. Warwick. 1984. Multivariate descriptive statistical analysis. Nueva York: John Wiley and Sons.
20 Captulo 1
Max, J. 1960. Quantizing for minimum distortion. Proceedings IEEE (Information Theory), 6, 712. Meulman, J. J. 1986. A distance approach to nonlinear multivariate analysis. Leiden: DSWO Press. Meulman, J. J. 1992. The integration of multidimensional scaling and multivariate analysis with optimal transformations of the variables. Psychometrika, 57, 539565. Nishisato, S. 1980. Analysis of categorical data: Dual scaling and its applications. Toronto: University of Toronto Press. Nishisato, S. 1994. Elements of dual scaling: An introduction to practical data analysis. Hillsdale (N.J.): Lawrence Erlbaum Associates, Inc. Rao, C. R. 1973. Linear statistical inference and its applications, 2nd ed. Nueva York: John Wiley and Sons. Rao, C. R. 1980. Matrix approximations and reduction of dimensionality in multivariate statistical analysis. En: Multivariate Analysis, Vol. 5, P. R. Krishnaiah, ed. msterdam: North-Holland, 322. Roskam, E. E. 1968. Metric analysis of ordinal data in psychology. Voorschoten: VAM. Shepard, R. N. 1966. Metric structures in ordinal data. Journal of Mathematical Psychology, 3, 287315. Wolter, K. M. 1985. Introduction to variance estimation. Berln: Springer-Verlag. Young, F. W. 1981. Quantitative analysis of qualitative data. Psychometrika, 46, 357387.
406 Bibliografa
De Leeuw, J. 1984. Canonical analysis of categorical data, 2nd ed. Leiden: DSWO Press. De Leeuw, J. 1984. The Gifi system of nonlinear multivariate analysis. En: Data Analysis and Informatics III, E. Diday, et al., ed., 415424. De Leeuw, J. 1990. Multivariate analysis with optimal scaling. En: Progress in Multivariate Analysis, S. Das Gupta, y J. Sethuraman, Editores. Calcuta: Indian Statistical Institute. De Leeuw, J., y W. J. Heiser. 1980. Multidimensional scaling with restrictions on the configuration. En: Multivariate Analysis, Vol. V, P. R. Krishnaiah, ed. msterdam: North-Holland, 501522. De Leeuw, J., y J. Van Rijckevorsel. 1980. HOMALS and PRINCALSSome generalizations of principal components analysis. En: Data Analysis and Informatics, E. Diday, et al., ed. msterdam: North-Holland, 231242. De Leeuw, J., F. W. Young, y Y. Takane. 1976. Additive structure in qualitative data: An alternating least squares method with optimal scaling features. Psychometrika, 41, 471503. Eckart, C., y G. Young. 1936. The approximation of one matrix by another one of lower rank. Psychometrika, 1, 211218. Fisher, R. A. 1938. Statistical methods for research workers. Edinburgh: Oliver and Boyd. Fisher, R. A. 1940. The precision of discriminant functions. Annals of Eugenics, 10, 422429. Gabriel, K. R. 1971. The biplot graphic display of matrices with application to principal components analysis. Biometrika, 58, 453467. Gifi, A. 1985. PRINCALS. Research Report UG-85-02. Leiden: Department of Data Theory, University of Leiden. Gifi, A. 1990. Nonlinear multivariate analysis. Chichester: John Wiley and Sons. Gilula, Z., y S. J. Haberman. 1988. The analysis of multivariate contingency tables by restricted canonical and restricted association models. Journal of the American Statistical Association, 83, 760771. Gower, J. C., y J. J. Meulman. 1993. The treatment of categorical information in physical anthropology. International Journal of Anthropology, 8, 4351. Green, P. E., y V. Rao. 1972. Applied multidimensional scaling. Hinsdale, Ill.: Dryden Press.
407 Bibliografa
Green, P. E., y Y. Wind. 1973. Multiattribute decisions in marketing: A measurement approach. Hinsdale, Ill.: Dryden Press. Greenacre, M. J. 1984. Theory and applications of correspondence analysis. Londres: Academic Press. Guttman, L. 1941. The quantification of a class of attributes: A theory and method of scale construction. En: The Prediction of Personal Adjustment, P. Horst, ed. Nueva York: Social Science Research Council, 319348. Guttman, L. 1968. A general nonmetric technique for finding the smallest coordinate space for configurations of points. Psychometrika, 33, 469506. Hartigan, J. A. 1975. Clustering algorithms. Nueva York: John Wiley and Sons. Hastie, T., y R. Tibshirani. 1990. Generalized additive models. Londres: Chapman and Hall. Hastie, T., R. Tibshirani, y A. Buja. 1994. Flexible discriminant analysis. Journal of the American Statistical Association, 89, 12551270. Hayashi, C. 1952. On the prediction of phenomena from qualitative data and the quantification of qualitative data from the mathematico-statistical point of view. Annals of the Institute of Statitical Mathematics, 2, 9396. Heiser, W. J. 1981. Unfolding analysis of proximity data. Leiden: Department of Data Theory, University of Leiden. Heiser, W. J., y F. M. T. A. Busing. 2004. Multidimensional scaling and unfolding of symmetric and asymmetric proximity relations. En: Handbook of Quantitative Methodology for the Social Sciences, D. Kaplan, ed. Thousand Oaks (Calif.): Sage Publications, Inc, 2548. Heiser, W. J., y J. J. Meulman. 1994. Homogeneity analysis: Exploring the distribution of variables and their nonlinear relationships. En: Correspondence Analysis in the Social Sciences: Recent Developments and Applications, M. Greenacre, y J. Blasius, Editores. Nueva York: Academic Press, 179209. Heiser, W. J., y J. J. Meulman. 1995. Nonlinear methods for the analysis of homogeneity and heterogeneity. En: Recent Advances in Descriptive Multivariate Analysis, W. J. Krzanowski, ed. Oxford: Oxford University Press, 5189. Horst, P. 1961. Generalized canonical correlations and their applications to experimental data. Journal of Clinical Psychology, 17, 331347. Horst, P. 1961. Relations among m sets of measures. Psychometrika, 26, 129149. Israels, A. 1987. Eigenvalue techniques for qualitative data. Leiden: DSWO Press.
408 Bibliografa
Kennedy, R., C. Riquier, y B. Sharp. 1996. Practical applications of correspondence analysis to categorical data in market research. Journal of Targeting, Measurement, and Analysis for Marketing, 5, 5670. Kettenring, J. R. 1971. Canonical analysis of several sets of variables. Biometrika, 58, 433460. Kruskal, J. B. 1964. Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis. Psychometrika, 29, 128. Kruskal, J. B. 1964. Nonmetric multidimensional scaling: A numerical method. Psychometrika, 29, 115129. Kruskal, J. B. 1965. Analysis of factorial experiments by estimating monotone transformations of the data. Journal of the Royal Statistical Society Series B, 27, 251263. Kruskal, J. B. 1978. Factor analysis and principal components analysis: Bilinear methods. En: International Encyclopedia of Statistics, W. H. Kruskal, y J. M. Tanur, Editores. Nueva York: The Free Press, 307330. Kruskal, J. B., y R. N. Shepard. 1974. A nonmetric variety of linear factor analysis. Psychometrika, 39, 123157. Krzanowski, W. J., y F. H. C. Marriott. 1994. Multivariate analysis: Part I, distributions, ordination and inference. Londres: Edward Arnold. Lebart, L., A. Morineau, y K. M. Warwick. 1984. Multivariate descriptive statistical analysis. Nueva York: John Wiley and Sons. Lingoes, J. C. 1968. The multivariate analysis of qualitative data. Multivariate Behavioral Research, 3, 6194. Max, J. 1960. Quantizing for minimum distortion. Proceedings IEEE (Information Theory), 6, 712. Meulman, J. J., A. J. Van der Kooij, y A. Babinec. 2000. New features of categorical principal components analysis for complicated data sets, including data mining. En: Classification, Automation and New Media, W. Gaul, y G. Ritter, Editores. Berln: Springer-Verlag, 207217. Meulman, J. J., A. J. Van der Kooij, y W. J. Heiser. 2004. Principal components analysis with nonlinear optimal scaling transformations for ordinal and nominal data. En: Handbook of Quantitative Methodology for the Social Sciences, D. Kaplan, ed. Thousand Oaks (Calif.): Sage Publications, Inc, 4970. Meulman, J. J. 1982. Homogeneity analysis of incomplete data. Leiden: DSWO Press.
409 Bibliografa
Meulman, J. J. 1986. A distance approach to nonlinear multivariate analysis. Leiden: DSWO Press. Meulman, J. J. 1992. The integration of multidimensional scaling and multivariate analysis with optimal transformations of the variables. Psychometrika, 57, 539565. Meulman, J. J. 1993. Principal coordinates analysis with optimal transformations of the variables: Minimizing the sum of squares of the smallest eigenvalues. British Journal of Mathematical and Statistical Psychology, 46, 287300. Meulman, J. J. 1996. Fitting a distance model to homogeneous subsets of variables: Points of view analysis of categorical data. Journal of Classification, 13, 249266. Meulman, J. J. 2003. Prediction and classification in nonlinear data analysis: Something old, something new, something borrowed, something blue. Psychometrika, 4, 493517. Meulman, J. J., y W. J. Heiser. 1997. Graphical display of interaction in multiway contingency tables by use of homogeneity analysis. En: Visual Display of Categorical Data, M. Greenacre, y J. Blasius, Editores. Nueva York: Academic Press, 277296. Meulman, J. J., y P. Verboon. 1993. Points of view analysis revisited: Fitting multidimensional structures to optimal distance components with cluster restrictions on the variables. Psychometrika, 58, 735. Nishisato, S. 1980. Analysis of categorical data: Dual scaling and its applications. Toronto: University of Toronto Press. Nishisato, S. 1984. Forced classification: A simple application of a quantification method. Psychometrika, 49, 2536. Nishisato, S. 1994. Elements of dual scaling: An introduction to practical data analysis. Hillsdale (N.J.): Lawrence Erlbaum Associates, Inc. Pratt, J. W. 1987. Dividing the indivisible: Using simple symmetry to partition variance explained. En: Proceedings of the Second International Conference in Statistics, T. Pukkila, y S. Puntanen, Editores. Tampere (Finlandia): Universidad de Tampere, 245260. Price, R. H., y D. L. Bouffard. 1974. Behavioral appropriateness and situational constraints as dimensions of social behavior. Journal of Personality and Social Psychology, 30, 579586. Ramsay, J. O. 1989. Monotone regression splines in action. Statistical Science, 4, 425441. Rao, C. R. 1973. Linear statistical inference and its applications, 2nd ed. Nueva York: John Wiley and Sons.
410 Bibliografa
Rao, C. R. 1980. Matrix approximations and reduction of dimensionality in multivariate statistical analysis. En: Multivariate Analysis, Vol. 5, P. R. Krishnaiah, ed. msterdam: North-Holland, 322. Rosenberg, S., y M. P. Kim. 1975. The method of sorting as a data-gathering procedure in multivariate research. Multivariate Behavioral Research, 10, 489502. Roskam, E. E. 1968. Metric analysis of ordinal data in psychology. Voorschoten: VAM. Shepard, R. N. 1962. The analysis of proximities: Multidimensional scaling with an unknown distance function I. Psychometrika, 27, 125140. Shepard, R. N. 1962. The analysis of proximities: Multidimensional scaling with an unknown distance function II. Psychometrika, 27, 219246. Shepard, R. N. 1966. Metric structures in ordinal data. Journal of Mathematical Psychology, 3, 287315. Tenenhaus, M., y F. W. Young. 1985. An analysis and synthesis of multiple correspondence analysis, optimal scaling, dual scaling, homogeneity analysis, and other methods for quantifying categorical multivariate data. Psychometrika, 50, 91119. Theunissen, N. C. M., J. J. Meulman, A. L. Den Ouden, H. M. Koopman, G. H. Verrips, S. P. Verloove-Vanhorick, y J. M. Wit. 2003. Changes can be studied when the measurement instrument is different at different time points. Health Services and Outcomes Research Methodology, 4, 109126. Tucker, L. R. 1960. Intra-individual and inter-individual multidimensionality. En: Psychological Scaling: Theory & Applications, H. Gulliksen, y S. Messick, Editores. Nueva York: John Wiley and Sons, 155167. Van der Burg, E. 1988. Nonlinear canonical correlation and some related techniques. Leiden: DSWO Press. Van der Burg, E., y J. De Leeuw. 1983. Nonlinear canonical correlation. British Journal of Mathematical and Statistical Psychology, 36, 5480. Van der Burg, E., J. De Leeuw, y R. Verdegaal. 1988. Homogeneity analysis with k sets of variables: An alternating least squares method with optimal scaling features. Psychometrika, 53, 177197. Van der Ham, T., J. J. Meulman, D. C. Van Strien, y H. Van Engeland. 1997. Empirically based subgrouping of eating disorders in adolescents: A longitudinal perspective. British Journal of Psychiatry, 170, 363368.
411 Bibliografa
Van der Kooij, A. J., y J. J. Meulman. 1997. MURALS: Multiple regression and optimal scaling using alternating least squares. En: Softstat 97, F. Faulbaum, y W. Bandilla, Editores. Stuttgart: Gustav Fisher, 99106. Van Rijckevorsel, J. 1987. The application of fuzzy coding and horseshoes in multiple correspondence analysis. Leiden: DSWO Press. Verboon, P., y I. A. Van der Lans. 1994. Robust canonical discriminant analysis. Psychometrika, 59, 485507. Verdegaal, R. 1985. Meer sets analyse voor kwalitatieve gegevens (en neerlands). Leiden: Department of Data Theory, University of Leiden. Vlek, C., y P. J. Stallen. 1981. Judging risks and benefits in the small and in the large. Organizational Behavior and Human Performance, 28, 235271. Wagenaar, W. A. 1988. Paradoxes of gambling behaviour. Londres: Lawrence Erlbaum Associates, Inc. Winsberg, S., y J. O. Ramsay. 1980. Monotonic transformations to additivity using splines. Biometrika, 67, 669674. Winsberg, S., y J. O. Ramsay. 1983. Monotone spline transformations for dimension reduction. Psychometrika, 48, 575595. Wolter, K. M. 1985. Introduction to variance estimation. Berln: Springer-Verlag. Young, F. W. 1981. Quantitative analysis of qualitative data. Psychometrika, 46, 357387. Young, F. W., J. De Leeuw, y Y. Takane. 1976. Regression with qualitative and quantitative variables: An alternating least squares method with optimal scaling features. Psychometrika, 41, 505528. Young, F. W., Y. Takane, y J. De Leeuw. 1978. The principal components of mixed measurement level multivariate data: An alternating least squares method with optimal scaling features. Psychometrika, 43, 279281. Zeijl, E., Y. te Poel, M. du Bois-Reymond, J. Ravesloot, y J. J. Meulman. 2000. The role of parents and peers in the leisure activities of young adolescents. Journal of Leisure Research, 32, 281302.
actualizaciones relajadas en Escalamiento multidimensional, 103 ajuste en Anlisis de correlacin cannica no lineal, 58 alfa de Cronbach en Anlisis de componentes principales categrico, 187 Anlisis de componentes principales categrico, 33, 41, 181, 197 almacenamiento de variables, 46 cuantificaciones, 189, 212 funciones adicionales del comando, 51 historial de iteraciones, 187 nivel de escalamiento ptimo, 36 puntos de categoras, 220 puntuaciones de los objetos, 191, 195, 218 resumen del modelo, 187, 195, 216 saturaciones en componentes, 193, 197, 216 Anlisis de correlacin cannica no lineal, 53, 5758, 237 centroides, 257 coordenadas de la categora, 256 cuantificaciones, 252 estadsticos, 53 funciones adicionales del comando, 60 grficos, 53 ponderaciones, 248 resumen de anlisis, 246 saturaciones en componentes, 248, 251
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