Keywords
goodness of fit
residual analysis
two sample configural frecuency analysis
tabla de contingencia
bondad de ajuste
análisis de residuos
Análisis de las frecuencias de las configuraciones de dos muestras
How to Cite
Abstract
Rudas, Clogg and Lindsay, en 1994, proposed a new index of lack of fit for contingency table analysis. For a contingency table P with N cells, and a model H, the new index is defined as the smallest π that satisfies the equation
Ph = (1 − π) Π1h + πΠ2h, h = 1, . . . , N
with 0 ≤ π ≤ 1, y Π1 y Π2 the tables of probabilities for each latent class. The model H applies to Π1 but not impose any restrictions on Π2. The interpretation of the index of lack of fit is the proportion of individuals of the population intrinsically outside model H. In this work we propose the analysis of the second latent class to the study of the causes of lack of fit of a model and to detect outlying cells. At the same time, we propose the new index of lack of fit as a concepto of non-independence in the two simple configural frequency analysis
References
Agresti, A. (1990) Categorical Data Analysis. Wiley, New York.
Andersen, E.B. (1992) “Diagnostic in categorical data analysis”, J.R.S.S. B54: 781–791.
Barnett, V.D.; Lewis, T. (1994) Outliers in Statistical Data, 3rd Ed. Wiley, New York.
Brown, M.B. (1974) “Identification of the sources of significance in two-way contingency tables”, Applied Statistics 23: 405–413.
Fuchs, C.; Kenett, R. (1980) “A test for detecting outlying cells in the multinomial distribution and two-way contingency tables”, JASA 75 395–398.
Goodman, L.A. (1991) “Measures, models and graphical displayas in the analysis of cross-classified data”, JASA 86: 1085–1111.
González, A.D. (1996) “Algo más acerca de la falta de ajuste de un modelo en el análisis de tablas de contingencia”, ponencia presentada en el VI Encuentro de Estad́ıstica Cuba-México, La Habana.
Haberman, S.J. (1973) “The analysis of residual in cross-classified tables”, Biometrics 29: 205–220.
Kieser, M.; Victor, N. (1991) “A test procedure for an alternative approach to configural frecuency analysis”, Methodika 5. 87–97.
Krauth, J.; Lienert, G.A. (1973) Die Konfigurationsfrequenzanalyse und ihre Anwendung in Psychologie und Medizin. Alber, Freiburg.
Little, R.F.A.; Rubin, B. (1987) Statistical Analysis with Missing Data. New York: Wiley.
Montero, M.D.; González, A.D.; Vidaillet, J. (1994) “Uso de los modelos jerárquicos loglineales y logísticos en el análsis de las frecuencias de las configuraciones de dos muestras”, Ciencias Técnicas, Fı́sicas y Matemáticas 15: 77–88.
Rudas, T.; Clogg, C.C.; Lindsay, B.G. (1994) “A new index of fit based on mixture methods for the analysis of contingency tables”, J.R.S.S. B56: 623–639.
Simonoff, T.S. (1988) “Detecting outlying cells in two-ways contingency tables via backwards- stepping”, Technometrics 30: 339–345.
Upton, G.J.G.; Guillén, M. (1995) “Perfect cells, direct models and contingency table outliers”, Commun. Statist.-Theory Meth., 24: 1843–1862.
Victor, N. (1989) “An alternative approach to configural frecuency analysis”, Methodika III: 61–73.
von Eye, A. (1990) Introduction to Configural Frecuency Analysis: The search for Types and Antitypes in Cross-Classiffications. Cambridge University Press.
von Eye, A.; Spiel, C.; Rovine, M.J. (1995) “Concepts of nonindependence in Configural Frecuency Analysis”, Journal of Mathematical Sociology 20: 41–54.
von Eye, A.; Spiel, C.; Wood, P.K. (1996) “Configural frecuency analysis in applied psychological research”, Applied Psychology: an International Review 45: 301–352.
Wickens, T.D. (1989) Multivariate contingency tables analysis for the behavioral sciences. Lawrence Erlbaum Associates Inc., Hillsdale, N.J.