Methodology and Statistics
International Conference, 17 - 19 September 2001
FDV, Ljubljana, Slovenia


SIMULTANEOUS LATENT ASSOCIATION MODELS
FOR CROSS-NATIONAL RESEARCH

Allan L. McCutcheon
UNL Gallup Research Center
University of Nebraska-Lincoln
USA

This paper presents a new methodology for analyzing association models that include latent scales in multiple groups. These methods are generalizable to a wide range of association models in which at least one of the variables in the analysis of association is latent; they are especially well suited to modeling cross-national differences and similarities in latent structures. The methods employed here derive from the work of Haberman (1974, 1979), Goodman (1974a, 1974b, 1979, 1984), Clogg (1982a, 1982b, 1988), and Hagenaars (1990, 1993), and extend the work of McCutcheon (1996, McCutcheon and Hagenaars 1997, Hagenaars and McCutcheon forthcoming). Following a discussion of the general and restricted model, and a comparison of the formal model to other latent variable models, an example is considered. This example focuses on a comparative analysis of the religious beliefs among the public's of five European Catholic nations (i.e., Austria, Ireland, Italy, Poland and Slovenia). Data from the 1991 International Social Survey Programme are examined.

References

  • Clogg, C. C. (1982a) "Some models for the analysis of association in multi-way cross-classifications having ordered categories," Journal of the American Statistical Association, 77: 803-815.
  • Clogg, C. C. (1982b) "Using association models in sociological research: Some examples," American Journal of Sociology, 88: 114-135.
  • Clogg, C. C. (1988) "Latent Class Models for Measuring." In R. Langeheine and J. Rost (eds.) Latent Trait and Latent Class Models. New York: Plenum.
  • Goodman, L. A. (1974a) "Exploratory latent structure analysis using both identifiable and unidentifiable models," Biometrika 61: 215-31.
  • Goodman, L. A. (1974b) "The analysis of systems of qualitative variables when some of the variables are unobservable. Part I: A modified latent structure approach," American Journal of Sociology 79: 1179-259.
  • Goodman, L. A. (1979) "Simple models for the analysis of association in cross-classifications having ordered categories," Journal of the American Statistical Association, 74: 537-552.
  • Goodman, L. A. (1984) The Analysis of Cross-classified Data Having Ordered Categories. Cambridge, MA: Harvard University Press.
  • Haberman, S. J. (1979) Analysis of Qualitative Data: New Developments, Vol. 2. New York: Academic.
  • Haberman, S. J. (1974) "Log-linear models for frequency tables with ordered classification," Biometrics, 30: 589-600.
  • Hagenaars, J. A. (1990) Categorical Longitudinal Data. Newbury Park, CA: Sage.
  • Hagenaars (1993) Loglinear Models with Latent Variables. Newbury Park, CA: Sage.
  • Hagenaars, J. A., and A. L. McCutcheon (eds.) (forthcoming) Applied Latent Class Analysis. New York: Cambridge University Press.
  • McCutcheon, A. L. (1996) "A Multiple Group Association Models with Latent Variables: An Analysis of Secular Trends in Abortion Attitudes, 1972-1988." In A. Raftery (ed.) Sociological Methodology, 1996. Cambridge, MA: Blackwell. Pp. 79-111.
  • McCutcheon, A. L., and J. A. Hagenaars (1997) "A Comparative Social Research with Multi-Sample Latent Class Models." In J. Rost and R. Langeheine (eds.) Applications of Latent Trait and Latent Class Models in the Social Sciences. New York: Waxmann. Pp. 266-277.