潛在類別變數模型專題

In many studies, the conceptually or clinically most meaningful outcome is unobservable. Hence, a set of multiple discrete indicators, for example, a set of questionnaires, is measured in place of this outcome. Latent variable models explore the relationships between unobservable outcomes and their measured indicators. This course focuses on the cases where the unobservable outcome is described by a categorical variable identifying subpopulations or "classes" with each of which has homogeneous outcome status (i.e., the latent class variable). In this course, we will go through the statistical methodological and theoretical research of latent class models. Also, some important research topics and unsolved issues in latent class modeling, including model diagnosis, variable selection, and model identifiability will be discussed. There will be some formal lectures, but most class meetings will be devoted to the discussion of recent papers or student projects.

Students are expected to be familiar with computer language R and/o Python. Background on probability, mathematical statistics and basic multivariate analysis are required.

The course grade will be based on class presentation, class attendance, class participation and a final project.

PAPERS TO BE DISCUSSED 1. Allman ES, Matias C, Rhodes JA (2009). Identifiability of parameters in latent structure models with many observed variables. Annals of Statistics, 37, 3099-3132. 2. Fraiman R, Justel A, Svarc M (2008). Selection of variables for cluster analysis and classification rules. Journal of the American Statistical Association, 103, 1294-1303. 3. Goodman LA (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215-231. 4. Hosmer DW, Lemeshow S (1980). Goodness-of-fit tests for the multiple logistic regression model. Communications in Statistics, A10, 1043-1069. 5. Huang GH (2005-a). Selecting the number of classes under latent class regression: a factor analytic analogue. Psychometrika, 70, 325-345. 6. Huang GH (2005-b). Model identifiability. Encyclopedia of Statistics in Behavioral Science. Editors: Brian S. Everitt and David C. Howell. Wiley, New York. Volume 3, 1249-1251. 7. Huang GH, Bandeen-Roche K (2004). Building an identifiable latent class model with covariate effects on underlying and measured variables. Psychometrika, 69, 5-32. 8. Huang GH, Wang SM, Hsu CC (2011). Optimization-based model fitting for latent class and latent profile analyses. Psychometrika, 76, 584-611. 9. Kruskal JB (1976). More factors than subjects, tests and treatments: an indeterminacy theorem for canonical decomposition and individual differences scaling. Psychometrika, 41, 281-293. 10. Kruskal JB (1977). Three-way arrays: rank and uniqueness of trilinear decompositions, with application to arithmetic complexity and statistics. Linear Algebra Application, 18, 95-138. 11. Pan JC, Huang GH (2013). Bayesian inferences of latent class models with an unknown number of classes. Psychometrika, doi:10.1007/s11336-013-9368-7. 12. Raftery AE, Dean N (2006). Variavle selection for model-based clustering. Journal of the American Statistical Association, 101, 168-178.

地點

A423 Joint Education Hall

時間

By appointment

聯絡方式

Email: ghuang@stat.nctu.edu.tw