Study-Unit Description

Study-Unit Description


CODE SOR5272

 
TITLE Generalized Latent Variable Modeling

 
UM LEVEL 05 - Postgraduate Modular Diploma or Degree Course

 
MQF LEVEL 7

 
ECTS CREDITS 10

 
DEPARTMENT Statistics and Operations Research

 
DESCRIPTION The following topics will be covered:

- Latent variables;
- Unobserved heterogeneity;
- Modelling different response processes;
- Generalized linear models;
- Extension of Generalized linear models;
- Latent response formulation;
- General framework for Latent class models;
- Distribution of the disturbances;
- Moment structure of the latent variables;
- Marginal moment structure of observed and latent responses;
- Reduced form distribution and likelihood;
- Maximum Likelihood Estimation: Closed and Approximate Marginal Likelihood;
- Numerical Integration: Gauss-Hermite, Adaptive Quadrature, Monte Carlo integration and Importance Sampling;
- Maximizing the Likelihood: EM algorithm and Gradient Methods;
- Nonparametric maximum likelihood estimation: Gateaux Derivative;
- Bayesian Estimation Methods: Bayes Modal, Hierarchical Bayesian and MCMC;
- Latent Class Models.

Study-Unit Aims:

- Understand the meaning of the concept of latent variables;
- Demonstrate through illustrations that latent variables may represent hypothetical constructs, unobserved heterogeneity, missing data and latent responses;
- Model different response processes;
- Describe the general framework for Latent class models and apply these models;
- Describe different estimation techniques including Restricted maximum likelihood, Maximum quasi likelihood, Nonparametric maximum likelihood and EM algorithm;
- Check model specification and use model fit to make inferences.

Learning Outcomes:

1. Knowledge & Understanding:

By the end of the study-unit the student will be able to:

- Discriminate between standard Generalized Linear Models that accommodate fixed effects only and Generalized Latent Variable Models that accommodate latent variables and random effects;
- Select an appropriate model for a given data set, check model adequacy and use model diagnostics to assess misspecifications.

2. Skills:
By the end of the study-unit the student will be able to.

- Fit Latent Class models to data sets with unexplained heterogeneity;
- Use two statistical packages GLM and GLLAMM that fit Latent Class Models;
- Use different estimation procedures and compare results.

Main Text/s and any supplementary readings:

- Clogg, C. C. (1995). Latent class models. In G. Arminger, C. C. Clogg, & M. E. Sobel (Eds.), Handbook of statistical modeling for the social and behavioral sciences (Ch. 6; pp. 311-359). New York: Plenum.
- Goodman, L. A. (1974), "Exploratory Latent Structure Analysis Using Both Identifiable and Unidentifiable Models," Biometrika, 61, 215-231.
- Haberman, S. J., Qualitative Data Analysis (Vols. 1 & 2), New York, Academic Press, 1979.
- Hagenaars, J. A. (1993). Loglinear models with latent variables. Sage Publications.
- Hagenaars J, McCutcheon A (Eds) (due Feb. 2001). Applied Latent Class Analysis. Cambridge University Press.
- Lazarsfeld, P. F., and Henry, N. W. (1968), Latent Structure Analysis, Boston: Houghton Mifflin.
- Langeheine, R. & Rost, J. (Eds.) (1988). Latent trait and latent class models. New York: Plenum.
- McCutcheon, A. C. (1987). Latent Class Analysis. Beverly Hills: Sage Publications.
- Skrondal, A & Rabe-Hesketh, S (2004) Generalized latent variable modeling: multilevel, longitudinal and structural equation models, Chapman and Hall CRCClogg, C. C. (1995). Latent class models. In G. Arminger, C. C. Clogg, & M. E. Sobel (Eds.), Handbook of statistical modeling for the social and behavioral sciences (Ch. 6; pp. 311-359). New York: Plenum.
- Goodman, L. A. (1974), "Exploratory Latent Structure Analysis Using Both Identifiable and Unidentifiable Models," Biometrika, 61, 215-231.
- Haberman, S. J., Qualitative Data Analysis (Vols. 1 & 2), New York, Academic Press, 1979.
- Hagenaars, J. A. (1993). Loglinear models with latent variables. Sage Publications.
- Hagenaars J, McCutcheon A (Eds) (due Feb. 2001). Applied Latent Class Analysis. Cambridge University Press.
- Lazarsfeld, P. F., and Henry, N. W. (1968), Latent Structure Analysis, Boston: Houghton Mifflin.
- Langeheine, R. & Rost, J. (Eds.) (1988). Latent trait and latent class models. New York: Plenum.
- McCutcheon, A. C. (1987). Latent Class Analysis. Beverly Hills: Sage Publications.
- Skrondal, A & Rabe-Hesketh, S (2004) Generalized latent variable modeling: multilevel, longitudinal and structural equation models, Chapman and Hall CRC.

 
ADDITIONAL NOTES Pre-requisite Study-units: SOR3221 and SOR3211

 
STUDY-UNIT TYPE Independent Study

 
METHOD OF ASSESSMENT
Assessment Component/s Assessment Due Sept. Asst Session Weighting
Project SEM2 Yes 100%

 
LECTURER/S

 

 
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The availability of optional units may be subject to timetabling constraints.
Units not attracting a sufficient number of registrations may be withdrawn without notice.
It should be noted that all the information in the description above applies to study-units available during the academic year 2024/5. It may be subject to change in subsequent years.

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