Study-Unit Description

Study-Unit Description


CODE SOR5273

 
TITLE Multi-Level Models

 
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:

- Linear Mixed Models;
- Two-level and Three-level Models;
- Random Intercept and Random Coefficient Models;
- Intraclass Correlation;
- Maximum Likelihood Estimation: Closed and Approximate Marginal Likelihood;
- Numerical Integration: Gauss-Hermite and Adaptive Quadrature;
- Maximizing the Likelihood: EM algorithm and Quasi Newton Methods;
- Restricted Maximum Likelihood Estimation (REML);
- Prediction of Random Effects: Empirical Bayes and Empirical Bayes Modal;
- Multilevel Models for Analyzing Repeated Measures Data;
- Generalized Linear Multilevel Models;
- Multilevel Logistic Models for dichotomous and multichotomous data: Logit and Probit transformation;
- Multilevel Models for Ordinal Categorical Data;
- Linear and Quadratic Growth Models;
- Poisson Multilevel Models for Count Data.

Study-Unit Aims:

- Familiarize with modeling techniques that accommodate repeated measures and nested data sets;
- Present a unified theoretical and conceptual framework that accommodate longitudinal and clustered data;
- Use the statistical software GLLAMM to fit various types of Multilevel Models and familiarize with GLLAMM syntax and directives;
- Familiarize with diagnostic tools to check the adequacy of Multilevel models and identify outliers and influential observations.

Learning Outcomes:

1. Knowledge & Understanding:

The student will familiarize with the theoretical framework of Multilevel models and learn how to use the statistical technique appropriately when analyzing longitudinal and clustered data structures that violate the assumption of independence. Moreover, the student is expected to familiarize with GLLAMM syntax to fit Multilevel models, interpret the statistical output and use diagnostic tools to check for model adequacy and identify oddities.

2. Skills:

The student gains experience in applying statistical techniques through statistical software, particularly GLLAMM which is a subroutine of STATA. Familiarize with GLLAMM code and procedures to fit correctly Multilevel Models. Moreover, the student are expected to use these models in a various Social Science applications where variables are measured in more than one level of a hierarchy. Applications where individuals are nested within groups and groups are nested within larger units.

Main Text/s and any supplementary readings:

- Bryk, A. S., Raudenbush, S. W. (1992). Hierarchical Linear Models: Applications and Data Analysis. Newbury Park, CA: Sage.
- Dobson, A.J. (2002). An Introduction to Generalized Linear Models, Chapman & Hall CRC Press.
- Gelman, A., and J. Hill. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge University Press.
- Goldstein, H. (2003). Multilevel Statistical Models (3rd Edition).
- Hox, J. J. 2002. Multilevel Analysis: Techniques and Applications. Lawrence Erlbaum Associates.
- Leyland, A. H., and H. Goldstein. (2001). Multilevel Modelling of Health Statistics. Wiley.
- Longford, N. T. 1993. Random Coefficient Models. Oxford University Press.
- Molenberghs, G. and Verbeke, G. (2005). Models for Discrete Longitudinal Data, Springer-Verlag, Berlin.
- Raudenbush, S.W., Bryk, A.S. (2002). Hierarchical Linear Models: Applications and Data Analysis Methods, Sage Publications, Newbury Park, CA.
- Skrondal, A., Rabe-Hesketh, S. (2004). Generalized Latent Variable Modelling: Multilevel, Longitudinal and Structural Equation Models, Chapman and Hall, CRC.
- Snijders, T.A.B. and Bosker, R.J. (1999). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling, Sage Publications, Newbury Park, CA.
- Verbeke, G. and Molenberghs, G. (2000). Linear Mixed Models for Longitudinal Data, Springer-Verlag, Berlin.
- West, B.T., Welch, K.B. and Galecki, A.T. (2007). Linear Mixed Models – A Practical Guide using Statistical Software, Chapman & Hall/CRC.

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

 
STUDY-UNIT TYPE Independent Study

 
METHOD OF ASSESSMENT
Assessment Component/s Assessment Due Sept. Asst Session Weighting
Project See note below Yes 100%
Note: Assessment due date will be notified by the Faculty/Institute/Centre/School.

 
LECTURER/S

 

 
The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
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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