Multi-level Regression Analysis
- The aim of the course is to develop a solid knowledge on the pros and cons of multilevel modeling as well as skills to apply the method in real-life research.
- Students understand the basic principles of multilevel modeling
- Students are able to access the results of multilevel modeling and interpret them statistically and sociologically.
- Students model individual cases within groups choosing the best model.
- Students apply multilevel modeling techniques in practical research.
- Topic 1. Introduction. The idea of hierarchical modeling. Pre-requisites for multilevel modeling. Alternatives to multilevel modeling.This class is designed to explain the limitations of multilevel research, and the opportunities it gives. We’ll work on issues of statistical treatment of clustered data, including multi-level propositions, micro-macro relations, the concept of levels of data and hierarchy as an organizational principle of certain types of data. We overview the most common situations when multilevel modeling is used in social and political science, and figure out the principle of grouping, nestedness, and cross-classification. We discuss what happens if we do not apply multilevel modeling to hierarchically organized data (taking it as pooled), what to do if the number of second level units is too low, if the sizes of groups vary strongly etc.
- Topic 2. A basic (empty) multilevel model. Intra-class correlation coefficient. Individual-level predictors. Group - level predictors. Fixed intercept. Fixed slopesAt this class, we start with the basic regression formula, and unfold the mathematical backstage of multilevel modeling by complicating it stepwise. We introduce the idea of dividing the explained variance between levels and discuss intra-class correlation coefficient as a measure of explained variance at the second level. We also train to distinguish predictors between levels. We estimate a regression model with fixed effects only and learn how to interpret its coefficients from the output, and match those coefficients to the regression formula. Using stargazer and sjPlot packages we start working on better visualization of the tables, paying special attention to nondefault solutions and modifications of the tables received.
- Topic 3. Varying intercepts. Varying slopes. Cross-level interaction in multilevel modelsWe continue complicating the regression formula by randomizing intercepts first, and slopes second, and accessing the interpretation of the coefficients provided by R. We deploy lme4 package in R to get calculate the regressions. Cross-level interaction effects are discussed and visualized with sjPlot package. We discuss the topic of marginal effects and work extensively on interpretation of the results received.
- Topic 4. Multilevel binary logistic regressionWe return to the basic logistic regression formula to repeat the concept of odds, log odds, logit, etc., and make it more complex by adding multi-level perspective to it. We estimate a model step-by-step in the same manner we used to practice with the basic multilevel model to see the difference. Some time is dedicated to discussing better ways to report logit models (choosing between odds and estimates in the tables, for example). Chapter 17 can be used for reference. Students are supposed to practice this type of modeling in their second home assignment that has to be submitted by class 7.
- Topic 6. Testing and model specification, model comparisonsWe work extensively on methods of quality assessment, as in multilevel models this process requires more sophistication due to numerous assumptions and complicated nature of modeling. Chapters 6 and 10 give a sense of the major issues here. We also extensively discuss the process of modeling, and recommend to follow the principles suggested by Snijders and Bosker starting from individual level, then adding second-level predictor, followed by interaction effects, and continue with randomization of slopes. Alternatives are also discussed.
- Topic 5. Mid-term project proposal presentation
- Topic 7. Discrete dependent variables in multilevel modelsBeing a more advanced topic, discrete variable multilevel analysis unites multinomial and ordered regressions. We discuss complications of such modeling. For ordinal models, we discuss the concept of thresholds, equidistance, and the assumption of latent concept behind the variable.
- Topic 8. Imperfect hierarchies, cross-classified data structuresHere we address the issue of imperfect hierarchies, when, for example, one person belongs to two groups that are non-nested, but rather residing on the same level (e.g. migrants who can be grouped to their country of origin as well as to their country of residence).
- Topic 9. Class discussion of issues in individual projects prior to submissionThis is a wrap-up session in an Q&A style. Students have an opportunity to ask their questions regarding all stages of modeling and reporting their results prior to final paper submission. Students are welcome to show their results so that their classmates can help with interpretation. Students are also encouraged to show some of their tables to see how other people perceive them. It helps figuring out the best way of presenting the results of complicated models. Graphs are also discussed.
- Homework Assignments
- Mid-term presentation of the individual project proposal
- Mid-term exam
- Individual research project essay in English (final project)Students need to submit their papers via LMS no later than June, 22. Late submissions will not be graded.
- Interim assessment (4 module)0.2 * Homework Assignments + 0.4 * Individual research project essay in English (final project) + 0.25 * Mid-term exam + 0.15 * Mid-term presentation of the individual project proposal
- Bickel, R. (2007). Multilevel Analysis for Applied Research : It’s Just Regression! New York: The Guilford Press. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=262458
- Bradford S. Jones, & Marco R. Steenbergen. (1997). Modeling Multilevel Data Structures. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.F4700E2E
- Gelman, A. B., & Hill, J. (2015). Data analysis using regression and multilevel/hierarchical models. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsbas&AN=edsbas.4E4FBAE7
- Meijer, E., & Leeuw, J. de. (2008). Handbook of Multilevel Analysis. New York: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=261439
- Antony, J. S., & Lott, J. L. (2012). Multilevel Modeling Techniques and Applications in Institutional Research : New Directions in Institutional Research, Number 154. San Francisco: Jossey-Bass. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=464973
- Smith, R. B. (2011). Multilevel Modeling of Social Problems : A Causal Perspective. Dordrecht: Springer. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsebk&AN=371921