## Multilevel Modeling

A 2-Day Seminar

Taught by Tenko Raykov, Ph.D

Researchers in the behavioral, social, biomedical, business and economics disciplines often collect data that have a hierarchical structure. Patients are nested (clustered) within treatment centers, employees are nested within firms, respondents are nested within cities, students are nested within schools, and so on. As a consequence of this nesting, the observations in the data set are not statistically independent, thus violating a basic assumption of standard methods of analysis. Ignoring the nesting effect and proceeding with conventional, single-level methods of analysis (like linear regression) can yield highly misleading results. That’s because traditional methods produce standard errors that are typically too small, leading to confidence intervals that are too short and p-values that are too low.

This two-day seminar provides a thorough introduction to multilevel modeling, a statistical framework that accounts for the nesting effect and avoids these problems, as well as those associated with earlier methods of aggregation and disaggregation. Throughout the seminar, many empirical examples are drawn from the behavioral, clinical, educational and economics disciplines. The popular software package Stata is used for all the examples, along with a detailed discussion of the command syntax and intepretation of the output.

Participants in this seminar can expect to come away with:

1. A nuanced understanding of the conceptual foundations and basic mathematical formulation of the multilevel model.

2. The ability to understand, interpret and explain the output from multilevel modeling software.

3. An appreciation of the advantages and disadvantages of multilevel modeling as compared with other approaches to nested data.

4. Practical tools and strategies for developing and testing multilevel models.

5. The ability to extend the multilevel model to dichotomous outcomes.

6. A clear understanding of the differences between fixed and random effects.

### Who should attend?

To benefit from this seminar, you should have the equivalent of two semesters of statistics: a good introductory course with some treatment of probability and random variables, and a course on linear models. Some knowledge of logistic regression will also be helpful but not essential.

### Schedule and materials

The class will meet from 9 to 4 each day with a 1-hour lunch break.

Participants receive a bound manual containing detailed lecture notes (with equations and graphics), examples of computer printout, and many other useful features. This book frees participants from the distracting task of note taking.

### Registration and Lodging

The fee of $895 includes all course materials. The early bird fee of $795 is available until October 1.

**Lodging Reservation Instructions**

A block of rooms has been reserved at the Club Quarters Hotel, 1628 Chestnut St., Philadelphia, PA at a nightly rate of $137 for a Standard room. This hotel is about a 5-minute walk from the seminar location. To make a reservation, you must call 203-905-2100 during business hours and identify yourself by giving the **group code STA131**. For guaranteed rate and availability, you must make your reservation by October 3, 2013.

### Seminar outline

1. Resources for the seminar.

2. Why do we need multilevel modeling (MLM)? Why are aggregation and disaggregation unsatisfactory?

3. The beginnings of MLM.

– Why what we already know about regression analysis is so useful.

– Centering of predictor variables.

4. The intra-class correlation coefficient – Do we really need a multilevel model?

5. How many levels? Proportions of third-level variance and at intermediate level, and how to evaluate them, in three-level settings.

6. Random intercept models and model adequacy assessment.

7. Robust modeling of lower-level variable relationships in the presence of clustering effects.

8. What are mixed models, what are they made of, and why are they useful?

9. A new look at random regression models – a general class of mixed/multilevel models of great utility great utility “5. How many levels

– Getting started and restricted maximum likelihood (REML) estimation.

– Random regression models.

– Multiple random slopes.

– Fixed effects, random effects, and total effects.

– Numerical issues and possible problems.

– Nested levels (higher-order nesting).

10. Mixed models with discrete response variables – what to do when the outcome is not continuous?

11. why do we need another modeling approach?

– Random intercept model with discrete outcome.

– Random regression model with discrete response.

– Model choice with discrete outcome.

– Applications of multilevel modeling in complex design studies.

12. Conclusion and outlook.

### COMPUTING

This seminar will use Stata for all examples, but prior knowledge of Stata is not essential. You are welcome to bring your own laptop computer, and outlets will be provided at each seat. No internet service will be provided, however.

### Comments from recent participants

“The instructor is great, very knowledgeable and answers to the question. I had a great refresher on this mixed model topic”* Chung-yuan Hu, University of Texas*

“I am very glad I decided to enroll in this course. The instructor is well-versed in MLM, and also has an effective teaching style; I appreciated the balance between theory and mathematical equations and application.”* Laura Podewils, Center for Disease Control and Prevention*

“Overall this is a great course for the practical researcher. It is based on clear non-technical explanations that do not compromise rigor. The instructor was excellent in getting to the point and answering all questions clearly. For someone who wants to work on research settings that involve more than one level, I would highly recommend this session.”* Panikos Georgallis, HEC Paris*

“After reading dozens of articles regarding the concept of multilevel modeling, the concepts were nicely brought together by this course. The real world examples were very helpful. A good launching point for learing this methodology.”* Shana Cox, CDC*

“I am a graduate student in epidemiology. My training has involved one level modeling only. This course was an essential part of preparing me for future work in population health, as I was able to learn about managing clustered date, a skill that is necessary in the analysis of complex design studies.”* Pascale Lajoie, Queen’s University, Canada*

“Dr. Raykov was incredibly knowledgeable about this topic and about the field of statistics in general. He’s an incredible resource and having this level of access presented the class with an amazing opportunity not just to see how to do MLM, but more importantly, to know why certain steps are taken and decisions are made. He gave me individual attention and answered my questions during our breaks in a way that I could clearly understand and far surpassed what could be gleaned from textbooks alone.”* Aaron Rosenbaum, Spring International** *

“I tried to teach myself multilevel modeling from a stats book and some SAS code in grad school when I only knew how to use SPSS. I think I got the concepts, but had no idea how to implement it, and/or what to do with the output if I were to get it. Now I typically use Stata and having this course reinforces the theoretical explanation of multilevel modeling (with equations) AND the practical Stata commands as to how to run it (and interpret the output make me feel that I could actually run these analyses myself now.”* Laura Gibson, University of Pennsylvania*

“Dr. Raykov provided an excellent conceptual understanding of the multilevel and mixed effects models. Within the limited time span, he also covered a great deal of software syntax for the participants. For a 2-day workshop, Dr. Raykov did an outstanding job! The workshop included both underlying theory and actual examples, creating a very sound foundation for participants to go on to more advanced textbooks/workshops of MLM.”

* Anonymous*

“Excellent approach that factors in both contextual and technical issues in a relatively easy to comprehend way.”

*Fatou Jah*

“”Knowledgeable teacher gives hands-on or practical examples in explaining the theory, which should be the most effective way of learning a new theory or technique. Besides, the teacher provides his insight on many statistics-related issues along the teachings, which is precious and valuable.”

*Robert Yu, University of Texas, MD Anderson Cancer Center*

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