1 / 22

Multilevel Modeling: Why, When and How?

Multilevel Modeling: Why, When and How?. Frank Dong 1-9-2013. Outline. Why do we need the Multilevel Modeling When do we need Multilevel Modeling How can we conduct Multilevel Modeling analysis (live demo). Background.

sakina
Download Presentation

Multilevel Modeling: Why, When and How?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Multilevel Modeling: Why, When and How? Frank Dong 1-9-2013

  2. Outline • Why do we need the Multilevel Modeling • When do we need Multilevel Modeling • How can we conduct Multilevel Modeling analysis (live demo)

  3. Background • Everyone knows about ordinary least squares regression, aka, linear regression • The formula is • We typically assume the error term has a normal distribution N(0,) • Everyone knows how to do it in SPSS

  4. Problems • Ordinary least squares analysis does not solve everything • There are often times where data present certain hierarchy • For example, the performance of students on the test score may depends on the students themselves, but also may depends on schools • School effects are often ignored

  5. Purpose of this presentation • To introduce the idea of multilevel modeling • Not everything can be done with the linear regression • Live demonstration of how to conduct multilevel analysis in SPSS.

  6. An example • This example is from a book called Multilevel Statistical Models, 4th Edition by Harvey Goldstein • Have data on 728 elementary students • N=50 schools • Interested in the following question: Does the student’s 8-year math score predict the 11-year math score? • Y= 11-year math score • X=8-year math score

  7. Some data points

  8. Inappropriate Analysis • For each school, • The overall model becomes • We have 50 pairs of to estimate, one for each school • We also have a variance term, to estimate

  9. Issues • Too many unknown (N=2*50+1) parameters • Unable to compare school performance if we desires to do so • Some schools have fewer students than other schools

  10. Solutions • Multilevel Modeling • Instead of estimating N=2*50+1 unknown parameters, we will simplify the model • -----Original model • More importantly, and are also treated as random variable • They are assumed to have a normal distribution with certain M and SD

  11. Final Solution • The final model becomes • The unknown parameters are , variance of , and , and covariance between • We reduced the number of parameters from 101 to 6

  12. Results

  13. Research Question 2 • We also have the gender (1=boy, 2=girl), and social class (1=manual, 0=non-manual), would those two variables affect the performance of the 11-year math grade? • Is gender significant? • Is social class significant?

  14. How to conduct a Multilevel Modeling • You do not need to do it by yourself • You are required to be aware of the existence of multilevel modeling • The benefit is to improve the estimate accuracy • Here is how to do it in SPSS (live demo)

  15. Summary • Ordinary least squares regression is not almighty • When there is a clear structure of hierarchy, multilevel modeling will be useful • Multilevel modeling can also be used to compare the performance of hospitals

More Related