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
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.
An example This example is from a book called Multilevel Statistical Models, 4 th Edition by Harvey Goldstein Have data on 728 elementary students N=50 schools Interested in the following question: Does the students 8-year math score predict the 11-year math score? Y= 11-year math score X=8-year math score
Some data points 11-year Math Score 8-year Math ScoreSchool ID Gender: Boy=1 Girl=0 Social class: Manual=1 Non-manual=0 3936110 1119101 3231101 2723100 3639100
Results ParameterMultilevel Modeling Estimate (s.e.) OLS Estimate (s.e.) Fixed Intercept13.913.8 8-year Math Score0.65 (0.025)0.65 (0.026) Random Effect Between School Variance 3.28 Between Students Variance 19.823.34 Variance Partition Coefficient 0.14
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?
ParametersMultilevel Modeling Estimate (s.e.) OLS Modeling Estimate (s.e.) Fixed Effects Intercept 14.8814.79 8-year Math Score 0.638 (0.025)0.638 (0.026) Gender (boy vs girl) -0.357 (0.340)-0.363 (0.358) Social Class (manual vs non-manual) -0.720 (0.387)-0.697 (0.397) Random Effect Between School Variance 3.312 Between Students Variance 19.72849.36 Variance Partition Coefficient 0.144
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)
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