1. From GLM to HLM Working with Continuous Outcomes
EPSY 5245
Michael C. Rodriguez

2. Continuous Variables
Review statistical procedures for continuous variables
Consider options on Variables Chart
Generalize options under the GLM approach

3. Statistical Paradigm Model Building Estimation of Parameters
Testing Fit of the Model

4. Model Building
Theory
Model Specification
Measurement
Data Collection

5. Estimation of Parameters
Conceptualizing Relevant Factors
A General Approach to Data Analysis
GLM Model Assumptions

6. General Approach to Data Analysis
Univariate & bivariate descriptive analyses
Specifying the model
Testing interaction terms
Removing insignificant terms
Examining outliers
Checking assumptions

7. General Linear Model Assumptions
STRUCTURAL
Independent observations
Linear relationships
Variable independence
Errorless measurement
Correct specification
STOCHASTIC
Independence
Normality
Mean of zero
Homogeneity of variance
Independence from explanatory variables

8. Testing Model-Data Fit
Parsimony
Indicators
Correlation
Simple Regression
Multiple Regression
Controlling Type-I error

9. Common Problems in the analysis of clustered (nested) data
The “unit of analysis” problem – misestimated precision
Testing hypotheses about effects occurring at each level and across levels
Problems related to measurement of change or growth

10. Estimation Requirements
Estimation of parameters requires some distributional assumptions. One requires the error term (the part of the outcome that is not explained by observed factors) to be independent and identically distributed.
This is in contrast with the idea that people exist within meaningful relationships in organizations.
Frank, K. (1998). Quantitative methods for studying social contexts. Review of Research in Education, 23,

11. The Notation of Regression
𝑌 𝑖 = β 0 + β 1 𝑋 1𝑖 + β 2 𝑋 2𝑖 +…+ β 𝑄 𝑋 𝑄𝑖 + ε 𝑖
𝑌 𝑖 = β β 1 𝑋 1𝑖 + ε 𝑖 or

12. What’s in a name… Sociology: Multilevel Models
Biometrics: Mixed-Effects Models or Random-Effects Models
Econometrics: Random-Coefficient Regression Models
Statistics: Covariance Components Models

13. When to use HLM Nested data: Dependent observations
Do children of different gender, race, or exposure to different reading programs grow at the same rate in reading?
Is the relationship between social status and achievement the same in schools of different size or sector (public v. catholic)?

14. Building Models in HLM
Level One
Within Units
Level Two
Between Units

15. Examples of Multiple Levels
Students
Classrooms
Schools
Teachers
School Districts
Children
Families
Neighborhoods
Cities
Nurses
Wards/Units
Hospitals
Workers
US-Based Firms
Multinational Firms
Juvenile Delinquents
Social Workers
Social Service Agencies
Longitudinal Scores

16. Advantages of HLM
Adjusting for nonindependence of observations within subjects
Larger framework for real-life problems
Unbalanced designs and missing data are accommodated

17. Alternatives to HLM
Individual level
Group level
Just use regression

18. What do we gain through HLM?
Improved estimation of effects within individual units.
Example: Developing an improved estimate of a regression model for an individual school by borrowing strength from the fact that similar relationships exist for other schools.

19. What do we gain through HLM?
Formulation and testing of hypotheses about cross-level effects.
Example: How school size might be related to the magnitude of the relationship between social class and academic achievement within schools.

20. What do we gain through HLM?
Partitioning variance and covariance components among levels.
Example: Decomposing the correlation among a set of student-level variables into within- and between-school components.
How much of the variance is within or between schools?

21. A relationship between 8th grade and 11th grade performance?
Goldstein (1999).

22. Accounting for school
Goldstein (1999).

23. When school is a meaningful organizational unit, relations may be a function of the unit.
Achievement
Socioeconomic Status

24. Example Model
β 0𝑗 = γ 00 + γ 01 𝐶𝑎𝑡ℎ𝑜𝑙𝑖𝑐 𝑗 + 𝑢 0𝑗
β 1𝑗 = γ 10 + γ 11 𝐶𝑎𝑡ℎ𝑜𝑙𝑖𝑐 𝑗 + 𝑢 1𝑗