Multilevel Modeling 1. Overview 2. Application #1: Growth Modeling Break 3. Application # 2: Individuals Nested Within Groups 4. Questions?
Overview • What is multilevel modeling? • Examples of multilevel data structures • Brief history • Current applications • Why multilevel modeling? • What types of studies use multilevel modeling? • Computer Programs (HLM 6 SAS Mixed • Resources
Multilevel Question • What effects do the following variables have on 3rd grade reading achievement? School Size Classroom Climate Student Gender
What is Multilevel or Hierarchical Linear Modeling? Nested Data Structures
Several Types of Nesting • 1. Individuals Nested Within Groups
Individuals Undivided Unit of Analysis = Individuals
Individuals Nested Within Groups Unit of Analysis = Individuals + Classes
… and Further Nested Unit of Analysis = Individuals + Classes + Schools
Examples of Multilevel Data Structures • Neighborhoods are nested within communities • Families are nested within neighborhoods • Children are nested within families
Examples of Multilevel Data Structures • Schools are nested within districts • Classes are nested within schools • Students are nested within classes
Multilevel Data Structures Level 4 District (l) Level 3 School (k) Level 2 Class (j) Level 1 Student (i)
2nd Type of Nesting • Repeated Measures Nested Within Individuals Focus = Change or Growth
Repeated Measures Nested Within Individuals Carlos Day Energy Level Monday = 0 98 Tuesday = 1 90 Wednes. = 2 85 Thursday = 3 72 Friday = 4 70
3rd Type of Nesting (similar to the 2nd) • Repeated Measures Nested Within Individuals Focus is not on change Focus in on relationships between variables within an individual
Repeated Measures Nested Within Individuals Carlos Day Hours of SleepEnergy Level Monday 9 98 Tuesday 8 90 Wednesday 8 85 Thursday 6 72 Friday 7 70
Repeated Measures Within Persons Level 2 Student (i) Level 1 Repeated Measures Over Time (t)
Nested Data • Data nested within a group tend to be more alike than data from individuals selected at random. • Nature of group dynamics will tend to exert an effect on individuals.
Nested Data • Intraclass correlation (ICC) provides a measure of the clustering and dependence of the data 0 (very independent) to 1.0 (very dependent) Details discussed later
Brief Historyof Multilevel Modeling Robinson, W. S. (1950). Ecological correlations and the behavior of individuals. Sociological Review, 15, 351-357. Burstein, Leigh (1976). The use of data from groups for inferences about individuals in educational research. Doctoral Dissertation, Stanford University.
Table 1 Frequency of HLM application evidenced in Scholarly Journals
Some Current Applications of Multilevel Modeling • Growth Curve Analysis • Value Added Modeling of Teacher and School Effects • Meta-Analysis
Multilevel Modeling Seems New But…. Extension of General Linear Modeling Simple Linear Regression Multiple Linear Regression ANOVA ANCOVA Repeated Measures ANOVA
Multilevel Modeling • Our focus will be on observed variables (not Latent Variables as in Structural Equation Modeling)
Why Multilevel Modelingvs. Traditional Approaches? Traditional Approaches – 1-Level • Individual level analysis (ignore group) • Group level analysis (aggregate data and ignore individuals)
Problems withTraditional Approaches • Individual level analysis (ignore group) Violation of independence of data assumption leading to misestimated standard errors (standard errors are smaller than they should be).
Problems withTraditional Approaches • Group level analysis (aggregate data and ignore individuals) Aggregation bias = the meaning of a variable at Level-1 (e.g., individual level SES) may not be the same as the meaning at Level-2 (e.g., school level SES)
Multilevel Approach • 2 or more levels can be considered simultaneously • Can analyze within- and between-group variability
What Types of Studies Use Multilevel Modeling? Quantitative Experimental *Nonexperimental (Survey, Observational)
How Many Levels Are Usually Examined? 2 or 3 levels very common 15 students x 10 classes x 10 schools = 1,500
Types of Outcomes • Continuous Scale (Achievement, Attitudes) • Binary (pass/fail) • Categorical with 3 + categories
Software to do Multilevel Modeling SPSS Users 2 SAV Files: Level 1 Level 2 HLM 6 (Menu Driven) (Raudenbush, Bryk, Cheong, & Congdon, 2004)
Software to do Multilevel Modeling SAS Users Proc Mixed
Resources (Sample…see handouts for more complete list) • Books • Hierarchical Linear Models: Applications and Data Analysis Methods, 2nd ed. Raudenbush & Bryk, 2002. • Introducing Multilevel Modeling. Kreft & DeLeeum, 1998. • Journals • Educational and Psychological Measurement • Journal of Educational and Behavioral Sciences • Multilevel Modeling Newsletter
Resources (cont)(Sample…see handouts for more complete list) • Software • HLM6 • SAS (NLMIXED and PROC MIXED) • MLwiN • Journal Articles • See Handouts for various methodological and applied articles • Data Sets • NAEP Data • NELS:88; High School and Beyond
Self-Check 1 • A teacher with 1 classroom of 24 students used weekly curriculum-based measurements to monitor reading over a 14 week period. The teacher was interested in individual students’ rates of change and differences in change by male and female students.
Self-Check 1 • How would you classify this situation? (a) not multilevel (b) 2-level (c) 3-level
Self-Check 2 • A researcher randomly selected 50 elementary schools and randomly selected 30 teachers within each school. The researcher was interested in the relationships between 2 predictors (school size and teachers’ years experience at their current school) and teachers’ job satisfaction.
Self-Check 2 • How would you classify this situation? (a) not multilevel (b) 2-level (c) 3-level
Self-Check 3 • 60 undergraduates from the research participant pool volunteered for a study that used written vignettes to manipulate the interactional style (warm, not warm) of a professor interacting with a student. 30 randomly assigned students read the vignette depicting warmth and 30 randomly assigned students read the vignette depicting a lack of warmth. After reading the vignette students used a questionnaire to rate the likeability of the professor.
Self-Check 3 • How would you classify this situation? (a) not multilevel (b) 2-level (c) 3-level (Select ONLY one)
Growth Curve Modeling • Studying the growth in reading achievement over a two year period • Studying changes in student attitudes over the middle school years