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Multilevel Modeling

Multilevel Modeling

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Multilevel Modeling

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  1. Multilevel Modeling 1. Overview 2. Application #1: Growth Modeling Break 3. Application # 2: Individuals Nested Within Groups 4. Questions?

  2. 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

  3. Multilevel Question • What effects do the following variables have on 3rd grade reading achievement? School Size Classroom Climate Student Gender

  4. What is Multilevel or Hierarchical Linear Modeling? Nested Data Structures

  5. Several Types of Nesting • 1. Individuals Nested Within Groups

  6. Individuals Undivided Unit of Analysis = Individuals

  7. Individuals Nested Within Groups Unit of Analysis = Individuals + Classes

  8. … and Further Nested Unit of Analysis = Individuals + Classes + Schools

  9. Examples of Multilevel Data Structures • Neighborhoods are nested within communities • Families are nested within neighborhoods • Children are nested within families

  10. Examples of Multilevel Data Structures • Schools are nested within districts • Classes are nested within schools • Students are nested within classes

  11. Multilevel Data Structures Level 4 District (l) Level 3 School (k) Level 2 Class (j) Level 1 Student (i)

  12. 2nd Type of Nesting • Repeated Measures Nested Within Individuals Focus = Change or Growth

  13. Time Points Nested Within Individuals

  14. Repeated Measures Nested Within Individuals Carlos Day Energy Level Monday = 0 98 Tuesday = 1 90 Wednes. = 2 85 Thursday = 3 72 Friday = 4 70

  15. Repeated Measures Nested Within Individuals

  16. Repeated Measures Nested Within Individuals

  17. Changes for 5 Individuals

  18. 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

  19. 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

  20. Repeated Measures Nested Within Individuals (Not Change)

  21. Repeated Measures Nested Within Individuals (Not Change)

  22. Repeated Measures Nested Within Individuals

  23. Repeated Measures Within Persons Level 2 Student (i) Level 1 Repeated Measures Over Time (t)

  24. 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.

  25. 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

  26. 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.

  27. Table 1 Frequency of HLM application evidenced in Scholarly Journals

  28. Multilevel Articles

  29. Some Current Applications of Multilevel Modeling • Growth Curve Analysis • Value Added Modeling of Teacher and School Effects • Meta-Analysis

  30. Multilevel Modeling Seems New But…. Extension of General Linear Modeling Simple Linear Regression Multiple Linear Regression ANOVA ANCOVA Repeated Measures ANOVA

  31. Multilevel Modeling • Our focus will be on observed variables (not Latent Variables as in Structural Equation Modeling)

  32. Why Multilevel Modelingvs. Traditional Approaches? Traditional Approaches – 1-Level • Individual level analysis (ignore group) • Group level analysis (aggregate data and ignore individuals)

  33. 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).

  34. 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)

  35. Multilevel Approach • 2 or more levels can be considered simultaneously • Can analyze within- and between-group variability

  36. What Types of Studies Use Multilevel Modeling? Quantitative Experimental *Nonexperimental (Survey, Observational)

  37. How Many Levels Are Usually Examined? 2 or 3 levels very common 15 students x 10 classes x 10 schools = 1,500

  38. Types of Outcomes • Continuous Scale (Achievement, Attitudes) • Binary (pass/fail) • Categorical with 3 + categories

  39. Software to do Multilevel Modeling SPSS Users 2 SAV Files: Level 1 Level 2 HLM 6 (Menu Driven) (Raudenbush, Bryk, Cheong, & Congdon, 2004)

  40. HLM 6

  41. Software to do Multilevel Modeling SAS Users Proc Mixed

  42. 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

  43. 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

  44. 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.

  45. Self-Check 1 • How would you classify this situation? (a) not multilevel (b) 2-level (c) 3-level

  46. 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.

  47. Self-Check 2 • How would you classify this situation? (a) not multilevel (b) 2-level (c) 3-level

  48. 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.

  49. Self-Check 3 • How would you classify this situation? (a) not multilevel (b) 2-level (c) 3-level (Select ONLY one)

  50. Growth Curve Modeling • Studying the growth in reading achievement over a two year period • Studying changes in student attitudes over the middle school years