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
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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
1.Overview
2.Application #1: Growth Modeling
Break
3.Application # 2: Individuals Nested Within Groups
4.Questions?
SAS Mixed
Multilevel Question
School Size
Classroom Climate
Student Gender
Nested Data Structures
Individuals Undivided
Unit of Analysis = Individuals
Unit of Analysis = Individuals + Classes
Unit of Analysis = Individuals + Classes + Schools
Level 4 District (l)
Level 3 School (k)
Level 2 Class (j)
Level 1 Student (i)
Focus = Change or Growth
Carlos
DayEnergy Level
Monday = 098
Tuesday = 190
Wednes. = 285
Thursday = 372
Friday= 470
Focus is not on change
Focus in on relationships between variables within an individual
Carlos
DayHours of SleepEnergy Level
Monday998
Tuesday890
Wednesday885
Thursday672
Friday770
Level 2 Student (i)
Level 1 Repeated Measures
Over Time (t)
0 (very independent) to 1.0 (very dependent)
Details discussed later
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
Extension of General Linear Modeling
Simple Linear Regression
Multiple Linear Regression
ANOVA
ANCOVA
Repeated Measures ANOVA
Traditional Approaches – 1-Level
Violation of independence of data assumption leading to misestimated standard errors (standard errors are smaller than they should be).
(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)
Quantitative
Experimental
*Nonexperimental
(Survey, Observational)
2 or 3 levels very common
15 students x 10 classes x 10 schools
= 1,500
SPSS Users
2 SAV Files: Level 1
Level 2
HLM 6 (Menu Driven)
(Raudenbush, Bryk, Cheong, & Congdon, 2004)
SAS Users
Proc Mixed
Kreft & DeLeeum, 1998.
(a) not multilevel
(b) 2-level
(c) 3-level
(a) not multilevel
(b) 2-level
(c) 3-level
(a) not multilevel
(b) 2-level
(c) 3-level
(Select ONLY one)
Rise
Run
Examples
Example: Students observed
A researcher was interested in changes in verbal fluency of 4th grade students, and differences in the changes between boys and girls.
IDGender Time______
t0 t4 t7
1 0 20 30 30
2 0 40 44 49
30 45 40 60
4 0 50 55 59
5 0 42 48 53
61 45 52 61
71 39 55 63
81 46 58 68
91 44 49 59
procmixed covtest;
class gender;
model score = time gender time*gender/s;
random intercept / sub=student s;
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
Intercept Student 62.5125 35.9682 1.74 0.0411
Residual 14.1173 4.9912 2.83 0.0023
Solution for Fixed Effects
Standard
Effect Gender Estimate Error DF t Value Pr > |t|
Intercept 39.8103 3.7975 7 10.48 <.0001
time 1.5077 0.3295 16 4.58 0.0003
Gender F 5.7090 5.6962 16 1.00 0.3311
Gender M 0 . . . .
time*Gender F 1.0692 0.4943 16 2.16 0.0460
time*Gender M 0 . . . .
intercept