MULTILEVEL MODELING

1
MULTILEVEL MODELING

• Multilevel what does it mean?
• Consider the following graph

L I K I N G
LO
HI
AGGRESSION
2
MULTILEVEL MODELING

• Each oval represents a classroom
• Each regression line has a b weight
• For a classroom,
• yi(j) b0j b1j xi(j) ei(j)
• but the regression weights also have a structure,
  for slopes
• b1j ?10 ?11Zj u1j

3
MULTILEVEL MODELING

• yi(j) b0j b1j xi(j) ei(j)
• And for intercepts,
• b0j ?00 ?01Zj u0j

4
MULTILEVEL MODELING

• So that by combining,
• yi(j) ?00 ?10Xi(j) ?01Zj
• ?11Xi(j) Zj
• u1jXi(j) u0j ei(j)

DETERMINISTIC or FIXED EFFECTS
STOCHASTIC or RANDOM EFFECTS
5
MULTILEVEL MODELING

• where ?00 common intercept,
• ?10Xi(j) 1st level aggression effect pooled
• ?01Zj second level slope (liking-aggression for
  classes)
• ?11Xi(j) Zj cross level interaction (classroom
  slope by level of classroom aggression)
• u1jXi(j) agression effect error
• u0j slope error, ei(j) individual error

6
MUTHEN PSEUDOBALANCED

• EQUAL SAMPLE SIZES ASSUMED
• ?T ?B ?w
• Swp pooled within groups
• SB Swp cSB
• C weight factor group sample size (or
  weighted average sample size)

7
MULTILEVEL ANALYSIS

• PROC MIXED IN SAS
• ANALYZES ALL REGRESSION-GLS BASED MODELS
• CANNOT ANALYZE CORRECTLY SEM
• POSSIBLE TO ANALYZE IN AMOS OR LISREL BUT NOT
  STRAIGHTFORWARD

8
ANALYSIS

• MUTHEN PSEUDOBALANCED
• AMOS OR LISREL
• TREAT B AND W COVARIANCE MATRICES AS SEPARATE
  GROUPS
• USE DEGREES OF FREEDOM ASSOCIATED WITH EACH

9
ANALYSIS

• SAStwo group modeling
• AMOS two group modeling
• MPLUS single group data with second level
  variables included

10
Mean Aggression-b
Mean Liking
n
n
Aggression
Liking
11
TWO GROUP MODELING
bB
Mean Aggression-b
Mean Liking
0/n
0/n
Aggression
Liking
bw