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MULTILEVEL MODELING

MULTILEVEL MODELING. Multilevel: what does it mean? Consider the following graph:. L I K I N G. LO. HI. AGGRESSION. MULTILEVEL MODELING. Each oval represents a classroom Each regression line has a b weight For a classroom, y i(j) = b 0j +b 1j x i(j) + e i(j)

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MULTILEVEL MODELING

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  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 • SAS:two 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

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