1. Multilevel analysis with EQS

2. Castello2004 Data is datamlevel.xls, datamlevel.sav, datamlevel.ess

6. /TITLE Single factor model for multilevel data /SPECIFICATIONS DATA='f:\seminarios sem\castello2004\datamlevel.ess'; VARIABLES=4; CASES=3609; GROUPS=2; METHOD=ML; ANALYSIS=COVARIANCE; MATRIX=RAW; MULTILEVEL=ML; CLUSTER=V1; /LABELS V1=SCHOOL; V2=EXAM1; V3=EXAM2; V4=EXAM3; /EQUATIONS V2 = *F1 + E2; V3 = *F1 + E3; V4 = *F1 + E4; /VARIANCES E2 = *; E3 = *; E4 = *; F1 =1; /COVARIANCES /END /TITLE Model built by EQS 6 for Windows in Group 2 /LABELS V1=SCHOOL; V2=EXAM1; V3=EXAM2; V4=EXAM3; /EQUATIONS V2 = *F1 + E2; V3 = *F1 + E3; V4 = *F1 + E4; /VARIANCES E2 = *; E3 = *; E4 = *; F1 = 1; /COVARIANCES /PRINT FIT=ALL; TABLE=EQUATION; /END

7. SIZE (S) CLUSTER ID WITH SIZE S 13 62 78 90 18 5 19 88 91 21 3 22 81 25 89 26 10 66 27 83 31 61 32 68 34 57 35 67 36 9 38 8 39 12 54 40 84 41 6 15 56 71 87 42 43 43 13 47 58 49 85 52 48 54 64 55 26 59 42 76 62 46 92 67 22 70 21 81 19 83 31 32 84 29 38 85 17 86 33 89 96 91 47 92 35 77 93 44 94 30 103 45 121 60 129 16 135 18 139 24 152 7 201 79 AVERAGE CLUSTER SIZE IS 61.169 ESTIMATED WITHIN-CLUSTERS COVARIANCE MATRIX FOR SATURATED MODEL EXAM1 EXAM2 EXAM3 V 2 V 3 V 4 EXAM1 V 2.501 EXAM2 V 3.523.698 EXAM3 V 4.504.640 1.073 ESTIMATED BETWEEN-CLUSTERS COVARIANCE MATRIX FOR SATURATED MODEL EXAM1 EXAM2 EXAM3 V 2 V 3 V 4 EXAM1 V 2.033 EXAM2 V 3.030.045 EXAM3 V 4.063.055.247

8. MULTI-LEVEL ANALYSIS: WITHIN-LEVEL MAXIMUM LIKELIHOOD SOLUTION (NORMAL DISTRIBUTION THEORY) MEASUREMENT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS STATISTICS SIGNIFICANT AT THE 5% LEVEL ARE MARKED WITH @. EXAM1 =V2 =.642*F1 + 1.000 E2.009 68.621@ EXAM2 =V3 =.815*F1 + 1.000 E3.011 77.356@ EXAM3 =V4 =.785*F1 + 1.000 E4.015 52.834@

9. E D --- --- E2 -EXAM1.089*I I.004 I I 23.560@I I I I E3 -EXAM2.034*I I.005 I I 6.690@I I I I E4 -EXAM3.457*I I.012 I I 38.944@I I I I STANDARDIZED SOLUTION: R-SQUARED EXAM1 =V2 =.907*F1 +.421 E2.823 EXAM2 =V3 =.975*F1 +.221 E3.951 EXAM3 =V4 =.758*F1 +.652 E4.574

10. MULTI-LEVEL ANALYSIS: BETWEEN-LEVEL MAXIMUM LIKELIHOOD SOLUTION (NORMAL DISTRIBUTION THEORY) MEASUREMENT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS STATISTICS SIGNIFICANT AT THE 5% LEVEL ARE MARKED WITH @. EXAM1 =V2 =.185*F1 +1.000 E2.020 9.204@ EXAM2 =V3 =.170*F1 +1.000 E3.027 6.193@ EXAM3 =V4 =.348*F1 +1.000 E4.057 6.079@

11. E D --- --- E2 -EXAM1.000*I I.152 I I.000 I I I I E3 -EXAM2.017*I I.003 I I 5.127@I I I I E4 -EXAM3.128*I I.024 I I 5.387@I I I I STANDARDIZED SOLUTION: R-SQUARED EXAM1 =V2 = 1.000*F1 +.000 E2 1.000 EXAM2 =V3 =.792*F1 +.611 E3.627 EXAM3 =V4 =.698*F1 +.717 E4.487

12. /TITLE Single factor model for multilevel data /SPECIFICATIONS DATA='f:\seminarios sem\castello2004\datamlevel.ess'; VARIABLES=4; CASES=3609; GROUPS=2; METHOD=ML; ANALYSIS=COVARIANCE; MATRIX=RAW; MULTILEVEL=ML; CLUSTER=V1; /LABELS V1=SCHOOL; V2=EXAM1; V3=EXAM2; V4=EXAM3; /EQUATIONS V2 = *F1 + E2; V3 = *F1 + E3; V4 = *F1 + E4; /VARIANCES E2 = *; E3 = *; E4 = *; F1 =1; /COVARIANCES /END /TITLE Model built by EQS 6 for Windows in Group 2 /LABELS V1=SCHOOL; V2=EXAM1; V3=EXAM2; V4=EXAM3; /EQUATIONS V2 = *F1 + E2; V3 = *F1 + E3; V4 = *F1 + E4; /VARIANCES E2 = *; E3 = *; E4 = *; F1 = 1; /COVARIANCES /CONSTRAINTS (2,V2,F1) = (2,V3,F1); /PRINT FIT=ALL; TABLE=EQUATION; /END

13. MULTI-LEVEL ANALYSIS: WITHIN-LEVEL MAXIMUM LIKELIHOOD SOLUTION (NORMAL DISTRIBUTION THEORY) EXAM1 =V2 =.642*F1 + 1.000 E2.009 68.612@ EXAM2 =V3 =.815*F1 + 1.000 E3.011 77.357@ EXAM3 =V4 =.785*F1 + 1.000 E4.015 52.832@

14. E D --- --- E2 -EXAM1.089*I I.004 I I 23.550@I I I I E3 -EXAM2.034*I I.005 I I 6.696@I I I I E4 -EXAM3.457*I I.012 I I 38.944@I I I I STANDARDIZED SOLUTION: R-SQUARED EXAM1 =V2 =.907*F1 +.421 E2.823 EXAM2 =V3 =.975*F1 +.221 E3.951 EXAM3 =V4 =.758*F1 +.653 E4.574

15. MULTI-LEVEL ANALYSIS: BETWEEN-LEVEL MAXIMUM LIKELIHOOD SOLUTION (NORMAL DISTRIBUTION THEORY) MEASUREMENT EQUATIONS WITH STANDARD ERRORS AND TEST STATISTICS STATISTICS SIGNIFICANT AT THE 5% LEVEL ARE MARKED WITH @. EXAM1 =V2 =.184*F1 +1.000 E2.021 8.550@ EXAM2 =V3 =.184*F1 +1.000 E3.021 8.550@ EXAM3 =V4 =.354*F1 +1.000 E4.059 6.026@

16. E D --- --- E2 -EXAM1.001*I I.003 I I.210 I I I I E3 -EXAM2.017*I I.004 I I 4.099@I I I I E4 -EXAM3.127*I I.025 I I 5.024@I I I I STANDARDIZED SOLUTION: R-SQUARED EXAM1 =V2 =.992*F1 +.126 E2.984 EXAM2 =V3 =.816*F1 +.577 E3.667 EXAM3 =V4 =.705*F1 +.710 E4.496

17. GOODNESS OF FIT SUMMARY FOR METHOD = ML INDEPENDENCE MODEL CHI-SQUARE = 8640.064 ON 6 DEGREES OF FREEDOM INDEPENDENCE AIC = 8628.06354 INDEPENDENCE CAIC = 8584.91642 MODEL AIC = -1.40119 MODEL CAIC = -8.59238 BENTLER-LIANG LIKELIHOOD RATIO STATISTIC =.599 BASED ON 1 D.F. PROBABILITY VALUE FOR THE CHI-SQUARE STATISTIC IS.43903