Multilevel analysis with EQS

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

/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

SIZE (S) CLUSTER ID WITH SIZE S AVERAGE CLUSTER SIZE IS ESTIMATED WITHIN-CLUSTERS COVARIANCE MATRIX FOR SATURATED MODEL EXAM1 EXAM2 EXAM3 V 2 V 3 V 4 EXAM1 V EXAM2 V EXAM3 V ESTIMATED BETWEEN-CLUSTERS COVARIANCE MATRIX FOR SATURATED MODEL EXAM1 EXAM2 EXAM3 V 2 V 3 V 4 EXAM1 V EXAM2 V EXAM3 V

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 EXAM1 =V2 =.642*F E2.009 EXAM2 =V3 =.815*F E3.011 EXAM3 =V4 =.785*F E4.015

E D E2 -EXAM1.089*I I.004 I I I I I E3 -EXAM2.034*I I.005 I I I I I E4 -EXAM3.457*I I.012 I I I I I STANDARDIZED SOLUTION: R-SQUARED EXAM1 =V2 =.907*F E2.823 EXAM2 =V3 =.975*F E3.951 EXAM3 =V4 =.758*F E4.574

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 EXAM1 =V2 =.185*F E2.020 EXAM2 =V3 =.170*F E3.027 EXAM3 =V4 =.348*F E4.057

E D E2 -EXAM1.000*I I.152 I I.000 I I I I E3 -EXAM2.017*I I.003 I I I I I E4 -EXAM3.128*I I.024 I I I I I STANDARDIZED SOLUTION: R-SQUARED EXAM1 =V2 = 1.000*F E EXAM2 =V3 =.792*F E3.627 EXAM3 =V4 =.698*F E4.487

/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

MULTI-LEVEL ANALYSIS: WITHIN-LEVEL MAXIMUM LIKELIHOOD SOLUTION (NORMAL DISTRIBUTION THEORY) EXAM1 =V2 =.642*F E2.009 EXAM2 =V3 =.815*F E3.011 EXAM3 =V4 =.785*F E4.015

E D E2 -EXAM1.089*I I.004 I I I I I E3 -EXAM2.034*I I.005 I I I I I E4 -EXAM3.457*I I.012 I I I I I STANDARDIZED SOLUTION: R-SQUARED EXAM1 =V2 =.907*F E2.823 EXAM2 =V3 =.975*F E3.951 EXAM3 =V4 =.758*F E4.574

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 EXAM1 =V2 =.184*F E2.021 EXAM2 =V3 =.184*F E3.021 EXAM3 =V4 =.354*F E4.059

E D E2 -EXAM1.001*I I.003 I I.210 I I I I E3 -EXAM2.017*I I.004 I I I I I E4 -EXAM3.127*I I.025 I I I I I STANDARDIZED SOLUTION: R-SQUARED EXAM1 =V2 =.992*F E2.984 EXAM2 =V3 =.816*F E3.667 EXAM3 =V4 =.705*F E4.496

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