! Factorial invariance and multi-sample analyses ! Example 9.1 from the Lisrel 7/8 User's Guides ! ! Because we are running several models, we put the input labels ! and covariance matrices in a separate file. For each pair ! of models, we specify REwind on the CM statement to get Lisrel ! to start over. ! ! --------------- Hypothesis A: Equal Covariance matrices -------- LISREL EX 12: Equality OF COVARIANCE MATRIX: Hypothesis A (Group A) DAta NGroup=2 NI=4 NObs=373 LAbels file=lisrel12.dat CMatrix file=lisrel12.dat ! To test the hypothesis of equal covariance matrices, set ! PHI=FRee in the first group, and PHI=INvariant in the second ! along with LX=ID and TD=ZEro, so that Sigma = PHI MOdel NX=4 NKSI=4 PHI=FRee LX=IDENTITY TD=ZEro OUtput LISREL EX 12: Equality OF COVARIANCE MATRIX: Hypothesis A (Group N-A) DAta NObs=249 LAbels file=lisrel12.dat CMatrix file=lisrel12.dat REwind MOdel PHI=INvariant OUtput ! --------- Hypothesis B: Two common factors for each group -------- LISREL EX12: 2 CORRELATED FACTORS: Hypothesis B (Group A) DAta NGroup=2 NI=4 NObs=373 LAbels file=lisrel12.dat CMatrix file=lisrel12.dat MOdel NX=4 NKSI=2 ! Two non-overlapping factors, for Grade 5 and Grade 7. We specify ! the pattern as 1 free parameter and one fixed parameter in each column FRee LX(2,1) LX(4,2) STart 1 LX(1,1) LX(3,2) OUtput LISREL EX12: 2 CORRELATED FACTORS: Hypothesis B (Group N-A) DAta NObs=249 LAbels file=lisrel12.dat CMatrix file=lisrel12.dat REwind ! LX=PS means same pattern and starting values as in previous group ! but loadings are not constrained to be equal MOdel LX=PS OUtput ! --------- Hypothesis C: Equal factor loadings for each group -------- LISREL EX12: Equality OF LAMBDA X : Hypothesis C (Group A) DAta NGroup=2 NI=4 NObs=373 LAbels file=lisrel12.dat CMatrix file=lisrel12.dat MOdel NX=4 NKSI=2 FRee LX(2,1) LX(4,2) STart 1 LX(1,1) LX(3,2) OUtput LISREL EX12: Equality OF LAMBDA X : Hypothesis C (Group N-A) DAta NObs=249 LAbels file=lisrel12.dat CMatrix file=lisrel12.dat REwind ! Constrain Lambda-X to be the same as in Group A MOdel LX=INvariant OUtput ! --------- Hypothesis D: Equal factor loadings and error variances -------- LISREL EX12: Equality OF LAMBDA X & THETA: Hypothesis D (Group A) DAta NGroup=2 NI=4 NObs=373 LAbels file=lisrel12.dat CMatrix file=lisrel12.dat MOdel NX=4 NKSI=2 ! Same as model C FRee LX(2,1) LX(4,2) STart 1 LX(1,1) LX(3,2) OUtput LISREL EX12: Equality OF LAMBDA X & THETA: Hypothesis D (Group N-A) DAta NObs=249 LAbels file=lisrel12.dat CMatrix file=lisrel12.dat REwind ! Constrain Lambda-X and Theta-Delta to be the same as in Group A MOdel LX=INvariant TD=INvariant OUtput ! --------- Hypothesis E: Equal loadings, error variances & factor correlations -------- LISREL EX12: Equality OF LAMBDA, PHI & THETA: Hypothesis E (Group A) DAta NGroup=2 NI=4 NObs=373 LAbels file=lisrel12.dat CMatrix file=lisrel12.dat MOdel NX=4 NKSI=2 ! Same as model C FRee LX(2,1) LX(4,2) STart 1 LX(1,1) LX(3,2) OUtput LISREL EX12: Equality OF LAMBDA, PHI & THETA: Hypothesis E (Group N-A) DAta NObs=249 LAbels file=lisrel12.dat CMatrix file=lisrel12.dat REwind MOdel LX=INvariant PHI=INvariant TD=INvariant OUtput