Appendix

This Appendix contains the LISREL Input Script for the analyses reported in:

FangFang Chen, Karen H. Sousa, and Stephen G. West (in press). Testing measurement invariance of a second-order factor model: An illustration using a measure of quality of life. Structural Equation Modeling: A multidisciplinary journal, xx, xxx-xxx.

Title: Model 1 Configural Invariance

Working Group

DA NG=2 NI=17 MA=CM

RA FI=Present.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=fu,fi GA=fi,fu ps=di,fr te=di,fr cn

TY=fr AL=fr KA=fi

QOL

Cogni Vitali MenHeal DisWorry

fr ly(2 1) ly(3 1) ly(4 1) ly(5 1)

fr ly(7 2) ly(8 2) ly(9 2)

fr ly(11 3) ly(12 3) ly(13 3) ly(14 3)

fr ly(16 4) ly(17 4)

va 1.0 ly(1 1) ly(6 2) ly(10 3) ly(15 4)

FR GA(2 1) GA(3 1) GA(4 1)

va 1.0 GA(1 1)

fi ty 1 ty 6 ty 10 ty 15

ou sc mi ad=off

Non-Working Group

DA NG=2 NI=17 MA=CM

RA FI=Absent.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=fu,fi GA=fi,fu ps=di,fr te=di,fr cn

TY=fr AL=fr KA=fi

QOL

Cogni Vitali MenHeal DisWorry

fr ly(2 1) ly(3 1) ly(4 1) ly(5 1)

fr ly(7 2) ly(8 2) ly(9 2)

fr ly(11 3) ly(12 3) ly(13 3) ly(14 3)

fr ly(16 4) ly(17 4)

va 1.0 ly(1 1) ly(6 2) ly(10 3) ly(15 4)

FR GA(2 1) GA(3 1) GA(4 1)

va 1.0 GA(1 1)

fi ty 1 ty 6 ty 10 ty 15

ou sc mi ad=off

Note. The four first-order factors are defined as endogenous latent variables (LE), and LYs are used to define the lower-order factor loadings; whereas the second-order factor are defined as an exogenous variable (LK), and GAs are used to defined the second-order factor loadings.

The first factor loading of each factor is set to 1, and the variance of that factor is estimated; if an observed variable’s factor loading is set to 1, that variable’s intercept is set to 0. The second-order factor mean is set to 0, and intercepts of the lower-order factors are estimated.

'diffeas' – difficulty in reasoning; 'sloract' – slow in reacting; 'confsed' – confused; 'diffconc' – difficulty in concentrating; 'enrgtic' – energetic; 'wornout' – worn out;

''frust’ – frustrated; 'hlthwry' – worry about health.

QOL - Quality of Life ; Cogni – Cognition ; Vitali – Vitality ; MenHeal – Mental Health ; DisWorry – Disease Worry.

Title: Model 2 Invariance of First-Order Factor Loadings

Working Group

DA NG=2 NI=17 MA=CM

RA FI=Present.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=fu,fi GA=fi,fu ps=di,fr te=di,fr cn

TY=fr AL=fr KA=fi

QOL

Cogni Vitali MenHeal DisWorry

fr ly(2 1) ly(3 1) ly(4 1) ly(5 1)

fr ly(7 2) ly(8 2) ly(9 2)

fr ly(11 3) ly(12 3) ly(13 3) ly(14 3)

fr ly(16 4) ly(17 4)

va 1.0 ly(1 1) ly(6 2) ly(10 3) ly(15 4)

FR GA(2 1) GA(3 1) GA(4 1)

va 1.0 GA(1 1)

fi ty 1 ty 6 ty 10 ty 15

ou sc mi ad=off

Non-Working Group

DA NI=17 MA=CM

RA FI=Absent.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry' se

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=IN GA=fi,fu ps=di,fr te=di,fr cn

TY=fr AL=fr KA=fi

QOL

Cogni Vitali MenHeal DisWorry

FR GA(2 1) GA(3 1) GA(4 1)

va 1.0 GA(1 1)

fi ty 1 ty 6 ty 10 ty 15

ou sc mi ad=off

Title: Model 3 Invariance of First-Order and Second-Order Factor Loading Invariance

Working Group

DA NG=2 NI=17 MA=CM

RA FI=Present.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=fu,fi GA=fi,fu ps=di,fr te=di,fr cn

TY=fr AL=fr KA=fi

QOL

Cogni Vitali MenHeal DisWorry

fr ly(2 1) ly(3 1) ly(4 1) ly(5 1)

fr ly(7 2) ly(8 2) ly(9 2)

fr ly(11 3) ly(12 3) ly(13 3) ly(14 3)

fr ly(16 4) ly(17 4)

va 1.0 ly(1 1) ly(6 2) ly(10 3) ly(15 4)

FR GA(2 1) GA(3 1) GA(4 1)

va 1.0 GA(1 1)

fi KA(1)

fi ty 1 ty 6 ty 10 ty 15

ou sc mi ad=off

Non-Working Group

DA NI=17 MA=CM

RA FI=Absent.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=IN GA=IN ps=di,fr te=di,fr cn

TY=fr AL=fr KA=fi

QOL

Cogni Vitali MenHeal DisWorry

fi KA(1)

fi ty 1 ty 6 ty 10 ty 15

ou sc mi ad=off

Title: Model 4 Invariance of First- and Second-Order Factor loadings and Intercepts of Observed Variables

Working Group

DA NG=2 NI=17 MA=CM

RA FI=Present.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=fu,fi GA=fi,fu ps=di,fr te=di,fr cn

TY=fr AL=fr KA=fi

QOL

Cogni Vitali MenHeal DisWorry

fr ly(2 1) ly(3 1) ly(4 1) ly(5 1)

fr ly(7 2) ly(8 2) ly(9 2)

fr ly(11 3) ly(12 3) ly(13 3) ly(14 3)

fr ly(16 4) ly(17 4)

va 1.0 ly(1 1) ly(6 2) ly(10 3) ly(15 4)

FR GA(2 1) GA(3 1) GA(4 1)

va 1.0 GA(1 1)

fi ty 1 ty 6 ty 10 ty 15

ou sc ad=off

Non-Working Group

DA NI=17 MA=CM

RA FI=Absent.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=IN GA=IN ps=di,fr te=di,fr cn

TY=IN AL=fr KA=fi

QOL

Cogni Vitali MenHeal DisWorry

ou sc ad=off

Title: Model 5 Invariance of First- and Second-Order Factor Loadings, and Intercepts of Observed Variables and First-Order Factor Loadings

Working Group

DA NG=2 NI=17 MA=CM

RA FI=Present.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=fu,fi GA=fi,fu ps=di,fr te=di,fr cn

TY=fr AL=fr KA=fi

QOL

Cogni Vitali MenHeal DisWorry

fr ly(2 1) ly(3 1) ly(4 1) ly(5 1)

fr ly(7 2) ly(8 2) ly(9 2)

fr ly(11 3) ly(12 3) ly(13 3) ly(14 3)

fr ly(16 4) ly(17 4)

va 1.0 ly(1 1) ly(6 2) ly(10 3) ly(15 4)

FR GA(2 1) GA(3 1) GA(4 1)

va 1.0 GA(1 1)

fi ty 1 ty 6 ty 10 ty 15

ou sc ad=off

Non-Working Group

DA NI=17 MA=CM

RA FI=Absent.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=IN GA=IN ps=di,fr te=di,fr cn

TY=IN AL=IN KA=fr

QOL

Cogni Vitali MenHeal DisWorry

ou sc ad=off

Title: Model 6 Invariance of First- and Second-Order Factor Loadings, Intercepts of Observed Variables and First-Order Factor Loadings, and Disturbance of First-Order Factors

Working Group

DA NG=2 NI=17 MA=CM

RA FI=Present.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=fu,fi GA=fi,fu ps=di,fr te=di,fr cn

TY=fr AL=fr KA=fi

QOL

Cogni Vitali MenHeal DisWorry

fr ly(2 1) ly(3 1) ly(4 1) ly(5 1)

fr ly(7 2) ly(8 2) ly(9 2)

fr ly(11 3) ly(12 3) ly(13 3) ly(14 3)

fr ly(16 4) ly(17 4)

va 1.0 ly(1 1) ly(6 2) ly(10 3) ly(15 4)

FR GA(2 1) GA(3 1) GA(4 1)

va 1.0 GA(1 1)

fi ty 1 ty 6 ty 10 ty 15

ou sc mi ad=off

Non-Working Group

DA NI=17 MA=CM

RA FI=Absent.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=IN GA=IN ps=IN te=di,fr cn

TY=IN AL=IN KA=fr

QOL

Cogni Vitali MenHeal DisWorry

fi ty 1 ty 6 ty 10 ty 15

ou sc mi ad=off

Title: Model 7 Invariance of First- and Second-Order Factor Loadings, Intercepts of Observed Variables and First-Order Factor Loadings, Disturbance of First-Order Factors, and Residual Variance

Working Group

DA NG=2 NI=17 MA=CM

RA FI=Present.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=fu,fi GA=fi,fu ps=di,fr te=di,fr cn

TY=fr AL=fr KA=fi

QOL

Cogni Vitali MenHeal DisWorry

fr ly(2 1) ly(3 1) ly(4 1) ly(5 1)

fr ly(7 2) ly(8 2) ly(9 2)

fr ly(11 3) ly(12 3) ly(13 3) ly(14 3)

fr ly(16 4) ly(17 4)

va 1.0 ly(1 1) ly(6 2) ly(10 3) ly(15 4)

FR GA(2 1) GA(3 1) GA(4 1)

va 1.0 GA(1 1)

fi ty 1 ty 6 ty 10 ty 15

ou sc mi ad=off

Non-Working Group

DA NI=17 MA=CM

RA FI=Absent.dat

'diffeas' 'sloract' 'confsed' 'forget' 'diffconc' 'tired' 'enrgtic' 'wornout' 'peppy'

'atpeace' 'feelblue' 'happy' 'nervous' 'down' 'afraid' 'frust' 'hlthwry'

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17/

mo ny=17 nk=1 ne=4 ly=IN GA=IN ps=IN te=IN cn

TY=IN AL=IN KA=fr

QOL

Cogni Vitali MenHeal DisWorry

ou sc mi ad=off