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Table 1 Model fit

From: A comparison of three approaches to covariate effects on latent factors

Model

# Free parameters

Chi-square value

Chi-square scale factor

Chi-square DF

Chi-square p-value

CFI

TLI

RMSEA estimate

90% CI RMSEA

RMSEA p-value

SRMR

1. Single-factor CFA

21

931.68

2.85

14

< 0.001

0.879

0.819

0.090

0.085

0.095

< 0.001

0.062

2. Single-factor CFA with Correlated Residuals

24

91.97

2.50

11

< 0.001

0.989

0.980

0.030

0.025

0.036

1.000

0.019

3. MIMIC Model

32

553.43

1.73

59

< 0.001

0.963

0.951

0.032

0.030

0.035

1.000

0.028

4. Multiple Group Measurement Invariance—Student Sex

 4a. Configural Invariance Model

48

133.62

2.11

22

< 0.001

0.986

0.973

0.035

0.030

0.041

1.000

0.021

 4b. Metric Model

42

135.36

2.37

28

< 0.001

0.987

0.980

0.031

0.026

0.036

1.000

0.031

 4c. Scalar Model

36

228.70

2.22

34

< 0.001

0.976

0.970

0.037

0.033

0.042

1.000

0.043

5. Multiple Group Measurement Invariance—Language At Home

 5a. Configural Invariance Model

48

1.94

126.03

22

< 0.001

0.990

0.980

0.034

0.029

0.040

1.000

0.019

 5b. Metric Model

42

1.83

138.77

28

< 0.001

0.989

0.983

0.031

0.026

0.037

1.000

0.023

 5c. Scalar Model

36

1.74

163.93

34

< 0.001

0.987

0.984

0.031

0.026

0.036

1.000

0.024

6. Multiple Group Measurement Invariance—Home Resources

 6a. Configural Invariance Model

72

2.02

139.50

33

< 0.001

0.990

0.980

0.035

0.029

0.041

1.000

0.020

 6b. Metric Model

60

1.85

190.56

45

< 0.001

0.986

0.980

0.035

0.030

0.040

1.000

0.042

 6c. Scalar Model

48

1.75

240.19

57

< 0.001

0.982

0.980

0.035

0.030

0.039

1.000

0.042

7. Multiple Group Measurement Invariance—Achievement Category

 7a. Configural Invariance Model

120

1.66

213.79

55

< 0.001

0.984

0.969

0.042

0.036

0.048

0.986

0.021

 7b. Metric Model

96

1.79

537.53

79

< 0.001

0.954

0.939

0.060

0.055

0.064

< 0.001

0.107

 7c. Scalar Model

72

1.76

825.92

103

< 0.001

0.927

0.926

0.066

0.061

0.070

< 0.001

0.115

  1. The estimator used was MLR. All models except Model 1 had correlated residuals among the three negatively worded indicators. Correlated residuals were not constrained to be equal across groups in multiple group analysis. In all models, the first factor loading was fixed to 1 to identify the latent factor in each group. For configural invariance and metric invariance models, the latent factor mean was fixed to 0 and the latent factor variance was free in all groups. For scalar invariance models, the latent factor mean for the reference group was fixed to 0 and was free for the other groups; the latent factor variance was free in all groups. CFI = comparative fit index; TLI = Tucker–Lewis index; RMSEA = root mean square error of approximation; SRMR = standardized root mean square residual