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Table 4 Model fit indices for all five competing exploratory Multidimensional Graded Response (MGR) models

From: How different domains of quality of life are associated with latent dimensions of mental health measured by GHQ-12

MGR Model

\({\chi }^{2}\)

df

RMSEA (90% CI)

SRMSR

TLI

CFI

Log-likelihood

AIC

AICc

BIC

SABIC

1

193.40

30

0.064 (0.056, 0.073)

0.157

0.967

0.977

 − 13,033.42

26,162.85

26,166.56

26,411.6

26,259.13

2

100.46

18

0.059 (0.048, 0.071)

0.036

0.972

0.988

 − 11,829.06

23,778.11

23,783.95

24,089.05

23,898.46

3

66.87

19

0.044 (0.033, 0.055)

0.046

0.985

0.993

 − 12,006.31

24,130.63

24,136.27

24,436.39

24,248.97

4

40.27

9

0.051 (0.036, 0.068)

0.033

0.979

0.996

 − 11,886.86

23,911.72

23,919.47

24,269.3

24,050.12

5

107.13

24

0.051 (0.042, 0.061)

0.028

0.984

0.994

 − 11,826

23,807.99

23,817.95

24,212.21

23,964.44

  1. df degree of freedom, RMSEA root mean squared error approximation, CI confidence interval, SRMSR Standardized Root Mean Square Residuals, TLI Tucker–Lewis Index, CFI Comparative Fit Index, AIC Akaike Information Criterion, BIC Bayesian Information Criterion, AICc corrected AIC, SABIC sample-Size Adjusted BIC; Model 1: one-dimensional model; Model 2: Bifactor model; Model3: two-dimensional model; Model 4: three-dimensional model; Model 5: four-dimensional model