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Table 3 Tests for Factorial Invariance of the Four Models across Different Age Groups: Goodness-of-Fit Statistics

From: Cross-cultural, age and gender validation of a computerised questionnaire measuring personal, social and environmental associations with children's physical activity: the European Youth Heart Study

Model

S-B χ2

Df

CFIa

Changes in CFIa

RMSEA (90%CI)a

SRMRa

Enjoyment-Competence Model

      

   1: Configual model

138.11

30

0.95

 

0.05(0.04–0.06)

0.03

   2: Measurement model

177.06

37

0.93

0.02

0.05(0.04–0.06)

0.04

   Partial measurement modelb

152.00

34

0.94

0.01

0.05(0.04–0.06)

0.04

   3. Structural model

151.80

35

0.94

0.01

0.05(0.04–0.06)

0.04

Outcome expectation Model

      

   1: Configual model

148.87

49

0.95

 

0.04(0.03–0.05)

0.03

   2: Measurement model

206.11

56

0.92

0.03

0.04(0.04–0.05)

0.05

Partial measurement modelc

172.05

54

0.94

0.01

0.04(0.03–0.05)

0.04

   3. Structural model

196.65

55

0.93

0.02

0.04(0.04–0.05)

0.05

Social Support Model

      

   1: Configual model

249.55

76

0.97

 

0.04(0.04–0.05)

0.03

   2: Measurement model

296.44

83

0.96

0.01

0.04(0.04–0.05)

0.04

Partial measurement modeld

253.31

81

0.97

0.00

0.04(0.03–0.04)

0.03

   3. Structural model

281.42

87

0.96

0.01

0.04(0.04–0.05)

0.05

Environment Model

      

   1: Configual model

54.93

20

0.97

 

0.04(0.02–0.05)

0.03

   2: Measurement model

72.25

24

0.96

0.01

0.04(0.03–0.05)

0.03

Partial measurement modele

68.13

23

0.96

0.01

0.04(0.03–0.05)

0.03

   3. Structural model

104.83

26

0.94

0.03

0.05(0.04–0.06)

0.03

  1. Based on the univariate χ2 incremental values (p < 0.05)
  2. a: The cut-off points of model fit: CFI greater than .90, Changes in CFI equal or less than 0.01, the point estimate of RMSEA less than 0.05 and the 90%CI of RMSEA less than 0.08, SRMR less than 0.08.
  3. b: Equality constraints related to item Enjoy3 and item Enjoy5 were removed sequentially
  4. c: Equality constraints related to item Socbel3 and item Socbel4 were removed sequentially
  5. d: Equality constraints related to item Parsupp3 and item Teacher2 were removed sequentially
  6. e: Equality constraints related to item Opp2 were removed