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. 2010 Feb;47(1):125–144. doi: 10.1353/dem.0.0090

Table 4.

Tests of Model Fit for Models Depicted in Figures 2 and 3 and Nested Models

Model Chi-squarea df p Value Scaled Correction Factor (c) for MLMb SRMRc CFId Chi-Square Difference Test TRde (df)
Model in Figure 2: Paths mediated through adolescent pre-pregnancy BMI and schooling 50.0 111 1.0 2.8 0.025 1.0 Full model
Nested model 2a: Path mediated through BMI (excludes paths from schooling to fertility outcomes) 110.2 116 .6 2.75 0.06 1.0 99.6* (5)
Nested model 2b: Path mediated through schooling (excludes paths from BMI to fertility outcomes) 129.9 121 .3 2.7 0.08 .9 132.7* (5)
Nested model 2c: Path mediated through BMI (excludes path from z24 to schooling) 60.0 116 .0 2.7 0.03 1.0 46.4* (10)
Nested model 2d: Path mediated through schooling (excludes paths from z24 BMI) 62.7 116 .0 2.7 0.03 1.0 61.6* (5)
Model in Figure 3: Paths through adolescent pre-pregnant height and schooling 50.0 111 1.0 2.9 0.02 1.0 Full model
Nested model 3a: Path mediated through height (excludes path from schooling to fertility outcomes) 116.6 116 .5 2.8 0.06 1.0 312.9* (5)
Nested model 3b: Path mediated through grades of schooling (excludes path from height to fertility outcomes) 117.7 121 .6 2.7 0.08 .9 360.0* (10)
Nested model 3c: Path mediated through height (excludes path from z24 to schooling) 59.9 116 1.0 2.8 0.03 1.0 39.2* (5)
Nested model 3d: Path mediated through schooling (excludes path from z24 to height) 174.2 116 < .01 2.8 0.05 0.9 591.0* (5)
a

Chi-square is based on MLM estimator.

b

The scaled correction factor (c) is multiplied with the chi-square for the MLM estimator (above) to get chi-square for ML estimator.

c

Standardized root mean square residual (SRMR) is the average difference between the predicted and observed variances and covariances in the model, based on standardized residuals. SRMR is 0 when the model fit is perfect; SRMR < 0.05 is considered a good fit.

d

Comparative fit index (CFI) compares the existing model fit with a null model to gauge the percent of lack of fit which is accounted for by going from the null model to the researcher’s SEM model. CFI is among the measures least affected by sample size (Fan, Thompson, and Wang 1999). CFI varies from 0 to 1. A CFI close to 1 indicates a very good fit. CFI should be equal to or greater than .90 to accept the model.

e

Satorra-Bentler scaled chi-square difference test comparing models depicted in Figures 2 and 3 with nested models. TRd = (ML chi-square for nested model – ML chi-square for full model) / cd, where cd (chi-square difference scaling correction) = (df for nested model × c for nested model – df for full model × c for full model) / df for nested model – df for full model.

*

p < .01