Structural Equation Modeling for Analyzing Erythrocyte Fatty Acids in Framingham

Table 2

Goodness-of-fit for testing gender invariance (among 13 fatty acids).

Model constraint; (𝑁=3196)	Absolute fit					Relative fit
	𝜒^2/DF^†	𝜒^2; Scaling	SRMSR	SBC	RMSEA; upper; 90% limit	CFI	TLI
M0: unrestricted by gender	1900/84	1.079	0.035	100055	0.121	0.888	0.791
M1: equal fatty acid means, 𝝂	2409/97	1.071	0.056	100480	0.126	0.857	0.770
M2: equal loadings, 𝚲	1965/114	1.097	0.040	99919	0.105	0.885	0.843
M3: equal unique Variances, 𝚯	1673/97	1.255	0.036	99999	0.105	0.902	0.843
M4: equal loadings and latent covariances, 𝚲,𝚿	1986/120	1.105	0.048	99909	0.102	0.884	0.850
M5: equal fatty acid covariance matrix, 𝚺	1793/133	1.251	0.050	99853	0.092	0.897	0.879
M6: SEM model	968.8/107	1.217	0.046	98999	0.075	0.947	0.922
M7: reduced SEM M6	967.5/111	1.225	0.046	98972	0.074	0.947	0.925

†The total degrees of freedom (DF) = 2 * (91 fatty acid variances/covariances + 13 fatty acid means) = 208 parameters in all models; hence, the number of estimated parameters equals 208−𝑋² DF; SRMSR = standardized root mean square residual; SBC = Schwarz Bayesian criteria; RMSEA = root mean square error of approximation; CFI = Bentler Comparative Fit Index; TLI = Tucker-Lewis Index.