The Vanishing Tetrad Test: Another Test of Model Misspecification

Click to increase image sizeClick to decrease image size

Notes

¹ The SBIC is also often referred to as the BIC, and it is calculated here using the formula from Raftery (1986), substituting the term χ2 for L2, though their meaning in this formula is identical.

² χ2 - df*ln(n), where df = the degrees of freedom for the chi-square test statistic, χ2 = the chi-square test statistic itself, and n = the sample size.

³ Bollen and Bauldry (2011, p. 8) note in footnote 9 that in some cases in which factor complexity is greater than 1, it is possible for effect indicators to be unassociated, though the authors note it is rare for this to occur.

⁴ It is unclear whether the sample size and model complexity adjustments of the SBIC are appropriate in cases in which the sample size is smaller than 200. In such cases the significance of the χ2 statistic alone may be a better signal of poor model fit.