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These fit indices are called comparative curve fit indices (CCFIs). One interpretive heuristic that is routinely applied in research is as follows: CCFIs less than .400 indicate the research data are more similar to bootstrapped, simulated data with dimensional latent structure and CCFIs greater than .600 indicate the research data are more similar to bootstrapped, simulated data with taxonic latent structure (Ruscio & Kaczetow, 2009; Ruscio, Walters, Marcus, & Kaczetow, 2010). This is a conservative test. A more liberal, yet still accurate, test, and the one Longpré et al. used, is that CCFIs less than .450 and greater than .550 are interpreted as meaningful.
In MAMBAC, a peak emerges when a “cut” is made along one indicator to group the sample into two groups and this cut provides the optimal separation between the groups on a second indicator. Dichotomous latent structure will therefore produce a curve with a single peak, and dimensional latent structure will produce a U-shaped curve. Trichotomous structure will produce a twin-pealed curve, but shapes will vary depending on other characteristics of the data (see Fig. 1 in McGrath, 2008). In MAXEIG, a peak emerges when a “window” captures a mixture of taxon and complement members, resulting in a high rate of covariance between indicator scores. When a window captures purely complement class or taxon class members, the covariance is low or non-existent, so the eigenvalue is lower. Dimensional data result in U-shaped curves that indicate that there is not much change in eigenvalue, as the windows are capturing roughly equivalent amounts of covariance, with the exception of the leftmost and rightmost windows, causing the tails to rise. Depending on other data characteristics, such as indicator skew, trichotomous latent structure will produce variably shaped MAXEIG curves (see Fig. 3 in McGrath, 2008).
My experience with taxometric analyses and understanding the potential for trichotomous latent structure comes from doing this research.
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McPhail, I.V. Of Dimensions, Dichotomies, and Trichotomies: Comments on the Taxometric Ghost that Haunts Longpré, Guay, Knight, and Benbouriche (2018). Arch Sex Behav 49, 19–23 (2020). https://doi.org/10.1007/s10508-019-01530-y
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DOI: https://doi.org/10.1007/s10508-019-01530-y