*I am interested in examining the role of three variables (family drug use, family conflict and family bonding) as mediators of the effect of neighborhood disorganization on adolescent drug use. I fit a structural equation model, but wonder which of the many fit statistics I should report?* — Signed, Befuddled by Fit

Dear Befuddled,

Generally, in structural equation modeling you should report several fit indices rather than only one. More specifically, simulation studies have shown that the Relative Normed Index and the Comparative Fit Index are both essentially unbiased (that is, they correctly estimate what the fit would be if the model were fit to the whole population).

Coffman (2008) found that the RMSEA was biased in most conditions; specifically, she found that this fit statistic underestimated the population value, which means that investigators would be more likely to conclude that their model fits when in some cases it does not. However, she found that the RMSEA confidence interval maintained 95% coverage, which is a very desirable characteristic. In other words, she found in a simulation study that roughly 95/100 times the RMSEA confidence interval contained the true population value of the RMSEA. This means that the Type I error rate based on the confidence intervals matched the specified alpha of .05. In addition, both the test of exact fit (i.e. RMSEA = 0) and the test of close fit (e.g. RMSEA < .05) based on these confidence intervals worked well in terms of Type I error rates and power.

Based on these findings, I recommend reporting either the Relative Normed Index or the Comparative Fit Index (since these two indices are quite similar), along with the RMSEA confidence interval, noting its width and the upper bound of the interval.

Coffman, D.L. (2008). Model misspecification in covariance structure models: Some implications for power and Type I error. *Methodology, 4*(4), 159-167.