Consensus Points on best reporting practices in ML/MLR, CFA and SEM

The best guide to assessing model fit is strong substantive theory.

The chi-square test statistic should not be the sole basis for determining model fit

The use of multiple fit statistics promotes more reliable and conservative evaluations

We should not ignore the fit of the components of a model. The researchers should always examine the components of fit along with the overall fit measures.

it is better to examine several alternative models than only a single model.


Outliers and influential cases should be traced and the distributional assumptions of an estimator should be satisfied as a perquisite. Next steps follow.

When reporting fit indices, choose ones that represent different families of measures or tap different aspects of the model.

Choose fit indices with sampling distribution means that are not or are only weakly related to the sample size.

Choose fit indices that take into consideration the model degrees of freedom

Evaluate the model adequacy based on prior studies. Decide on the optimal model on the basis of comparison

The objective of fitting SEMs is to understand a substantive area, not simply to obtain an adequate fit (e.g local optimum)

The test statistics and fit indices are useful, but they cannot replace sound judgment and Expertise

As proposed by Bollen and Long, (1992) pp. 127-130 .