How and When to Use Which Fit Indices? A Practical and Critical Review of the Methodology

With the help of statistical software programs, such as AMOS, Lisrel, R, Matlab, and many equivalents, most of the complicated research models have become more computable and easily understandable. Even the most complicated and complex models with various relationships can be easily computed with the help of software. Although with slight differences, outputs are consistent, and tables are mostly comprehensible. However, with the increasing curiosity and amount of knowledge about the research methodology, these simple looking outputs start to become more complicated and deeper. Even though aforementioned statements seem contradictory, what we imply here is very sound to a midlevel researcher because, as knowledge and understanding of statistics deepens, questions and doubts about from where, how, and why these numbers are calculated increase. Curiosity about the fit indices, chi-square and degrees of freedom, modification indices, covariances, and residuals begin to arouse. In this review and commentary, we focus on the infamous CMIN (or chi-square), different model definitions, and calculation of fit indices by the help of these models while avoiding statistical jargon as much as possible. With the aim of putting an end to a decade long debate, when and how to use which fit indices, what they really indicate, and which numbers refer to good or bad fit is also discussed.