IBM® SPSS® Amos™ 28

Models with relatively few parameters (and relatively many degrees of freedom) are sometimes said to be high in parsimony, or simplicity. Models with many parameters (and few degrees of freedom) are said to be complex, or lacking in parsimony. This use of the terms, simplicity and complexity, does not always conform to everyday usage. For example, the saturated model would be called complex while a model with an elaborate pattern of linear dependencies but with highly constrained parameter values would be called simple.

While one can inquire into the grounds for preferring simple, parsimonious models (e.g., Mulaik, et al., 1989), there does not appear to be any disagreement that parsimonious models are preferable to complex ones. When it comes to parameters, all other things being equal, less is more. At the same time, well fitting models are preferable to poorly fitting ones. Many fit measures represent an attempt to balance these two conflicting objectives—simplicity and goodness of fit.

"In the final analysis, it may be, in a sense, impossible to define one best way to combine measures of complexity and measures of badness-of-fit in a single numerical index, because the precise nature of the best numerical tradeoff between complexity and fit is, to some extent, a matter of personal taste. The choice of a model is a classic problem in the two-dimensional analysis of preference." (Steiger, 1990, p. 179)