Model Modification

An analysis of empirical data often leads to a rejection of a hypothesized model, even if the researcher has spent considerable efforts in including all available information in the formulation of the model. Thus, the researcher must reformulate the model in some way, but in most instances there is, at least theoretically, an overwhelming number of possible actions that could be taken. In this paper a “modification index” will be discussed which should serve as a guide in the search for a “better” model. In statistical terms, the index measures how much we will be able to reduce the discrepancy between model and data, as defined by a general fit function, when one parameter is added or freed or when one equality constraint is relaxed. The modification index discussed in this paper is an improvement of the one incorporated in the LISREL V computer program in that it takes into account changes in all the parameters of the model when one particular parameter is freed.