Educational and Psychological Measurement, Ahead of Print.
Descriptive fit indices that do not require a formal statistical basis and do not specifically depend on a given estimation criterion are useful as auxiliary devices for judging the appropriateness of unrestricted or exploratory factor analytical (UFA) solutions, when the problem is to decide the most appropriate number of common factors. While overall indices of this type are well known in UFA applications, especially those intended for item analysis, difference indices are much more scarce. Recently, Raykov and collaborators proposed a family of effect-size-type descriptive difference indices that are promising for UFA applications. As a starting point, we considered the simplest measure of this family, which (a) can be viewed as absolute and (b) from which only tentative cutoffs and reference values have been provided so far. In this situation, this article has three aims. The first is to propose a relative version of Raykov’s effect-size measure, intended to be used as a complement of the original measure, in which the increase in explained common variance is related to the overall prior estimated amount of common factor variance. The second is to establish reference values for both indices in item-analysis scenarios using simulation. And the third aim (instrumental) is to implement the proposal in both R language and a well-known non-commercial factor analysis program. The functioning and usefulness of the proposal is illustrated using an existing empirical dataset.
Author Archives: Pere J. Ferrando
Measuring Unipolar Traits With Continuous Response Items: Some Methodological and Substantive Developments
Educational and Psychological Measurement, Ahead of Print.
In recent years, some models for binary and graded format responses have been proposed to assess unipolar variables or “quasi-traits.” These studies have mainly focused on clinical variables that have traditionally been treated as bipolar traits. In the present study, we have made a proposal for unipolar traits measured with continuous response items. The proposed log-logistic continuous unipolar model (LL-C) is remarkably simple and is more similar to the original binary formulation than the graded extensions, which is an advantage. Furthermore, considering that irrational, extreme, or polarizing beliefs could be another domain of unipolar variables, we have applied this proposal to an empirical example of superstitious beliefs. The results suggest that, in certain cases, the standard linear model can be a good approximation to the LL-C model in terms of parameter estimation and goodness of fit, but not trait estimates and their accuracy. The results also show the importance of considering the unipolar nature of this kind of trait when predicting criterion variables, since the validity results were clearly different.
In recent years, some models for binary and graded format responses have been proposed to assess unipolar variables or “quasi-traits.” These studies have mainly focused on clinical variables that have traditionally been treated as bipolar traits. In the present study, we have made a proposal for unipolar traits measured with continuous response items. The proposed log-logistic continuous unipolar model (LL-C) is remarkably simple and is more similar to the original binary formulation than the graded extensions, which is an advantage. Furthermore, considering that irrational, extreme, or polarizing beliefs could be another domain of unipolar variables, we have applied this proposal to an empirical example of superstitious beliefs. The results suggest that, in certain cases, the standard linear model can be a good approximation to the LL-C model in terms of parameter estimation and goodness of fit, but not trait estimates and their accuracy. The results also show the importance of considering the unipolar nature of this kind of trait when predicting criterion variables, since the validity results were clearly different.