Problems with formative and higher-order reflective variables

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Abstract

Cadogan and Lee (this issue) discuss the problems inherent in modeling formative latent variables as endogenous. In response to the commentaries by Rigdon (this issue) and Finn and Wang (this issue), the present article extends the discussion on formative measures. First, the article shows that regardless of whether statistical identification is achieved, researchers are unable to illuminate the nature of a formative latent variable. Second, the study clarifies issues regarding formative indicator weighting, highlighting that the weightings of formative components should be specified as part of the construct definition. Finally, the study shows that higher-order reflective constructs are invalid, highlights the damage their use can inflict on theory development and knowledge accumulation, and provides recommendations on a number of alternative models which should be used in their place (including the formative model).

Introduction

The invited commentaries by Rigdon (this issue), and Finn & Wang (this issue), on the paper, "Improper Use of Endogenous Formative Variables (IFV)," (Cadogan and Lee, this issue). are greatly appreciated. Both comments throw important light on significant problems in contemporary understanding of the formative model and in current measurement practices in business research. The current authors share with Rigdon and with Finn and Wang a desire to expand understanding of measurement theory, and to make a positive impact on the application of measurement by practicing business researchers.

Nevertheless, the commentaries contain a number of important points that require counter comment or elaboration. The goals of the present paper are threefold. First, to re-examine the original intentions behind IFV, and in so doing, place a variety of Rigdon's comments in context, demonstrating that he is in agreement with the current authors in many places. In particular, the current paper clarifies why one can never know how a formative latent variable varies — regardless of statistical identification issues. Second, building on Rigdon's comments, the current paper demonstrates that, for formative variables to have utility in theoretical models, the loadings of the formative indicators should be specified as part of the construct definition prior to any analysis. Third, while the current authors share a number of important views with Finn and Wang, the authors show that the idea of a higher-order reflective construct makes no conceptual sense, and that the latter's use impedes theory development efforts and knowledge accumulation.

Section snippets

Response to Rigdon

Rigdon's commentary on IFV provides some important points which help make the case that IFV presents even stronger. In fact, in essence, Rigdon agrees entirely with the key message underpinning IFV — that researchers should not model antecedents to formative variables at the construct/aggregate level. Instead, antecedents should be modeled at the individual formative item level. However, a number of aspects of Rigdon's commentary require clarification.

Response to Finn and Wang

The authors are also grateful for Finn and Wang's commentary on their work, since it raises a number of key issues for business researchers. In particular, the authors strongly support Finn and Wang's call for researchers to devote far more effort to construct conceptualization, and in turn to theorizing about the link between constructs and measures.

An area of particular interest, mentioned repeatedly in Finn and Wang's comment, concerns the idea of higher-order constructs. It is certainly

Conclusions

The authors are grateful to have the opportunity to provide a rejoinder to the comments Rigdon and Finn and Wang make on the IFV paper. Both commentaries provide key supports and suggested extensions to the core thesis underpinning IFV (that formative endogenous variables should not be predicted at the construct / aggregate level), and the current rejoinder uses these commentaries as points of departure into other critical areas of measurement theory, closely related to the original thesis. The

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