Dealing with Nonlinearity in Importance-Performance Map Analysis (IPMA): An Integrative Framework in a PLS-SEM Context

Abstract

Importance-performance map analysis (IPMA) combines PLS-SEM estimates, indicating the importance of an exogenous construct’s influence on another endogenous construct of interest, with an additional dimension comprising the exogenous construct’s performance in a two-dimensional map. From a practical point of view, IPMA contributes to more rigorous management decision-making. The basic principles of IPMA are well understood, yet the inter-construct relationships are typically modeled as being linear. An abundance of empirical literature indicates that this may lead to erroneous conclusions. In an IPMA context, this can lead to false conclusions regarding an exogenous construct’s importance. Although several approaches exist to account for nonlinear inter-construct relationships, these approaches are characterized by drawbacks impeding their applications in practice. Overall, this serves as a backdrop for the current chapter which aims to contribute to (PLS-SEM) IPMA theory in the following ways. First, we provide an integrative framework to guide IPMAs using PLS-SEM. Second and synergistically with the first contribution, we introduce a so-called log-log model that allows to capture the most common functional forms (i.e., both linear and nonlinear) without the need to make a priori assumptions about the correct functional form specification. Third, a comprehensive empirical application is provided that illustrates our proposed IPMA framework as well as the proposed log-log model to more adequately capture the nature of the PLS-SEM relationships ultimately defining the IPMA’s importance dimension.