Eight Simple Guidelines for Improved Understanding of Transformations and Nonlinear Effects

Abstract

Transforming variables before analysis or applying a transformation as a part of a generalized linear model are common practices in organizational research. Several methodological articles addressing the topic, either directly or indirectly, have been published in the recent past. In this article, we point out a few misconceptions about transformations and propose a set of eight simple guidelines for addressing them. Our main argument is that transformations should not be chosen based on the nature or distribution of the individual variables but based on the functional form of the relationship between two or more variables that is expected from theory or discovered empirically. Building on a systematic review of six leading management journals, we point to several ways the specification and interpretation of nonlinear models can be improved.

Inflection Points, Kinks, and Jumps: A Statistical Approach to Detecting Nonlinearities

“…Extant research has shown the theoretical and empirical perils of dealing with unknown potential limitations in the data, and in existing statistical methods (Dul, 2016; Ostroff, 1993; Rönkkö et al, 2021). Within this context, we provide an integrative framework for the identification of nonlinearities that constitutes a precursor step that researchers will want to conduct to subsequently make better decisions about an appropriate model specification and estimation method (e.g., quadratic terms vs. split samples, etc.).…”

“…In the spirit of Ostroff (1993), Dul (2016), and Rönkkö et al (2021), our contribution fits with research dealing with unknown potential limitations of data and existing statistical tools. Our approach overcomes a number of challenges associated with the use and interpretation of linear models and sample splitting, and it allows for comparing our theories with what the data actually say, without our theoretical beliefs influencing the results spuriously.…”

Empirical research methods department: Mission, learnings, and future plans

“…In addition, the normality assumption of the error term (and consequently the distribution of the dependent variable) is mostly irrelevant in the (large enough) sample sizes that we typically use. Rönkkö and Aguirre-Urreta (2018) provided a clear explanation of the issue and Rönkkö et al (2022) expanded it further. Thus, non-normality alone is a bad reason for transforming data.…”

“…The real reason that we want to transform a variable (e.g., log-transformation) is that in many cases the effects of one variable on another are expected to be relative instead of absolute. The choice of a functional form for transformation should be justified primarily by theory and supplemented with empirical analysis (Rönkkö et al, 2022).…”

Taking the time for range testing: an approach to account for temporal resolution in acoustic telemetry detection range assessments

“…After variable selection, the final logistic regression models for both hourly and daily response variables included the explanatory variables distance, noise, power output, the interactions of distance-noise and distance-power output (Table 3). Visual inspection of the relationship with distance led us to include distance transformed to the second power [37], which contributed to an improved model fit. In summary, high levels of ambient noise and low transmitting output power significantly reduced the probability of a transmission being detected, whereby these negative effects were exacerbated at greater distance (Fig.…”