Controlling for Spurious Moderation in Marketing: A Review of Statistical Techniques

Using only squared terms (and not exponents greater than two) as covariates when controlling for spurious moderation is a pragmatic convention advocated in the research methods literature. The main reason is that, while nonlinear terms can take a variable to the nth degree polynomial, imperfectly measured variables taken to powers greater than two may then be mostly comprised of measurement error (Busemeyer and Jones 1983). We should also point out that a quadratic function is usually a good approximation of nonlinear trends displayed by organizational and market phenomena—just as it is for most trends displayed by psychological phenomena for which the convention of using quadratic terms as covariates was first proposed (Ganzach 1997).
In the next sections, we review specific spurious moderation control techniques involving squared terms as covariates. We then provide illustrations using simulated data.