Measuring Differentials in Communication Research: Issues With Multicollinearity in Three Methods

Abstract

Models of communication processes sometimes require the computation of the difference between two variables. For example, information insufficiency is the difference between what people know and what they think they need to know about an issue, and it can motivate information seeking and processing. Common methods that compute this differential may bias model estimates as a function of the correlation between the differentiated variables and other variables in the model. This article describes the general form of Cohen and Cohen's (1983) analysis of partial variance for computing differentials and analyzes simulated data to contrast that method with two alternative methods. The discussion recommends the use of the general form of the Cohen and Cohen method in other areas of communication research, such as studies of third-person perception.

Notes

¹For example, information insufficiency is the difference between current knowledge and desired knowledge. Although these variables are measured at the same time, they imply a time order: current knowledge precedes future knowledge.

²The literature uses the terms “perceived knowledge” and “sufficiency threshold” to describe current knowledge and desired knowledge, respectively. However, for readers who are not familiar with that line of research, the latter two terms may have more intuitive meaning.

³I cite the second edition of Cohen and Cohen's work. The 2003 third edition, with coauthors West and Aiken, dedicates considerably less space to the APV and gives less extensive statistical derivations and examples. Compare currently cited pages with pp. 59–60 and 570–571 in the 2003 edition.

⁴Consider the following example: A researcher measures a prescore (PRE) and a postscore (POST). For the set of observations, it is given that POST = PRE + 1. Thus, r_pre,post  = 1.00, σ _pre = σ _post , and B _pre,post  = 1.00. The index of change thus equals POST – PRE*B = (PRE + 1) – PRE*1 = PRE + 1 – PRE = 1 for all observations. The raw difference score would yield an identical result.

⁵The covariate can be either a predictor variable of direct interest or a control variable; however, it must either be a predictor of the differential or a predictor with the differential of a dependent variable. In Study 1, the covariate predicts the differential. In Study 2, the covariate and the differential predict the dependent variable.

⁶I do not use the dependent variable until Study 2, in which the differential is an independent variable. For example, in the model of risk information seeking and processing, information insufficiency (the differential) predicts risk information seeking intention (the dependent variable).

⁷The different levels of multicollinearity reflect differences in the correlation between the prescore and covariate, which ranged from 0 to .95 in increments of .05. The remaining correlations among the full set of variables remained constant.

⁸Estimates of B were identical to more than 10 decimal places.