Linear Versus Nonlinear Relationships

The Sphinx’s Riddle states,

When toddlers first learn to walk, changing from 4 feet to 2, they do so slowly and cautiously. As children age, they become faster and faster as they mature into adults. Adults slow down again, walking more slowly, perhaps using a cane. This is an example of a nonlinear relationship. The nature of a nonlinear relationship makes the Sphinx’s Riddle perplexing, and empirical research both interesting and challenging. A nonlinear relationship occurs when the association between two variables is not a simple straight line but is curved. This particular nonlinear relationship is curvilinear. Over a lifetime, walking speed increases to a point and then it decreases. The point of change is called the point of inflection. Essentially a nonlinear relationship means that change in X (age) is not consistently related to change in Y (walking speed)—sometimes it increases, sometimes it decreases, and sometimes it flattens out. The nature of the curve (or curves) and where it happens (i.e., the points of inflection) make nonlinear relationships interesting.

Communication is a dynamic process. As such, many phenomena communication researchers study are nonlinear in nature. Sometimes relationships between concepts that seem to be linear are actually nonlinear. In an interpersonal context, self-disclosure and intimacy may seem to have a positive linear relationship, wherein the more information relational partners disclose, the closer they feel. At early stages of a relationship, however, there is probably a point of inflection between these two variables. Beyond the threshold of what is appropriate, self-disclosure can lead to decreases in intimacy or maybe even repulsion. The saying “TMI” or “too much information” was created for this very situation. In an intercultural context, international students’ or sojourners’ acculturative stress and adaptation to the host culture have a curvilinear relationship. Upon the arrival to an unfamiliar culture, it is generally the case that the feeling of disorientation motivates the sojourner to change herself or himself to fit the new environment. Yet, overly stressed or too disoriented sojourners may shut down completely, leading to zero adaptation. Empirical observation and theory are filled with interesting examples of nonlinear relationships.

In practice, however, researchers usually start with hypotheses or research questions about linear relationships, and then speculate about nonlinear ones. This may render nonlinear relationships nearly invisible. Linear relationships, like correlations, attempt to find the line that best fits the data. All of the X, Y coordinates are used in an equation that attempts to minimize the distance between all points and the line of best fit. The closer all of the coordinates are to the line, the stronger the relationship between X and Y. In the case where a relationship is actually curvilinear, it is quite possible that a linear estimate is nearly a zero correlation, suggesting no relationship between X and Y. In this case, the linear relationship is poor fit to the data, but a curvilinear or cubic relationship might be an excellent fit.

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