Understanding L.O.V.E. (left out variables error): A method for estimating the effects of omitted variables.

Abstract

Whenever nonexperimental methods are used to test a hypothesis and 1 or more predictor (independent) variables that may affect the criterion (dependent) variable are omitted from the analyses, it is possible that the estimates of the effects of the predictors are biased or that the omitted variable could account entirely for the effects attributed to one or more of the predictors. In this article, a technique is developed for determining when a variable omitted from a linear model can account for the effects attributed to a predictor included in that model. Social scientists are rarely able to obtain information on all of the factors that may affect their criterion (outcome, dependent) variables. Whenever researchers use nonexperimental methods and fail to account for all of the variables that affect a criterion, their inferences about the effects of the predictors (independent variables) on that criterion may be biased. 1 Whenever a relevant variable is neither held constant nor entered into an analysis, that variable could account entirely for the effects attributed to one or more of the predictor variables included in the analysis. In this article, a technique is developed for determining when a variable omitted from a linear model can account for the effects attributed to a predictor included in that model. This technique is designed to provide a general indication of the potential effects of an omitted variable. There is no associated statistical distribution theory. For an omitted variable to account for the effect of a specific predictor, the omitted variable must (a) have a substantial effect on the criterion variable, (b) be substantially correlated with the predictor in question, and (c) not be substantially correlated with the other predictors in the model. For example, a clinical psychologist might theorize that a disorder is the result of a genetic aberration, whereas another researcher theorizes that this disorder is the result of sociocultural factors and a high level of life stress. The first investigator might then conduct a study in which the family histories of patients are examined and conclude that controlling for age, sex, and socioeconomic status, family history (reflecting the genetic component) of the disorder is a significant predictor of the disorder. The second researcher could criticize this research for not including measures of other potentially important variables, such as life stress, and hypothesize that had a measure of