False Positives in Multiple Regression

Unanticipated Consequences of Measurement Error in the Predictor Variables

Bibliographic Data

ID20286133
AuthorsBenjamin R Shear (0000-0002-9236-2927, University of British Columbia, Vancouver, British Columbia, Canada), Bruno D Zumbo (0000-0003-2885-5724, University of British Columbia, Vancouver, British Columbia, Canada)
Year2013
Volume73
Issue5
Pages733-756
Publication date2013-10-01
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueEducational and Psychological Measurement (JOURNAL)
Journal identifiersISSN: 0013-1644 • E-ISSN: 1552-3888
PublisherSAGE Publications (PUBLISHER • US)
DOI10.1177/0013164413487738
OpenAlexW1975494033
LanguageEN
Citations received17
References cited56

Type I error rates in multiple regression, and hence the chance for false positive research findings, can be drastically inflated when multiple regression models are used to analyze data that contain random measurement error. This article shows the potential for inflated Type I error rates in commonly encountered scenarios and provides new insights into the causes of this problem. Computer simulations and an illustrative example are used to demonstrate that when the predictor variables in a multiple regression model are correlated and one or more of them contains random measurement error, Type I error rates can approach 1.00, even for a nominal level of 0.05. The most important factors causing the problem are summarized and the implications are discussed. The authors use Zumbo’s Draper–Lindley–de Finetti framework to show that the inflation in Type I error rates results from a mismatch between the data researchers have, the assumptions of the statistical model, and the inferences they hope to make

Confidence interval · Econometrics · False positive paradox · False positives and false negatives · Inflation (cosmology) · Linear regression · Nominal level · Observational error · Polynomial regression · Regression · Regression analysis · Regression diagnostic · Statistics · Type I and type II errors · Advanced Statistical Methods and Models · Computer Science · Mathematics · Statistical Methods and Bayesian Inference · Statistical Methods in Clinical Trials