Regression Toward the Mean, Lord’s Paradox, and Modeling or Forecasting Change in Longitudinal Analyses

Session Type: Paper Symposium

Abstract

Francis Galton discovered regression toward the mean 134 years ago. Frederic Lord showed that analyses of difference scores can contradict ANCOVA analyses 53 years ago. Decades later, their implications for addressing causal research questions with longitudinal analyses remain unclear.

This symposium addresses these issues in several ways. The first paper uses causal graphs to distinguish regression toward the mean due to spurious effects and negative feedback loops in control-system processes. The second paper introduces dual-centered ANCOVA, which brings ANCOVA’s superior statistical power to difference-score estimates. The third paper looks at high-stakes testing, distinguishing confounding due to indirect vs. direct selection bias. The fourth paper introduces new strategies to correct the usual inflationary bias in forecasting future academic performance from longitudinal data. All four papers show how these factors can bias causally relevant estimates in longitudinal analyses of simple or residualized change scores, depending on the actual processes that produced the data. Two of the papers show how these artifacts cause typical ANCOVA-type analyses of residualized scores to be biased against most actions to help at-risk children and adults. The residual confounding that remains after analyses of residualized change makes the following corrective actions appear to be harmful: warning adolescents about unprotected sex, disciplinary reasoning with 5-year-olds, hospitalizations, and teaching underprivileged students. Consistent with Lord’s paradox, analyses of difference scores make these corrective actions look beneficial from the same data. Further work needs done to clarify how longitudinal analyses can best approximate valid causal estimates given these pervasive biases.

Sub Unit

• Methods, History, Theory

Chair

• Robert E Larzelere, Oklahoma State University - Stillwater

Individual Presentations

• Causal Graphical Analysis of Regression to the Mean - Presenting Author: Yongnam Kim, Seoul National University

• Dual-Centered ANCOVA Overcomes Bias in ANCOVA with More Statistical Power than Difference-Score Analyses - Presenting Author: Hua Lin, Oklahoma State University - Stillwater; Non-Presenting Author: Robert E Larzelere, Oklahoma State University - Stillwater

• Estimating School Effectiveness: An Application of Lord’s Paradox - Presenting Author: Daniel B Wright, University of Nevada at Las Vegas

• Design and Analytic Features for Reducing Biases in Skill-Building Intervention Impact Forecasts - Presenting Author: Daniela Alvarez-Vargas, University of California - Irvine; Non-Presenting Author: Sirui Wan, University of Wisconsin - Madison; Non-Presenting Author: Drew Bailey, University of California - Irvine