Dual-centered ANCOVA: Resolving contradictory results from Lord's paradox with implications for reducing bias in longitudinal analyses

Abstract

Introduction: Valid causal inferences are necessary to use developmental research to improve adolescent outcomes. What type of change should be analyzed to approximate causal inferences from longitudinal data? Difference-score and ANCOVA-type analyses often produce contradictory results, a problem known as Lord's paradox. This study investigates 2-group, 2-wave difference-score analyses and ANCOVA, and introduces a method that produces consistent results, namely dual-centered ANCOVA, which is compared to pretest matching.

Methods: These methods are tested first on two datasets simulated to fit each of Lord's contrasting results. The methods are then applied to data investigating the longitudinal associations of parent-adolescent discussions about sexual risks on subsequent unprotected sexual behaviors in 4753 American adolescents (62.2% whites).

Results: The results replicate Lord's contradictory results for all datasets. Dual-centered ANCOVA and pretest matching both produce consistent results, but dual-centered ANCOVA replicates the original results for difference-score analyses, whereas pretest matching replicates the original ANCOVA results. Thus, the two sets of consistent results differ from each other as much as the original discrepancy rather than reducing bias.

Conclusion: The least biased analysis is the one whose null hypothesis best approximates a plausible change pattern to represent a no-treatment effect. When difference-score analyses are thought to approximate valid causal inferences as closely as ANCOVA-type analyses, dual-centered ANCOVA estimates the difference-score effect while retaining the advantages of ANCOVA in statistical power and covariate inclusion. These findings are widely applicable to longitudinal analyses that incorporate one or both of these basic methods to analyze change.

Keywords: Causal validity; Difference scores; Dual-centered ANCOVA; Lord's paradox; Sexual socialization; Unprotected sex.