Random Item Slope Regression: An Alternative Measurement Model That Accounts for Both Similarities and Differences in Association With Individual Items

In psychology, researchers often predict a dependent variable (DV) consisting of multiple measurements (e.g., scale items measuring a concept). To analyze the data, researchers typically aggregate (sum/average) scores across items and use this as a DV. Alternatively, they may define the DV as a common factor using structural equation modeling. However, both approaches neglect the possibility that an independent variable (IV) may have different relationships to individual items. This variance in individual item slopes arises because items are randomly sampled from an infinite pool of items reflecting the construct that the scale purports to measure. Here, we offer a mixed-effects model called random item slope regression, which accounts for both similarities and differences of individual item associations. Critically, we argue that random item slope regression poses an alternative measurement model to common factor models prevalent in psychology. Unlike these models, the proposed model supposes no latent constructs and instead assumes that individual items have direct causal relationships with the IV. Such operationalization is especially useful when researchers want to assess a broad construct with heterogeneous items. Using mathematical proof and simulation, we demonstrate that random item slopes cause inflation of Type I error when not accounted for, particularly when the sample size (number of participants) is large. In real-world data (n = 564 participants) using commonly used surveys and two reaction time tasks, we demonstrate that random item slopes are present at problematic levels. We further demonstrate that common statistical indices are not sufficient to diagnose the presence of random item slopes.