Within-Between Persons Distinction — Overview
Summary
Rohrer & Murayama (2023) clarify the relationship between the within-/between-persons distinction and causal inference in longitudinal data. Their key argument: the within/between distinction is informative but not decisive for causal inference. Between-persons data from experiments can inform average causal effects. Within-persons data is not necessary and not sufficient for causal inference, but can be very helpful. Researchers should start from well-defined estimands, not from statistical models.
Overview
Published in Advances in Methods and Practices in Psychological Science, 6(1), pp. 1–14, 2023 (Rohrer & Murayama). Addresses widespread confusion in psychological research about what within-persons longitudinal analysis can and cannot accomplish for causal inference.
Three Main Claims
Claim 1: Between-Persons Data Can Inform Average Causal Effects
From the potential outcomes framework: randomization makes treatment groups exchangeable with respect to potential outcomes. Therefore, . Between-persons comparisons from randomized experiments recover average causal effects. Longitudinal / within-persons data is not required.
Claim 2: Within-Persons Data Are Not Sufficient for Causal Inference
Within-persons designs (fixed effects, within-person mean centering) control for time-invariant confounders (stable personality traits, sociodemographics, genetics) but cannot control for time-varying confounders — events and circumstances that vary within a person over time and affect both X and Y simultaneously.
Example: On days with social events, both talkativeness () and happiness () may be elevated. The within-person association is confounded by social events even in a pure within-persons design.
Claim 3: Within-Persons Data Can Be Very Helpful for Causal Inference
Within-persons data: (1) eliminates a large class of confounders — all stable time-invariant traits; (2) enables individual-level causal inference (N-of-1 designs); (3) maps how effects unfold over time including reciprocal dynamics.
Central Recommendation: Estimands First
The paper’s most actionable message: start with a well-defined theoretical estimand, not a statistical model.
Researchers should not choose a “sophisticated” longitudinal model (CLPM, dynamic panel) because it appears methodologically advanced. Instead:
- Define the causal effect of interest precisely in potential outcomes notation
- Identify what assumptions are needed to estimate it from observational data
- Choose the study design and statistical model that can, under those assumptions, recover the estimand
Three Longitudinal Models Covered
| Model | Targets | Key Assumption Violated By | See |
|---|---|---|---|
| Fixed-effects (FE) | Contemporaneous within-person effects | Time-varying confounders, lagged dynamics | Fixed-Effects Model |
| Cross-lagged panel (CLPM) | Lagged reciprocal effects | Trait-like stable confounders | Cross-Lagged and Dynamic Panel Models |
| Dynamic panel (DPM) | Lagged reciprocal effects + time-invariant control | Contemporaneous effects, heterogeneous slopes | Cross-Lagged and Dynamic Panel Models |
Connections
- Directly extends The Selection Problem to the longitudinal setting
- Directed Acyclic Graphs underlie all three model specifications (Boxes 1–3 in the paper)
- Garden of Forking Paths — choosing a longitudinal model post-hoc without pre-specified estimand is a form of researcher degrees of freedom
- Researcher Degrees of Freedom — the menu of longitudinal models (FE, CLPM, DPM, RI-CLPM) creates analytic flexibility
- Causal Estimands — the general framework for defining causal targets
- Differences-in-Differences — DiD exploits the same within-vs-between logic: within-unit variation over time differences out time-invariant confounders, making it the natural econometric complement to the FE model
- Omitted Variables Bias — between-persons confounding in observational panel data is an instance of OVB from stable unobserved traits
See Also
- Within-Between Persons Causal Inference — detailed treatment of when each approach helps
- Fixed-Effects Model — Box 1 content
- Cross-Lagged and Dynamic Panel Models — Box 2 and Box 3
- Estimands in Longitudinal Research — how to define the right causal target
- Differences-in-Differences — econometric panel estimator that controls for time-invariant confounders via the within-unit design logic
- Omitted Variables Bias — econometric framing of between-persons confounding