Thinking clearly about time-invariant confounders in cross-lagged panel models: A guide for choosing a statistical model from a causal inference perspective.

Do people’s work experiences (i.e., work conditions and outcomes) influence their self-esteem, and does people’s self-esteem influence their work experiences? In this preregistered research, data used by Kuster et al. (2013) were reanalyzed using new types of statistical models. Whereas the previous study used the traditional cross-lagged panel model, we used the random intercept cross-lagged panel model and the dynamic panel model, which allow for better control of unmeasured time-invariant confounders, enhancing the validity of causal conclusions. Data came from two longitudinal studies with five assessments over eight months ( N = 663) and three assessments over two years ( N = 600). Thirteen of the 36 cross-lagged paths tested were significant, and all significant effects were in the expected direction: Self-esteem predicted increases in positive outcomes (i.e., coworker justice) and decreases in negative outcomes (e.g., effort-reward imbalance). Positive work variables (e.g., job satisfaction) predicted increases in self-esteem, and negative work variables (e.g., time pressure) predicted decreases in self-esteem. The pattern of findings aligns with theoretical perspectives suggesting reciprocal effects between self-esteem and work experiences. Moderator analyses indicated that effects held across gender. The findings advance the understanding of dynamic self-esteem–work relations and inform interventions that could benefit employees and organizations.

The cross-lagged panel(regression) model (CLPM) is the usual framework of choice to test the longitudinal reciprocal effects between self-concept and achievement. Criticisms of the CLPM are that causal paths are over-estimated as they fail to discriminate between- and within-person variation. The random-intercept cross-lagged panel model (RI-CLPM) is one alternative that extends the CLPM by partialling out between-person variance. We compare analyses from a CLPM and a RI-CLPM which examine the reciprocal relationships between self-concept, self-efficacy, and achievement and determine the extent CLPM estimates are inflated by between-person variance. Participants (n=314) were first-year undergraduate psychology students recruited as part of the STudent Engagement with Education and Learning (STEEL) project. Participants completed measures of self-efficacy and self-concept prior to completing fortnightly quiz assessments. Cross-Lagged Panel(regression) Model estimates are likely over-estimated in comparison with RI-CLPM estimates. Cross-Lagged Panel(regression) Model analyses identified a reciprocal effects relationship between self-concept and achievement, confirming established literature. In RI-CLPM analyses, these effects were attenuated and a skill development association between achievement and self-concept was supported. A reciprocal relationship between self-efficacy and achievement was supported. Better model fit was reported for the RI-CLPM analyses. Prior findings relating to the reciprocal effects of self-concept and achievement need to be reconsidered. Whilst such a relationship was supported in a CLPM analysis in this study, within an RI-CLPM framework, only achievement predicted self-concept. However, in both CLPM and RI-CLPM models a reciprocal effects model of self-efficacy and achievement was supported.

Panel models in structural equation modeling that combine static and dynamic components make it possible to investigate reciprocal relations while controlling for time-invariant unobserved heterogeneity. Recently, the latent curve model with structured residuals and the random-intercept cross-lagged panel model were suggested as "residual-level" versions of the more traditional autoregressive latent trajectory and dynamic panel models, respectively. Their main benefit is that they allow for a more straightforward interpretation of the trajectory factors. It is not widely known, however, that the residual-level models place potentially strong assumptions on the initial conditions-that is, the process that was occurring before the observation period began. If the process under investigation is not both stationary and at equilibrium then the residual-level models are not appropriate. They then do not control for all time-invariant unobserved heterogeneity and can result in biased cross-lagged and autoregressive estimates. I demonstrate this using the problem behavior of cigarette smoking among adolescents: Because the mean and variance of this process changes as a young person's smoking behavior develops, early stages of this process should not be examined using the residual-level models. This issue potentially exists for a wide variety of psychological and sociological subjects, essentially whenever the process under investigation is changing over the course of the observation period. This article discusses strategies to help researchers decide which model to use when, and compares some of their relative advantages and drawbacks. An amendment to the residual-level models is suggested in which the latent individual effects are allowed to covary with the initial residuals. This makes the residual-level models robust to violations of the assumptions surrounding the initial conditions, while retaining their other beneficial aspects. (PsycInfo Database Record (c) 2022 APA, all rights reserved).

Self-efficacy inertia: The role of competency beliefs and academic burden in achievement

In this study we compare results obtained when applying the monozygotic twin difference cross-lagged panel model (MZD-CLPM) and a random intercept cross-lagged panel model (RI-CLPM) to the same data. Each of these models is designed to strengthen researchers' ability to draw causal inference from cross-lagged associations. We explore differences and similarities in how each model does this, and in the results each model produces. Specifically, we examine associations between maladaptive parenting and child emotional and behavioural problems in identical twins aged 9, 12 and 16. Child reports of 5698 identical twins from the Twins Early Development Study (TEDS) were analysed. We ran a regular CLPM to anchor our findings within the current literature, then applied the MZD-CLPM and the RI-CLPM. The RI-CLPM and MZD-CLPM each enable researchers to evaluate the direction of effects between correlated variables, after accounting for unmeasured sources of potential confounding. Our interpretation of these models therefore focusses primarily on the magnitude and significance of cross-lagged associations. In both the MZD-CLPM and the RI-CLPM behavioural problems at age 9 resulted in higher levels of maladaptive parenting at age 12. Other effects were not consistently significant across the two models, although the majority of estimates pointed in the same direction. In light of the triangulated methods, differences in the results obtained using the MZD-CLPM and the RI-CLPM underline the importance of careful consideration of what sources of unmeasured confounding different models control for and that nuance is required when interpreting findings using such models. We provide an overview of what the CLPM, RI-CLPM and MZD-CLPM can and cannot control for in this respect and the conclusions that can be drawn from each model.

The relation between nonword repetition and vocabulary has been the focus of a theoretical controversy for several decades. The point of contention is whether the ability underlying nonword repetition drives vocabulary growth or vice versa. The present study examines longitudinal interrelations between nonword repetition and vocabulary from age 3 to 5 with random intercept cross-lagged panel models (RI-CLPMs). RI-CLPMs have the advantage of separating within-child dynamic processes from more stable differences between children, including time-stable unmeasured confounders. For n = 260 monolingual German-speaking children assessed at three time points with a lag of eleven months, RI-CLPM and, for comparison purposes, "classical" cross-lagged panel models (CLPMs) were estimated. The ill-fitting CLPMs in which cross-lagged effects combine within-child processes and stable differences between children yielded evidence consistent with reciprocal effects between nonword repetition and vocabulary (without covariates) or from nonword repetition to vocabulary (with covariates). Adding a random intercept markedly improved model fit. All within-child cross-lagged effects in the RI-CLPM were nonsignificant. Thus, the results provided no evidence consistent with within-child processes such as nonword repetition affecting vocabulary or vice versa for preschool-age children. Instead, results are more consistent with, for example, third variable explanations, within-child processes fading out by age 3 or occurring on a time frame that is not captured with a lag of approximately 1 year. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

BackgroundThe directionality of longitudinal associations between children’s food fussiness and parental feeding behaviors remains contested. This study aimed to assess the dynamic relationship between children’s food fussiness and feeding behaviors.MethodsTo disentangle these effects, this study employed cross-lagged panel models (CLPMs) and random-intercept cross-lagged panel models (RI-CLPMs) using longitudinal data from 588 Chinese children (Mean age = 3.7 years, SD = 0.3, 51.7% boys) across three waves over two years. CLPMs capture between-person associations, while RI-CLPMs isolate within-person dynamics over time. Within-person effects represent how temporary deviations predict subsequent changes beyond stable traits, whereas between-person effects reflect enduring cross-family differences.ResultsAnalyses revealed distinct patterns depending on the feeding behavior and model type: for restrictions, the CLPM showed parent-driven effects (restrictions at 3.7 years→ fussiness at 4.8 years, β = −0.104, p = 0.003), whereas the RI-CLPM identified child-driven effects (fussiness at 4.8 years → restrictions at 5.7 years, β = 0.179, p = 0.033). Both models consistently revealed child-driven effects for pressure to eat (CLPM: β = 0.151, p = 0.002; RI-CLPM: β = 0.218, p = 0.013). Food as a reward showed bidirectionality in CLPM (reward at 4.8 years → fussiness at 5.7 years: β = 0.112, p < 0.001; fussiness at 4.8 years→ reward at 5.7 years: β = 0.144, p = 0.005) but no significant cross-lagged paths in the RI-CLPM. Notably, the multi-group analysis revealed no moderating effect of child sex.ConclusionsAfter accounting for stable between-person differences, RI-CLPM findings reveal that child food fussiness prospectively drives increases in parental use of restriction and pressure to eat at the within-person level. This suggests that these specific feeding behaviors may function more as reactive responses to children’s eating behaviors than as caregiver-initiated strategies.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12966-025-01830-8.

This study examines the implications of including random components, specifically random intercepts and slopes, in cross-lagged panel models commonly used in longitudinal psychological research. Prior work has shown that the Random-Intercept Cross-Lagged Panel Model (RI-CLPM) can reduce bias in cross-lagged estimates when time-invariant confounders are present. More recent findings suggest that even in the absence of such traits, the RI-CLPM may still produce “illusory” intercept variance that helps mitigate bias from time-varying confounders. Building on this work, we use analytical derivations, simulations, and empirical data to evaluate when random intercepts and slopes act as useful or problematic adjustments. We show that random intercepts can reduce estimation bias under certain conditions but may underestimate longer-lag effects by absorbing variance attributable to unmodeled mediating processes. We also find that adding random slopes to the model can introduce additional bias by conditioning on post-treatment variation. These results highlight the complexities of correctly specifying longitudinal models of psychological characteristics and offer guidance for researchers using longitudinal panel models to study dynamic psychological processes.

Cross-lagged models are by far the most commonly used method to test the prospective effect of one construct on another, yet there are no guidelines for interpreting the size of cross-lagged effects. This research aims to establish empirical benchmarks for cross-lagged effects, focusing on the cross-lagged panel model (CLPM) and the random intercept cross-lagged panel model (RI-CLPM). We drew a quasirepresentative sample of studies published in four subfields of psychology (i.e., developmental, social-personality, clinical, and industrial-organizational). The dataset included 1,028 effect sizes for the CLPM and 302 effect sizes for the RI-CLPM, based on data from 174 samples. For the CLPM, the 25th, 50th, and 75th percentiles of the distribution corresponded to cross-lagged effect sizes of .03, .07, and .12, respectively. For the RI-CLPM, the corresponding values were .02, .05, and .11. Effect sizes did not differ significantly between the CLPM and RI-CLPM. Moreover, effect sizes did not differ significantly across subfields and were not moderated by design characteristics. However, effect sizes were moderated by the concurrent correlation between the constructs and the stability of the predictor. Based on the findings, we propose to use .03 (small effect), .07 (medium effect), and .12 (large effect) as benchmark values when interpreting the size of cross-lagged effects, for both the CLPM and RI-CLPM. In addition to aiding in the interpretation of results, the present findings will help researchers plan studies by providing information needed to conduct power analyses and estimate minimally required sample sizes. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Psychological measures frequently show trait-like properties, and the ontological status of stable psychological traits has been discussed for decades. We argue that these properties can emerge from causal dynamics of time-varying processes, which are omitted from the analysis model, potentially leading to the estimation of traits that are, at least in part, illusory. Theories positing the importance of a large set of dynamic psychological causes across development are consistent with the existence of illusory traits. We show via simulation that even a linear system with many processes can generate a covariance matrix with trait-like properties. We then attempt to examine how illusory traits affect our conclusions drawn from a common statistical model, which assumes stable traits to analyze longitudinal panel data-a random-intercept cross-lagged panel model (RI-CLPM). We find that the RI-CLPM sometimes falsely detects the existence of traits in the presence of omitted processes, even when the data-generating model does not include any traits. However, in this scenario, the RI-CLPM estimates less causally biased autoregressive and cross-lagged effects than an analysis model, which does not assume traits (i.e., the cross-lagged panel model). The results indicate that the detection of trait variance should not be inferred as strong evidence for the existence of time-invariant trait causes. On the other hand, even when traits are illusory, statistical models assuming stable traits may sometimes be useful for causal inference. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

ObjectiveThis article provides an overview of the Cross‐Lagged Panel Model (CLPM), Random‐Intercept Cross‐Lagged Panel Model (RI‐CLPM), and Latent Curve Model with Structured Residuals (LCM‐SR), highlighting the major issues of the CLPM for relationship science, and discusses dyadic extensions of those three models.BackgroundUnderstanding interdependencies among people and constructs is a central interest in relationship science. Addressing such research questions requires complex designs ideally using data collected at multiple measurement occasions of multiple constructs from at least two persons (e.g., both partners of a couple). The Cross‐Lagged Panel Model (CLPM) has been widely used to analyze such data, however, particularly during the last decade, it has been pointed out that the CLPM confounds between‐ and within‐person variation. As a consequence, alternative models such as the Random‐Intercept Cross‐Lagged Panel Model (RI‐CLPM) and the Latent Curve Model with Structured Residuals (LCM‐SR) were proposed that aim to disentangle between‐ and within‐person variation and, hence, allow conclusions regarding within‐person dynamics.MethodAs an illustrative example, we apply dyadic extensions of the CLPM, RI‐CLPM, and LCM‐SR to investigate the dynamic interplay between depression and relationship satisfaction in a sample of 1699 mixed‐gender couples surveyed in the German Family Panel.ResultsWhile the CLPM indicated a reciprocal relationship between depression and satisfaction, the RI‐CLPM and LCM‐SR indicated a unidirectional association flowing from depression to satisfaction.ConclusionWe discuss how findings like this can foster theory‐building and, ultimately, strengthen relationship science.

The Random-Intercept Cross-Lagged Panel Model (RICLPM) has gained popularity in longitudinal research due to its ability to disaggregate within- and between-subjects variance. This approach more accurately depicts processes over time compared to traditional Cross-Lagged Panel Models (CLPMs). While RICLPMs are increasingly used, their application to data from behavioral interventions still is underexplored. This study aims to address this gap by demonstrating the application of RICLPM using data from a clinical trial of the digital Unified Protocol (iUP), a transdiagnostic cognitive-behavioral intervention applicable to mental and physical health comorbidities. We focus specifically on how RICLPM can be used to examine dynamic psychological processes during treatment, a central yet under-addressed question in behavioral medicine. We provide a methodological tutorial on adapting the model to intervention outcomes data, compare model fit statistics from an RICLPM and a traditional CLPM, and interpret results specifically in the context of psychological processes during a cognitive-behavioral intervention. Our findings show that RICLPM offers superior fit and more precise estimates of within-subject processes, underscoring its value in clinical research. We argue that adopting RICLPM in behavioral medicine research can help accurately identify psychological mechanisms and processes during behavioral interventions in health settings, aiding intervention personalization. The tutorial offers a resource for researchers interested in using RICLPM for more robust longitudinal analyses of behavioral intervention outcomes.

In virtually all areas of psychology, the question of whether a particular construct has a prospective effect on another is of fundamental importance. For decades, the cross-lagged panel model (CLPM) has been the model of choice for addressing this question. However, CLPMs have recently been critiqued, and numerous alternative models have been proposed. Using the association between low self-esteem and depression as a case study, we examined the behavior of seven competing longitudinal models in 10 samples, each with at least four waves of data and sample sizes ranging from 326 to 8,259. The models were compared in terms of convergence, fit statistics, and consistency of parameter estimates. The traditional CLPM and the random intercepts cross-lagged panel model (RI-CLPM) converged in every sample, whereas the other models frequently failed to converge or did not converge properly. The RI-CLPM exhibited better model fit than the CLPM, whereas the CLPM produced more consistent cross-lagged effects (both across and within samples) than the RI-CLPM. We discuss the models from a conceptual perspective, emphasizing that the models test conceptually distinct psychological and developmental processes, and we address the implications of the empirical findings with regard to model selection. Moreover, we provide practical recommendations for researchers interested in testing prospective associations between constructs and suggest using the CLPM when focused on between-person effects and the RI-CLPM when focused on within-person effects. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

This article considers identification, estimation, and model fit issues for models with contemporaneous and reciprocal effects. It explores how well the models work in practice using Monte Carlo studies as well as real-data examples. Furthermore, by using models that allow contemporaneous and reciprocal effects, the paper raises a fundamental question about current practice for cross-lagged panel modeling using models such as cross-lagged panel model (CLPM) or random intercept cross-lagged panel model (RI-CLPM): Can cross-lagged panel modeling be relied on to establish cross-lagged effects? The article concludes that the answer is no, a finding that has important ramifications for current practice. It is suggested that analysts should use additional models to probe the temporalities of the CLPM and RI-CLPM effects to see if these could be considered contemporaneous rather than lagged. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Using random-intercept cross-lagged panel models (RI-CLPM), researchers have concluded that within-individual need for cognition (WI-NFC) negatively affects subsequent within-individual anxiety and depression symptoms (WI-ADS). However, RI-CLPM may be susceptible to spurious results due to regression to the mean. We investigated the risk of spurious associations by fitting two different RI-CLPM:s and evaluating whether results were consistent. A traditional RI-CLPM, an alternative RI-CLPM where covariance between WI-NFC and WI-ADS at the same wave was replaced by a directional regression effect, as well as a stable trait, autoregressive trait, state (STARTS) model, were fitted to data from a representative community-dwelling Dutch sample. Both the traditional and the alternative RI-CLPM indicated a negative effect of initial WI-NFC on subsequent WI-ADS. However, while the former effect implies a negative association the latter effect implies, contrarily, that an increase in WI-NFC predicted an increase in WI-ADS. The STARTS model indicated strong autoregressive effects but no cross-lagged effects between WI-NFC and WI-ADS. Spurious effects may occur in RI-CLPM due to regression to the mean. Specifically, a cross-lagged effect of WI-NFC on subsequent WI-ADS, demonstrated in earlier research, may be spurious.