Residual Structural Equation Models

Abstract The residual variables in a structural equation model can be used to create a secondary structural model which we call the residual structural equation model (RSEM). We describe the maximum-likelihood, weighted least squares and Bayesian estimations for RSEM. The methodology is illustrated with several examples and simulation studies. We discuss the implementation of RSEM in the Mplus software package and provide scripts for the simulation studies. The RSEM framework is utilized to estimate and simplify popular models such as the random intercept cross-lagged panel model (RI-CLPM) and the latent curve model with structured residuals (LCM-SR). We discuss in details RSEM models with categorical observed variables as well as categorical latent variables in the context of mixture modeling.

• Publication year

  2022

• Venue

  Structural Equation Modeling: A Multidisciplinary Journal

• Publication date

  2022-06-14

• Fields of study

  Not labeled

• Identifiers
  DOI 10.1080/10705511.2022.2074422
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Advances in Bayesian Model Fit Evaluation for Structural Equation Models

  2020cited by this paper
• On the Differences between General Cross-Lagged Panel Model and Random-Intercept Cross-Lagged Panel Model: Interpretation of Cross-Lagged Parameters and Model Choice

  2020cited by this paper
• Three Extensions of the Random Intercept Cross-Lagged Panel Model

  2020cited by this paper
• Testing prospective effects in longitudinal research: Comparing seven competing cross-lagged models.

  2020influential reference
• A unified framework of longitudinal models to examine reciprocal relations.

  2019cited by this paper
• From Data to Causes I: Building A General Cross-Lagged Panel Model (GCLM)

  2019influential reference
• From Data to Causes II: Comparing Approaches to Panel Data Analysis

  2019influential reference
• Comparison of Models for the Analysis of Intensive Longitudinal Data

  2019influential reference
• Dynamic Structural Equation Models

  2018cited by this paper
• Latent Variable Centering of Predictors and Mediators in Multilevel and Time-Series Models

  2018influential reference
• A critique of the cross-lagged panel model.

  2015cited by this paper
• Bayesian Structural Equation Modeling With Cross-Loadings and Residual Covariances

  2015cited by this paper
• Multiple-Group Factor Analysis Alignment

  2014cited by this paper
• The separation of between-person and within-person components of individual change over time: a latent curve model with structured residuals.

  2014cited by this paper
• Bayesian structural equation modeling: a more flexible representation of substantive theory.

  2012cited by this paper
• General Random Effect Latent Variable Modeling : Random Subjects , Items , Contexts , and Parameters

  2012cited by this paper
• Using Bayesian Priors for More Flexible Latent Class Analysis

  2011influential reference
• A General Panel Model with Random and Fixed Effects: A Structural Equations Approach

  2010cited by this paper
• Bayesian Analysis Using Mplus: Technical Implementation

  2010influential reference
• Effects of selection and training on unit-level performance over time: a latent growth modeling approach.

  2009cited by this paper
• Auxiliary Variables Predicting Missing Data

  2008influential reference
• Limited Information Goodness-of-fit Testing in Multidimensional Contingency Tables

  2006cited by this paper
• Combined pharmacotherapies and behavioral interventions for alcohol dependence: the COMBINE study: a randomized controlled trial.

  2006cited by this paper
• Empirical and conceptual problems with longitudinal trait-state models: introducing a trait-state-occasion model.

  2005cited by this paper
• Latent Variable Analysis With Categorical Outcomes : Multiple-Group And Growth Modeling In Mplus

  2002cited by this paper
• STRUCTURAL ANALYSIS OF COVARIANCE AND CORRELATION MATRICES

  2000cited by this paper
• The trait-state-error model for multiwave data.

  1995cited by this paper
• Model modification

  1989cited by this paper
• Time Series Modelling and Interpretation

  1976cited by this paper
• Time series analysis, forecasting and control

  1972cited by this paper
• The Effects of Selection

  1915cited by this paper

• Is social responsibility a factor that influences athletes’ environmental intention and behaviours? A case study on a university football club members in Japan

  2026cites this paper
• The Construction of a Growth Model with Residual Structure Equation Modeling: An Example Analysis

  2026cites this paper
• Analyzing the Dynamics of Auditory Distraction Using Multigroup Multilevel Structural Equation Modeling

  2026cites this paper
• Emotions following social media use and their relations to mental health in young people: An ecological momentary assessment study.

  2025cites this paper
• Within-person prospective associations between depressive symptoms, abstinence self-efficacy and smoking cessation following smoking cessation treatment.

  2025cites this paper
• Residual Structural Equation Modeling with Nonnormal Distribution

  2025influential citation
• Prospective associations between smoking abstinence and anhedonia among people who seek smoking cessation treatment.

  2025cites this paper
• Mobile phone addiction impairs intuitive eating among Chinese adolescents: A network analysis and a chain mediation model

  2025cites this paper
• Longitudinal causal dynamics between perceived burdensomeness and suicidal ideation: Population-based cohort study.

  2025cites this paper
• Longitudinal changes in environmental understanding and sensitivity in adolescent years

  2025cites this paper
• The Motivational Intelligence Test-Questionnaire (MOTI): development and validation

  2025cites this paper
• The assessment of physiotherapy practice is a robust measure of entry-level physiotherapy standards: Reliability and validity evidence from a large, representative sample

  2025cites this paper
• Non-normal GMM with Covariates: A Modified 3-Step Analysis

  2025cites this paper
• Review of Dynamic Structural Equation Models for Real-Time Consumer Behaviour: Methodological Advances and Applications Insights

  2025cites this paper
• Analyzing cost impacts across the entire process of prefabricated building components from design to application

  2025influential citation
• The dynamic interplay between neuroticism, extraversion, and problematic gaming in adolescents: A 4-wave longitudinal study

  2025cites this paper
• Assessing Measurement Invariance in a University Entrance Exam: A Comparison of Multigroup Confirmatory Factor Analysis Alignment Method vs. Multigroup Item Response Theory

  2024cites this paper
• Can cross-lagged panel modeling be relied on to establish cross-lagged effects? The case of contemporaneous and reciprocal effects.

  2024influential citation
• Considering between- and within-person relations in auto-regressive cross-lagged panel models for developmental data.

  2024cites this paper
• The interdependence of substance use, satisfaction with life, and psychological distress: a dynamic structural equation model analysis

  2024cites this paper
• Fitting Cross-Lagged Panel Models with the Residual Structural Equations Approach

  2024influential citation
• Yapısal Eşitlik Modellemesi Uygulamalarının Raporlanmasında Kullanılabilecek Bir Kontrol Listesi YEM-KL

  2024cites this paper
• Time-lagged panel models in psychotherapy process and mechanisms of change research: Methodological challenges and advances.

  2024cites this paper
• Residual Graph Convolution Collaborative Filtering with Asymmetric neighborhood aggregation

  2024cites this paper
• Cracking Chicken-Egg Conundrums: Juxtaposing Contemporaneous and Lagged Reciprocal Effects Models of Academic Self-Concept and Achievement’s Directional Ordering

  2024cites this paper
• Cross-lagged panel modeling with binary and ordinal outcomes.

  2024cites this paper
• A meta-analytic examination of sensitive responsiveness as a mediator between depression in mothers and psychopathology in children

  2024cites this paper
• Linear and Nonlinear Indices of Score Accuracy and Item Effectiveness for Measures That Contain Locally Dependent Items

  2024cites this paper
• Prognostic prediction and analysis of key factors: a study of haemorrhagic stroke based on LGBM regression and structural equation modelling Prognostic Prediction of Haemorrhagic Stroke Factors LGBM Regression and Structural Equation Modelling Analysis

  2024cites this paper
• Dynamic interplay of developing internalising and externalising mental health from early childhood to mid-adolescence: Teasing apart trait, state, and cross-cohort effects

  2024cites this paper
• Latent Interaction Effect in the CLPM Model: A Two-Step Multiple Imputation Analysis

  2024influential citation
• The reciprocal relationships between economic status and mental health: Investigating the between-person and within-person effects in a three-wave longitudinal study.

  2024cites this paper
• Subjective well-being and attitudes toward outgroup members

  2024cites this paper
• Tracking adolescent students’ educational pathways to university through school engagement, parental expectations, and student aspirations

  2024cites this paper
• Disentangling the temporal relationship between alcohol‐related attitudes and heavy episodic drinking in adolescents within a randomized controlled trial

  2024cites this paper
• Dynamic structural equation models with binary and ordinal outcomes in Mplus

  2023cites this paper
• Effects of multicultural education on student engagement in low- and high-concentration classrooms: the mediating role of student relationships

  2023cites this paper
• A Simple Two-Step Procedure for Fitting Fully Unrestricted Exploratory Factor Analytic Solutions with Correlated Residuals

  2023cites this paper
• Latent Profile Transition Analysis with Random Intercepts (RI-LPTA)

  2023cites this paper
• Structural equation model of the spatial distribution of water engineering facilities along the Beijing-Hangzhou grand canal and its relationship with natural factors

  2023cites this paper
• One Does Not Simply Correct for Serial Dependence

  2023cites this paper
• Prevalence and stability of blood–injection–injury phobia in childhood—A prospective community study in Norway

  2023cites this paper
• Daily links between leisure activities, stress, and well-being during the transition to university

  2023cites this paper
• Photoperiod effects on guar (Cyamopsis tetragonoloba L.)

  2023cites this paper
• Penalized Structural Equation Models

  2023cites this paper
• Maternal Mental Health and Children’s Problem Behaviours: A Bi-directional Relationship?

  2023influential citation
• Design of orthognathic virtual surgery based on deep learning

  2023cites this paper
• The future is dynamic: A call for intensive longitudinal data in immunopsychiatry.

  2023cites this paper
• Assessing model fit for SEM models with categorical variables via contingency tables

  2022influential citation
• Directional Ordering of Self-Concept, School Grades, and Standardized Tests Over Five Years: New Tripartite Models Juxtaposing Within- and Between-Person Perspectives

  2022cites this paper
• A Comparison of Different Approaches for Estimating Cross-Lagged Effects from a Causal Inference Perspective

  2022cites this paper
• Heterogeneity in Temporal Dynamics of Pain and Affect Among Individuals With Chronic Back Pain and Associations With Risk for Future Opioid-Related Problems

  2021cites this paper
• Cross-Lagged Panel Modeling with Categorical Outcomes

  year unknowninfluential citation