scholarly journals Model-Based Manifest and Latent Composite Scores in Structural Equation Models

2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Norman Rose ◽  
Wolfgang Wagner ◽  
Axel Mayer ◽  
Benjamin Nagengast
Keyword(s):  
Latent Variables ◽  
Structural Equation ◽  
Missing Values ◽  
Structural Equation Models ◽  
Likelihood Estimation ◽  
Average Score ◽  
Estimation Model ◽  
Model Based ◽  
Sum Score ◽  
Composite Scores

Composite scores are commonly used in the social sciences as dependent and independent variables in statistical models. Typically, composite scores are computed prior to statistical analyses. In this paper, we demonstrate the construction of model-based composite scores that may serve as outcomes or predictors in structural equation models (SEMs). Model-based composite scores of manifest variables are useful in the presence of ignorable missing data, as full-information maximum likelihood estimation can be used for parameter estimation. Model-based composite scores of latent variables account for measurement error in the aggregated variables. We introduce the pseudo-indicator model (PIM) for the construction of three composite scores: (a) the sum score, (b) the weighted sum score, and (c) the average score of manifest and latent variables in SEM. The utility of manifest model-based composite scores in the case of missing values is shown by a simulation study. The use of multiple manifest and latent model-based composite scores in SEM is illustrated with data from motivation research.

scholarly journals Croon’s Bias-Corrected Factor Score Path Analysis for Small- to Moderate-Sample Multilevel Structural Equation Models

2019 ◽  
Vol 24 (1) ◽  
pp. 55-77 ◽  
Author(s):  
Benjamin Kelcey ◽  
Kyle Cox ◽  
Nianbo Dong
Keyword(s):  
Maximum Likelihood ◽  
Path Analysis ◽  
Latent Variables ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Factor Score ◽  
Likelihood Estimation ◽  
Bias Error ◽  
Parameter Estimates ◽  
Multilevel Structural Equation

Maximum likelihood estimation of multilevel structural equation model (MLSEM) parameters is a preferred approach to probe theories involving latent variables in multilevel settings. Although maximum likelihood has many desirable properties, a major limitation is that it often fails to converge and can incur significant bias when implemented in studies with a small to moderate multilevel sample (e.g., fewer than 100 organizations with 10 or less individuals/organization). To address similar limitations in single-level SEM, literature has developed Croon’s bias-corrected factor score path analysis estimator that converges more regularly than maximum likelihood and delivers less biased parameter estimates with small to moderate sample sizes. We derive extensions to this framework for MLSEMs and probe the degree to which the estimator retains these advantages with small to moderate multilevel samples. The estimator emerges as a useful alternative or complement to maximum likelihood because it often outperforms maximum likelihood in small to moderate multilevel samples in terms of convergence, bias, error variance, and power. The proposed estimator is implemented as a function in R using lavaan and is illustrated using a multilevel mediation example.

A Cautionary Note on Incremental Fit Indices Reported by LISREL

Methodology ◽  
2005 ◽  
Vol 1 (2) ◽  
pp. 81-85 ◽  
Author(s):  
Stefan C. Schmukle ◽  
Jochen Hardt
Keyword(s):  
Factor Analysis ◽  
Maximum Likelihood ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Null Model ◽  
Likelihood Estimation ◽  
Parameter Estimates ◽  
Fit Indices ◽  
Cautionary Note ◽  
Confirmatory Factor

Abstract. Incremental fit indices (IFIs) are regularly used when assessing the fit of structural equation models. IFIs are based on the comparison of the fit of a target model with that of a null model. For maximum-likelihood estimation, IFIs are usually computed by using the χ2 statistics of the maximum-likelihood fitting function (ML-χ2). However, LISREL recently changed the computation of IFIs. Since version 8.52, IFIs reported by LISREL are based on the χ2 statistics of the reweighted least squares fitting function (RLS-χ2). Although both functions lead to the same maximum-likelihood parameter estimates, the two χ2 statistics reach different values. Because these differences are especially large for null models, IFIs are affected in particular. Consequently, RLS-χ2 based IFIs in combination with conventional cut-off values explored for ML-χ2 based IFIs may lead to a wrong acceptance of models. We demonstrate this point by a confirmatory factor analysis in a sample of 2449 subjects.

scholarly journals Evaluating the Observed Log-Likelihood Function in Two-Level Structural Equation Modeling with Missing Data: From Formulas to R Code

Psych ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 197-232
Author(s):  
Yves Rosseel
Keyword(s):  
Structural Equation ◽  
Structural Equation Models ◽  
Likelihood Function ◽  
Likelihood Estimation ◽  
Missing At Random ◽  
Equation Modeling ◽  
Computationally Efficient ◽  
Log Likelihood ◽  
Efficient Expression ◽  
Special Case

This paper discusses maximum likelihood estimation for two-level structural equation models when data are missing at random at both levels. Building on existing literature, a computationally efficient expression is derived to evaluate the observed log-likelihood. Unlike previous work, the expression is valid for the special case where the model implied variance–covariance matrix at the between level is singular. Next, the log-likelihood function is translated to R code. A sequence of R scripts is presented, starting from a naive implementation and ending at the final implementation as found in the lavaan package. Along the way, various computational tips and tricks are given.

Clarifying the Factor Structure of the Self-Compassion Scale

2021 ◽  
Author(s):  
Noelle J. Strickland ◽  
Raquel Nogueira-Arjona ◽  
Sean Mackinnon ◽  
Christine Wekerle ◽  
Sherry H. Stewart
Keyword(s):  
Factor Structure ◽  
Lower Order ◽  
Latent Variables ◽  
Structural Equation ◽  
Structural Equation Models ◽  
Well Being ◽  
The Self ◽  
Self Compassion ◽  
The Hierarchical Structure ◽  
Compassion Scale

Abstract. Self-compassion is associated with greater well-being and lower psychopathology. There are mixed findings regarding the factor structure and scoring of the Self-Compassion Scale (SCS). Using confirmatory factor analysis, we tested and conducted nested comparisons of six previously posited factor structures of the SCS. Participants were N = 1,158 Canadian undergraduates (72.8% women, 26.6% men, 0.6% non-binary; Mage = 19.0 years, SD = 2.3). Results best supported a two-factor hierarchical model with six lower-order factors. A general self-compassion factor was not supported at the higher- or lower-order levels; thus, a single total score is not recommended. Given the hierarchical structure, researchers are encouraged to use structural equation models of the SCS with two latent variables: self-caring and self-coldness. A strength of this study is the large sample, while the undergraduate sample may limit generalizability.

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