Implementation Aspects in Regularized Structural Equation Models

Robitzsch, Alexander

doi:10.3390/a16090446

Cited by 3 publications

(7 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For this goal, model selection based on information criteria can prove helpful in order to control type-I error rates. Second, if the focus lies on structural parameters (such as group means or factor correlations), choosing a parsimonious model that tries to penalize the number of estimated parameters, like in information criteria, may not be beneficial in terms of bias and variability of structural parameters [21]. It can be advantageous to use a sufficiently small regularization parameter λ to ensure the empirical identifiability of the model but not to focus on effect selection if structural parameters are of interest [63].…”

Section: Discussionmentioning

confidence: 99%

“…Hence, particular estimation techniques for nondifferentiable optimization problems must be applied [14,17,18]. As an alternative, the nondifferentiable optimization function can be replaced by a differentiable approximation [19][20][21][22]. For example, the absolute value function x → |x| in the SCAD penalty can be replaced with x → √ x 2 + ε for a sufficiently small ε such as ε = 0.001.…”

Section: Introductionmentioning

confidence: 99%

“…O'Neill and Burke [26] proposed an estimation approach to regularized estimation that directly minimizes a smooth version of the BIC (i.e., smooth Bayesian information criterion, SBIC) for regression models. This direct estimation approach has been successfully implemented for structural equation models [21,27]. For these models, the optimization based on SBIC had similar, if not better, performance than the ordinary estimation of regularized models based on the AIC and BIC.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Smooth Information Criterion for Regularized Estimation of Item Response Models

Robitzsch

2024

Algorithms

Self Cite

View full text Add to dashboard Cite

Item response theory (IRT) models are frequently used to analyze multivariate categorical data from questionnaires or cognitive test data. In order to reduce the model complexity in item response models, regularized estimation is now widely applied, adding a nondifferentiable penalty function like the LASSO or the SCAD penalty to the log-likelihood function in the optimization function. In most applications, regularized estimation repeatedly estimates the IRT model on a grid of regularization parameters λ. The final model is selected for the parameter that minimizes the Akaike or Bayesian information criterion (AIC or BIC). In recent work, it has been proposed to directly minimize a smooth approximation of the AIC or the BIC for regularized estimation. This approach circumvents the repeated estimation of the IRT model. To this end, the computation time is substantially reduced. The adequacy of the new approach is demonstrated by three simulation studies focusing on regularized estimation for IRT models with differential item functioning, multidimensional IRT models with cross-loadings, and the mixed Rasch/two-parameter logistic IRT model. It was found from the simulation studies that the computationally less demanding direct optimization based on the smooth variants of AIC and BIC had comparable or improved performance compared to the ordinarily employed repeated regularized estimation based on AIC or BIC.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Smooth Information Criterion for Regularized Estimation of Item Response Models

Robitzsch

2024

Algorithms

Self Cite

View full text Add to dashboard Cite

show abstract

“…The ingenious idea of O'Neill and Burke [15] was to replace the nondifferentiable L 0 loss function χ with its differentiable approximation χ ε (see (8) and Ref. [16] for a more comprehensive treatment). Therefore, the parameter θ can be estimated as…”

Section: A Direct Bic Minimization In Regularized Maximum Likelihood ...mentioning

confidence: 99%

“…To sum up, this article focuses on implementation details of SEM estimation based on the L p (0 < p ≤ 1) and the newly proposed L 0 loss functions, while [16] was devoted to regularized SEM estimation, which can also be utilized for model-robust estimation. A comparison of regularized estimation and robust loss functions can be found in [14].…”

Section: Introductionmentioning

confidence: 99%

L0 and Lp Loss Functions in Model-Robust Estimation of Structural Equation Models

Robitzsch

2023

Psych

Self Cite

View full text Add to dashboard Cite

The Lp loss function has been used for model-robust estimation of structural equation models based on robustly fitting moments. This article addresses the choice of the tuning parameter ε that appears in the differentiable approximations of the nondifferentiable Lp loss functions. Moreover, model-robust estimation based on the Lp loss function is compared with a recently proposed differentiable approximation of the L0 loss function and a direct minimization of a smoothed version of the Bayesian information criterion in regularized estimation. It turned out in a simulation study that the L0 loss function slightly outperformed the Lp loss function in terms of bias and root mean square error. Furthermore, standard errors of the model-robust SEM estimators were analytically derived and exhibited satisfactory coverage rates.

show abstract

Implementation Aspects in Invariance Alignment

Robitzsch

2023

Stats

View full text Add to dashboard Cite

In social sciences, multiple groups, such as countries, are frequently compared regarding a construct that is assessed using a number of items administered in a questionnaire. The corresponding scale is assessed with a unidimensional factor model involving a latent factor variable. To enable a comparison of the mean and standard deviation of the factor variable across groups, identification constraints on item intercepts and factor loadings must be imposed. Invariance alignment (IA) provides such a group comparison in the presence of partial invariance (i.e., a minority of item intercepts and factor loadings are allowed to differ across groups). IA is a linking procedure that separately fits a factor model in each group in the first step. In the second step, a linking of estimated item intercepts and factor loadings is conducted using a robust loss function L0.5. The present article discusses implementation alternatives in IA. It compares the default L0.5 loss function with Lp with other values of the power p between 0 and 1. Moreover, the nondifferentiable Lp loss functions are replaced with differentiable approximations in the estimation of IA that depend on a tuning parameter ε (such as, e.g., ε=0.01). The consequences of choosing different values of ε are discussed. Moreover, this article proposes the L0 loss function with a differentiable approximation for IA. Finally, it is demonstrated that the default linking function in IA introduces bias in estimated means and standard deviations if there is noninvariance in factor loadings. Therefore, an alternative linking function based on logarithmized factor loadings is examined for estimating factor means and standard deviations. The implementation alternatives are compared through three simulation studies. It turned out that the linking function for factor loadings in IA should be replaced by the alternative involving logarithmized factor loadings. Furthermore, the default L0.5 loss function is inferior to the newly proposed L0 loss function regarding the bias and root mean square error of factor means and standard deviations.

show abstract

Implementation Aspects in Regularized Structural Equation Models

Cited by 3 publications

References 60 publications

Smooth Information Criterion for Regularized Estimation of Item Response Models

Smooth Information Criterion for Regularized Estimation of Item Response Models

L0 and Lp Loss Functions in Model-Robust Estimation of Structural Equation Models

Implementation Aspects in Invariance Alignment

Contact Info

Product

Resources

About