Robustness of Individual Score Methods against Model Misspeciﬁcation in Autoregressive Panel Models

Hardt, Katinka; Hecht, Martin; Voelkle, Manuel C.

doi:10.1080/10705511.2019.1642755

Cited by 5 publications

(4 citation statements)

References 42 publications

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“…Often, the residual covariance matrix Θ is replaced with the model implied covariance matrix, which yields identical results (Bentler & Yuan, 1997; Loncke et al, 2018). Standard errors for the Bartlett scores can be computed by taking the square root of the diagonal elements of the estimation error variance-covariance matrix PB (Hardt et al, 2020; Lawley & Maxwell, 1971), which is defined as …”

Section: Designs As Confirmatory Factor Analysis Modelsmentioning

confidence: 99%

“…Regression scores of a subject j are defined as where Φ is the covariance matrix of the factors, Λ is the factor loading matrix, Σ is the model-implied covariance matrix of the observed variables and yj is the response vector of subject j (Hardt et al, 2019; Thomson, 1938; Thurstone, 1934). Standard errors for the estimated regression scores can be computed by taking the square root of the diagonal elements of the estimation error variance-covariance matrix PR (Hardt et al, 2020; Lawley & Maxwell, 1971), which is defined as …”

Section: Designs As Confirmatory Factor Analysis Modelsmentioning

confidence: 99%

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Factor score estimation in multimethod measurement designs with planned missing data.

Lawes¹,

Eid²

2023

Psychological Methods

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Multimethod measurement designs with planned missing data (MMM-PMD) aim at combining cheap proxy methods (e.g., self-reports) with an expensive gold standard method (e.g., biomarker) in order to improve the cost-efficiency of research designs. This article presents a comprehensive simulation study investigating whether accurate factor scores with trustworthy confidence or credible intervals for the gold standard method can be obtained in MMM-PMD designs. The results indicate that the Bartlett-FIML, regression-FIML, and fully Bayesian estimator perform equally well in terms of recovering the true rank-order and absolute level of the factor scores for subjects with complete data. However, for subjects with planned missing data the estimated factor scores are considerably biased and cannot be computed with the Bartlett-FIML estimator. The confidence or credible intervals for the estimated factor scores are trustworthy for complete cases. For subjects with planned missing data, the coverage rates vary considerably across conditions. Thus, the present study illustrates that individual scores from MMM-PMD designs should not be used for consequential individual decisions. Still, factor scores from MMM-PMD designs might be useful when used for secondary analyses that rely on group-level statistics like computing propensity scores for matching purposes or for factor score regression. The simulation results underline that multiple reliable proxy methods that are highly correlated with the gold standard method but are not highly correlated with each other should be administered to maximize the accuracy of the estimated factor scores as well as the trustworthiness of the corresponding confidence or credible intervals.

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Section: Designs As Confirmatory Factor Analysis Modelsmentioning

confidence: 99%

Section: Designs As Confirmatory Factor Analysis Modelsmentioning

confidence: 99%

Factor score estimation in multimethod measurement designs with planned missing data.

Lawes¹,

Eid²

2023

Psychological Methods

View full text Add to dashboard Cite

show abstract

“…Standard errors for the Bartlett scores can be computed by taking the square root of the diagonal elements of the estimation error variance-covariance matrix B P (Hardt et al, 2020;Lawley & Maxwell, 1971), which is defined as…”

Section: Maximum Likelihood Estimator For Factor Scoresmentioning

confidence: 99%

“…where Φ is the covariance matrix of the factors, Λ is the factor loading matrix, Σ is the model-implied covariance matrix of the observed variables and j y is the response vector of subject j (Hardt et al, 2019;Thomson, 1938;Thurstone, 1934). Standard errors for the estimated regression scores can be computed by taking the square root of the diagonal elements of the estimation error variance-covariance matrix R P (Hardt et al, 2020;Lawley & Maxwell, 1971), which is defined as…”

Section: Empirical Bayes Estimatormentioning

confidence: 99%

Factor Score Estimation in Multi-Method Measurement Designs With Planned Missing Data

Lawes¹,

Eid²

2022

Preprint

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Multi-method measurement designs with planned missing data (MMM-PMD) aim at combining cheap proxy methods (e.g., self-reports) with an expensive gold standard method (e.g., biomarker) in order to improve the cost-efficiency of research designs. This article presents a comprehensive simulation study investigating whether accurate factor scores with trustworthy confidence or credible intervals for the gold standard method can be obtained in MMM-PMD designs. The results indicate that the Bartlett-FIML, regression-FIML and fully Bayesian estimator perform equally well in terms of recovering the true rank-order and absolute level of the factor scores for subjects with complete data. However, for subjects with planned missing data the estimated factor scores are considerably biased and cannot be computed with the Bartlett-FIML estimator. The confidence or credible intervals for the estimated factor scores are trustworthy for complete cases. For subjects with planned missing data, the coverage rates vary considerably across conditions. Thus, the present study illustrates that individual scores from MMM-PMD designs should not be used for consequential individual decisions. Still, factor scores from MMM-PMD designs might be useful when used for secondary analyses that rely on group-level statistics like computing propensity scores for matching purposes or for factor score regression. The simulation results underline that multiple reliable proxy methods that are highly correlated with the gold standard method but are not highly correlated with each other should be administered to maximize the accuracy of the estimated factor scores as well as the trustworthiness of the corresponding confidence or credible intervals.

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Integrating Out Nuisance Parameters for Computationally More Efficient Bayesian Estimation – An Illustration and Tutorial

Hecht

Gische

Vogel

et al. 2019

Structural Equation Modeling: A Multidisciplinary Journal

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Bayesian estimation has become very popular. However, run time of Bayesian models is often unsatisfactorily high. In this illustration, we show how to reduce run time by (a) integrating out nuisance model parameters and by (b) reformulating the model based on covariances and means. The core concept is to use the sample scatter matrix which is in our case Wishart distributed with the model-implied covariance matrix as the scale matrix. To illustrate this approach, we choose the popular multi-level null (intercept-only) model, provide a step-by-step instruction on how to implement this model in a multipurpose Bayesian software, and show how structural equation modeling techniques can be employed to bypass mathematically challenging derivations. A simulation study showed that run time is considerably reduced and an empirical example illustrates our approach. Further, we show how the JAGS sampling progress can be monitored and stopped automatically when convergence and precision criteria are reached.

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Robustness of Individual Score Methods against Model Misspeciﬁcation in Autoregressive Panel Models

Cited by 5 publications

References 42 publications

Factor score estimation in multimethod measurement designs with planned missing data.

Factor score estimation in multimethod measurement designs with planned missing data.

Factor Score Estimation in Multi-Method Measurement Designs With Planned Missing Data

Integrating Out Nuisance Parameters for Computationally More Efficient Bayesian Estimation – An Illustration and Tutorial

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