A Semi-Hierarchical Confirmatory Factor Model for Speeded Data

Schweizer, Karl; Gold, Andreas; Krampen, Dorothea

doi:10.1080/10705511.2019.1707083

Cited by 4 publications

(6 citation statements)

References 30 publications

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“…The avoidance of replacements of missings is a way of preventing any kind of influence on the properties of an incomplete data set ( Schweizer, Gold, Krampen, & Wang, 2020 ). This approach of dealing with missing data assumes that missing data give rise to systematic variation that can be captured by a latent variable in factor analysis.…”

Section: Discussionmentioning

confidence: 99%

On Modeling Missing Data in Structural Investigations Based on Tetrachoric Correlations With Free and Fixed Factor Loadings

Schweizer

Gold

Krampen

2022

Educational and Psychological Measurement

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In modeling missing data, the missing data latent variable of the confirmatory factor model accounts for systematic variation associated with missing data so that replacement of what is missing is not required. This study aimed at extending the modeling missing data approach to tetrachoric correlations as input and at exploring the consequences of switching between models with free and fixed factor loadings. In a simulation study, confirmatory factor analysis (CFA) models with and without a missing data latent variable were used for investigating the structure of data with and without missing data. In addition, the numbers of columns of data sets with missing data and the amount of missing data were varied. The root mean square error of approximation (RMSEA) results revealed that an additional missing data latent variable recovered the degree-of-model fit characterizing complete data when tetrachoric correlations served as input while comparative fit index (CFI) results showed overestimation of this degree-of-model fit. Whereas the results for fixed factor loadings were in line with the assumptions of modeling missing data, the other results showed only partial agreement. Therefore, modeling missing data with fixed factor loadings is recommended.

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Section: Discussionmentioning

confidence: 99%

On Modeling Missing Data in Structural Investigations Based on Tetrachoric Correlations With Free and Fixed Factor Loadings

Schweizer

Gold

Krampen

2022

Educational and Psychological Measurement

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“…When arranged as a regular array, variation originating from missing data can be expected to be more systematic, i.e., it leads to the larger explained variance. The missing data CFA model and the semi-hierarchical CFA model performed equally well although the semi-hierarchical CFA model was supposed to perform slightly better (Schweizer et al, 2020a ). This lack of difference was presumably due to not enough variability in the sizes of the subsamples of the generated datasets.…”

Section: Discussionmentioning

confidence: 99%

“…Such a model is referred to as semi-hierarchical CFA model (Schweizer et al, 2020a). Figure 1 provides an illustration of the semi-hierarchical CFA model.…”

Section: The Modeling Of the Hierarchical Structurementioning

confidence: 99%

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On Modeling Missing Data of an Incomplete Design in the CFA Framework

et al. 2020

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The paper reports an investigation on whether valid results can be achieved in analyzing the structure of datasets although a large percentage of data is missing without replacement. Two types of confirmatory factor analysis (CFA) models were employed for this purpose: the missing data CFA model with an additional latent variable for representing the missing data and the semi-hierarchical CFA model that also includes the additional latent variable and reflects the hierarchical structure assumed to underlie the data. Whereas, the missing data CFA model assumes that the model is equally valid for all participants, the semi-hierarchical CFA model is implicitly specified differently for subgroups of participants with and without omissions. The comparison of these models with the regular one-factor model in investigating simulated binary data revealed that the modeling of missing data prevented negative effects of missing data on model fit. The investigation of the accuracy in estimating the factor loadings yielded the best results for the semi-hierarchical CFA model. The average estimated factor loadings for items with and without omissions showed the expected equal sizes. But even this model tended to underestimate the expected values.

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“…This coefficient includes probabilities (Pr). For binary variables X(X ∈ {0, 1}) and Y(Y ∈ {0, 1}) it is defined as cov Pb (X, Y) Pr(X 1∧Y 1) − Pr(X 1)Pr(Y 1) (8) where 1 serves as the code for the target response that may be the correct response [10]. The computing of the probabilitybased covariance starts with counting followed by the transformation of the counts into probabilities that show interval-level quality.…”

Section: The Input To Confirmatory Factor Analysismentioning

confidence: 99%

Effect of Dichotomization on the Latent Structure of Data

Schweizer

Gold

Krampen

2021

Front. Appl. Math. Stat.

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We investigated whether dichotomous data showed the same latent structure as the interval-level data from which they originated. Given constancy of dimensionality and factor loadings reflecting the latent structure of data, the focus was on the variance of the latent variable of a confirmatory factor model. This variance was shown to summarize the information provided by the factor loadings. The results of a simulation study did not reveal exact correspondence of the variances of the latent variables derived from interval-level and dichotomous data but shrinkage. Since shrinkage occurred systematically, methods for recovering the original variance were fleshed out and evaluated.

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A Semi-Hierarchical Confirmatory Factor Model for Speeded Data

Cited by 4 publications

References 30 publications

On Modeling Missing Data in Structural Investigations Based on Tetrachoric Correlations With Free and Fixed Factor Loadings

On Modeling Missing Data in Structural Investigations Based on Tetrachoric Correlations With Free and Fixed Factor Loadings

On Modeling Missing Data of an Incomplete Design in the CFA Framework

Effect of Dichotomization on the Latent Structure of Data

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