Not Positive Definite Correlation Matrices in Exploratory Item Factor Analysis: Causes, Consequences and a Proposed Solution

Lorenzo‐Seva, Urbano; Ferrando, Pere J.

doi:10.1080/10705511.2020.1735393

Cited by 61 publications

(46 citation statements)

References 35 publications

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“…Considering that the SDQ items are polytomous ordinal items, network and factor models were both estimated based on the zero-order polychoric correlation matrix (Epskamp and Fried, 2018). While the use of zero-order polychoric correlation matrix is recommended for ordinal items, "polychoric interitem correlation matrices that fail to be positive definitive are relatively common" (Lorenzo-Seva and Ferrando, 2021). In case of a non-positive definite correlation matrix, we used the Straight Smoothing algorithm (Bentler and Yuan, 2011) recommended by Lorenzo-Seva and Ferrando (2021).…”

Section: Model Fitmentioning

confidence: 99%

“…While the use of zero-order polychoric correlation matrix is recommended for ordinal items, "polychoric interitem correlation matrices that fail to be positive definitive are relatively common" (Lorenzo-Seva and Ferrando, 2021). In case of a non-positive definite correlation matrix, we used the Straight Smoothing algorithm (Bentler and Yuan, 2011) recommended by Lorenzo-Seva and Ferrando (2021). Kan et al (2020) recommended that for both factor and network models, the absolute fit indices (i.e., RMSEA, CFI) should be calculated based on the discrepancy between the zero-order correlation matrix implied by the factor or network model and the observed zeroorder correlation matrix.…”

Section: Model Fitmentioning

confidence: 99%

“…The unrestricted five-factor model could not be estimated in LSIC Wave 4K and SAABC Wave 5 as convergence was not achieved. One problem with the unrestricted factor model is that, while they are preferred to the restricted factor model in the presence of cross-loadings, convergence cannot always be achieved (Lorenzo-Seva and Ferrando, 2021).…”

Section: Model Fitmentioning

confidence: 99%

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Exploratory Graph Analysis of the Strengths and Difficulties Questionnaire for Aboriginal and/or Torres Strait Islander Children

et al. 2021

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In Australia, one of the most frequently used measures for assessing social and emotional well-being (SEWB) of Aboriginal and/or Torres Strait Islander children is the Strengths and Difficulties Questionnaire (SDQ). Previous studies on state-level validations have indicated the problems associated with the original five-factor SDQ structure, especially in the dimension of Peer Problems. The aim of this study was to use a novel psychometric methodology, namely Exploratory Graph Analysis (EGA), to evaluate the dimensionality of caregiver-informant SDQ version 4–10 years at a national level in Australia. Data for this study were retrospectively collected from two independent longitudinal studies: the Longitudinal Study of Indigenous Children (LSIC) and South Australian Aboriginal Birth Cohort (SAABC). The caregiver-informed SDQ version 4–10 years was applied across several study waves, including more than 4,000 responses. To conduct EGA, Gaussian graphical models (GGMs) were estimated using the Least Absolute Shrinkage and Selection Operator. About 2,500 bootstrap samples were also employed to investigate dimensions and item stability. The findings indicated robust evidence against the construct validity of the original five-factor SDQ structure. Future studies should conduct a direct external validation of the findings with Aboriginal and/or Torres Strait Islander parents/carers and community groups to develop the guidelines for future use of the instrument among Aboriginal and/or Torres Strait Islander children in Australia.

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Section: Model Fitmentioning

confidence: 99%

Section: Model Fitmentioning

confidence: 99%

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Exploratory Graph Analysis of the Strengths and Difficulties Questionnaire for Aboriginal and/or Torres Strait Islander Children

et al. 2021

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“…Therefore, applying them to covariance matrices would result in unchanged diagonal elements and consequently further changes in off-diagonal elements. Several of those methods are explained by Marée [11], and Lorenzo-Seva and Ferrando [13]. As examples, here, a few methods are explained briefly.…”

Section: Other Methodsmentioning

confidence: 99%

mbend: an R package for bending non-positive-definite symmetric matrices to positive-definite

Nilforooshan

2020

BMC Genet

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Background: R package mbend was developed for bending symmetric non-positive-definite matrices to positivedefinite (PD). Bending is a procedure of transforming non-PD matrices to PD. The covariance matrices used in multi-trait best linear unbiased prediction (BLUP) should be PD. Two bending methods are implemented in mbend. The first is an unweighted bending with small positive values in a descending order replacing negative eigenvalues (LRS14), and the second method is a weighted (precision-based) bending with a custom small positive value (ϵ) replacing smaller eigenvalues (HJ03). Weighted bending is beneficial, as it relaxes low precision elements to change and it reduces or prohibits the change in high precision elements. Therefore, a weighted version of LRS14 was developed in mbend. In cases where the precision of matrix elements is unknown, the package provides an unweighted version of HJ03. Another unweighted bending method (DB88) was tested, by which all eigenvalues are changed (eigenvalues less than ϵ replaced with 100 × ϵ), and it is originally designed for correlation matrices. Results: Different bending procedures were conducted on a 5 × 5 covariance matrix (V), V converted to a correlation matrix (C) and an ill-conditioned 1000 × 1000 genomic relationship matrix (G). Considering weighted distance statistics between matrix elements before and after bending, weighting considerably improved the bending quality. For weighted and unweighted bending of V and C, HJ03-4 (HJ03, ϵ = 10 −4) performed the best. HJ03-2 (HJ03, ϵ = 10 −2) ranked better than LRS14 for V, but not for C. Though the differences were marginal, LRS14 performed the best for G. DB88-4 (DB88, ϵ = 10 −4) was used for unweighted bending and it ranked the last. This method could perform considerably better with a lower ϵ. Conclusions: R package mbend provides necessary tools for transforming symmetric non-PD matrices to PD, using different methods and parameters. There were benefits in both weighted bending and small positive values in a descending order replacing negative eigenvalues. Thus, weighted LRS14 was implemented in mbend. Different bending methods might be preferable for different matrices, depending on the matrix type (covariance vs. correlation), number and the magnitude of negative eigenvalues, and the matrix size.

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“…Since our correlation matrix was not positive definite due to a small sample size, the FACTOR program allowed us to apply a smoothing algorithm [15]. However, this algorithm destroyed a substantial amount of covariance in the process, which required us to remove several items that were highly correlated to other items in order to generate a correlation matrix acceptable for EFA.…”

Section: B Exploratory Factor Analysismentioning

confidence: 99%

Exploratory factor analysis of the QMCA

Quaal¹,

Passante²,

Pollock³

et al. 2020

2020 Physics Education Research Conference Proceedings

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This investigation is situated within an ongoing project which seeks to understand student thinking in upperdivision introductory quantum mechanics courses. Recently, the Quantum Mechanics Concept Assessment (QMCA) was revised to include additional items in spin-basis contexts to reflect the rising prevalence of the "spins-first" instructional paradigm. In this work, we utilize exploratory factor analysis to group items on the QMCA based on common variance. Student responses were collected from several large institutions over the 2018-2019 academic year, with the three largest institutions following a "spins-first" curriculum. In interpreting our factor structure, we focus on the placement of isomorphic questions and the original concept framework of the QMCA, as well as a tentative interpretation of factor groupings. We conclude by discussing how these groupings may be further investigated, as well as implications for subsequent iterations of the QMCA and research on student thinking in these two contexts.

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Not Positive Definite Correlation Matrices in Exploratory Item Factor Analysis: Causes, Consequences and a Proposed Solution

Cited by 61 publications

References 35 publications

Exploratory Graph Analysis of the Strengths and Difficulties Questionnaire for Aboriginal and/or Torres Strait Islander Children

Exploratory Graph Analysis of the Strengths and Difficulties Questionnaire for Aboriginal and/or Torres Strait Islander Children

mbend: an R package for bending non-positive-definite symmetric matrices to positive-definite

Exploratory factor analysis of the QMCA

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