Parallel Analysis with Unidimensional Binary Data

Weng, Li-Jen; Chêng, Chu-yüan

doi:10.1177/0013164404273941

Cited by 62 publications

(87 citation statements)

References 32 publications

(55 reference statements)

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“…The PA results were slightly superior to the OPA results, were nonetheless unsatisfactory. Similarly, Horn (1965) reported that the PA produced consistently determines the threshold values of important components (Beaducel, 2001;Franklin, Gibson, Robertson, Pohlmann, & Fralish, 1995;Weng & Cheng, 2005). This finding is also consistent with the parallel analysis results of data obtained from a 5-point Likert scale (Kalkan, 2014).…”

Section: Discussionsupporting

confidence: 76%

“…Because sample size exerts the largest effect on RMSR, increasing the sample size increases the estimation accuracy (Hooper et al, 2008;Thomas, 2003). Weng and Cheng (2005) stated that tetrachoric correlations in small samples introduces errors in large samples. Eight sample sizes yielded good fits (RMSR < .05) when based on the Pearson correlation, decreasing to 5 when using tetrachoric correlation.…”

Section: Discussionmentioning

confidence: 99%

“…This situation might arise from the partially skewed (0.17-0.54) data in our study. According to Weng and Cheng (2005), Horn's PA method reasonably determine unidimensionality, but is weakened when an items are skewed. Tabachnick and Fidell (2006) stated that transforming a discrete variable into a series of dichotomous variables would degrade the linear relationship between the dichotomous variables and the other variables.…”

Section: Discussionmentioning

confidence: 99%

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The Effect of Sample Size on Parametric and Nonparametric Factor Analytical Methods

2016

EDUC SCI-THEOR PRACT

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Linear factor analysis models used to examine constructs underlying the responses are not very suitable for dichotomous or polytomous response formats. The associated problems cannot be eliminated by polychoric or tetrachoric correlations in place of the Pearson correlation. Therefore, we considered parameters obtained from the NOHARM and FACTOR programs (which use parametric methods) and from the DETECT and DIMTEST programs (which use nonparametric methods) for different sample sizes of a real large dataset (50, 80, 100, 160, 200, 300, 500, 1000, 3000, 5000). A parallel analysis (PA) based on the tetrachoric correlation with the FACTOR program produced inconsistent results among the sampling sizes. However, the analyses based on the Pearson correlation could not adequately determine the dimension numbers.Although DETECT and NOHARM determined the multidimensionality at acceptable level for the 50 sample size, they yielded the most consistent results at sample sizes of 1000 and above.

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Section: Discussionsupporting

confidence: 76%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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The Effect of Sample Size on Parametric and Nonparametric Factor Analytical Methods

2016

EDUC SCI-THEOR PRACT

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“…Timmerman and Lorenzo-Seva (2011) demonstrated that when using the minimum rank factor analysis extraction method, polychoric correlations are preferred to Pearson correlations for parallel analysis when the item data are ordered categorical. Weng and Cheng (2005) found that a parallel analysis yielded quite accurate decisions regarding the number of factors retained for binary data, but their study considered only a one-factor model. Cho, Li, and Bandalos (2009) evaluated the accuracy of parallel analysis for ordinal item data.…”

mentioning

confidence: 99%

On the number of factors to retain in exploratory factor analysis for ordered categorical data

Yang

Xia

2014

Behav Res

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Conducting exploratory factor analysis (EFA) using statistical extraction methods has been recommended, but little is known about the accuracy of the decisions regarding the number of factors to retain for ordered categorical item data by considering a chi-square test, fit indices, and conventional criteria, such as eigenvalue >1 and parallel analysis. With computer-generated data, the authors examined the accuracy of decisions regarding the number of factors to retain for categorical item data, by combining these pieces of information using weighted least-square with mean and variance adjustment estimation methods based on polychoric correlations. A chi-square difference test was also conducted to compare nested EFA models. The results showed that the eigenvalue >1 criterion resulted in too many factors, in general. The chi-square test, chi-square difference test, fit indices, and parallel analysis performed reasonably well when the number of scale points was four, the number of items was 24, the sample size was at least 200, and the categorical distributions were similar across items. However, parallel analysis had a tendency toward factor underextraction when the correlation among factors was .50, particularly for two-point and 12-item scales.

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“…Clarification for findings in Green (1983), Collins et al (1986), and Roznowski et al (1991) was provided by Weng and Cheng (2005). Weng and Cheng varied the number of items, the factor loadings and difficulties of the items, and sample size.…”

Section: Assumptions Associated With the Classical Factor Modelsmentioning

confidence: 99%

On the Relevance of Assumptions Associated with Classical Factor Analytic Approaches†

Kasper¹,

Ünlü²

2013

Front. Psychol.

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A personal trait, for example a person’s cognitive ability, represents a theoretical concept postulated to explain behavior. Interesting constructs are latent, that is, they cannot be observed. Latent variable modeling constitutes a methodology to deal with hypothetical constructs. Constructs are modeled as random variables and become components of a statistical model. As random variables, they possess a probability distribution in the population of reference. In applications, this distribution is typically assumed to be the normal distribution. The normality assumption may be reasonable in many cases, but there are situations where it cannot be justified. For example, this is true for criterion-referenced tests or for background characteristics of students in large scale assessment studies. Nevertheless, the normal procedures in combination with the classical factor analytic methods are frequently pursued, despite the effects of violating this “implicit” assumption are not clear in general. In a simulation study, we investigate whether classical factor analytic approaches can be instrumental in estimating the factorial structure and properties of the population distribution of a latent personal trait from educational test data, when violations of classical assumptions as the aforementioned are present. The results indicate that having a latent non-normal distribution clearly affects the estimation of the distribution of the factor scores and properties thereof. Thus, when the population distribution of a personal trait is assumed to be non-symmetric, we recommend avoiding those factor analytic approaches for estimation of a person’s factor score, even though the number of extracted factors and the estimated loading matrix may not be strongly affected. An application to the Progress in International Reading Literacy Study (PIRLS) is given. Comments on possible implications for the Programme for International Student Assessment (PISA) complete the presentation.

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Parallel Analysis with Unidimensional Binary Data

Cited by 62 publications

References 32 publications

The Effect of Sample Size on Parametric and Nonparametric Factor Analytical Methods

The Effect of Sample Size on Parametric and Nonparametric Factor Analytical Methods

On the number of factors to retain in exploratory factor analysis for ordered categorical data

On the Relevance of Assumptions Associated with Classical Factor Analytic Approaches†

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