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Tugay Kaçak; Abdullah Faruk Kiliç – International Journal of Assessment Tools in Education, 2025
Researchers continue to choose PCA in scale development and adaptation studies because it is the default setting and overestimates measurement quality. When PCA is utilized in investigations, the explained variance and factor loadings can be exaggerated. PCA, in contrast to the models given in the literature, should be investigated in…
Descriptors: Factor Analysis, Monte Carlo Methods, Mathematical Models, Sample Size
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Liu, Yan; Zumbo, Bruno D. – Educational and Psychological Measurement, 2007
The impact of outliers on Cronbach's coefficient [alpha] has not been documented in the psychometric or statistical literature. This is an important gap because coefficient [alpha] is the most widely used measurement statistic in all of the social, educational, and health sciences. The impact of outliers on coefficient [alpha] is investigated for…
Descriptors: Psychometrics, Computation, Reliability, Monte Carlo Methods
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Kano, Yutaka – Psychometrika, 1990
Based on the usual factor analysis model, this paper investigates the relationship between improper solutions and the number of factors. The properties of the noniterative estimation method of M. Ihara and Y. Kano in exploratory factor analysis are also discussed. The estimators were compared in a Monte Carlo experiment. (TJH)
Descriptors: Comparative Analysis, Estimation (Mathematics), Factor Analysis, Mathematical Models
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Isaac, Paul D.; Poor, David D. S. – Psychometrika, 1974
Descriptors: Error Patterns, Factor Analysis, Goodness of Fit, Mathematical Models
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Ichikawa, Masanori – Psychometrika, 1992
Asymptotic distributions of the estimators of communalities are derived for the maximum likelihood method in factor analysis. It is shown that equating the asymptotic standard error of the communality estimate to the unique variance estimate is not correct for the unstandardized case. Monte Carlo simulations illustrate the study. (SLD)
Descriptors: Computer Simulation, Equations (Mathematics), Estimation (Mathematics), Factor Analysis
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Cudeck, Robert – Journal of Educational Statistics, 1991
Two algorithms that automatically select subsets of variables (PACE algorithm) and reference variables (Fabin estimators), respectively, used for the noniterative estimators are presented. The PACE algorithm is based on a nonsymmetric matrix sweep operator. A Monte Carlo experiment compares the relative performance of these estimators and others.…
Descriptors: Algorithms, Comparative Analysis, Equations (Mathematics), Estimation (Mathematics)
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Velicer, Wayne F.; And Others – Multivariate Behavioral Research, 1982
Factor analysis, image analysis, and principal component analysis are compared with respect to the factor patterns they would produce under various conditions. The general conclusion that is reached is that the three methods produce results that are equivalent. (Author/JKS)
Descriptors: Comparative Analysis, Data Analysis, Factor Analysis, Goodness of Fit
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Anderson, James C.; Gerbing, David W. – Psychometrika, 1984
This study of maximum likelihood confirmatory factor analysis found effects of practical significance due to sample size, the number of indicators per factor, and the number of factors for Joreskog and Sorbom's (1981) goodness-of-fit index (GFI), GFI adjusted for degrees of freedom, and the root mean square residual. (Author/BW)
Descriptors: Factor Analysis, Factor Structure, Goodness of Fit, Mathematical Models
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Segawa, Eisuke – Journal of Educational and Behavioral Statistics, 2005
Multi-indicator growth models were formulated as special three-level hierarchical generalized linear models to analyze growth of a trait latent variable measured by ordinal items. Items are nested within a time-point, and time-points are nested within subject. These models are special because they include factor analytic structure. This model can…
Descriptors: Bayesian Statistics, Mathematical Models, Factor Analysis, Computer Simulation
Pohlmann, John T. – 1972
The Monte Carlo method was used, and the factors considered were (1) level of main effects in the population; (2) level of interaction effects in the population; (3) alpha level used in determining whether to pool; and (4) number of degrees of freedom. The results indicated that when the ratio degrees of freedom (axb)/degrees of freedom (within)…
Descriptors: Analysis of Variance, Computer Programs, Factor Analysis, Hypothesis Testing
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Broodbooks, Wendy J.; Elmore, Patricia B. – Educational and Psychological Measurement, 1987
The effects of sample size, number of variables, and population value of the congruence coefficient on the sampling distribution of the congruence coefficient were examined. Sample data were generated on the basis of the common factor model, and principal axes factor analyses were performed. (Author/LMO)
Descriptors: Factor Analysis, Mathematical Models, Monte Carlo Methods, Predictor Variables
Kaplan, David – 1993
The impact of the use of data arising from balanced incomplete block (BIB) spiralled designs on the chi-square goodness-of-fit test in factor analysis is considered. Data from BIB designs posses a unique pattern of missing data that can be characterized as missing completely at random (MCAR). Standard approaches to factor analyzing such data rest…
Descriptors: Chi Square, Computer Simulation, Correlation, Factor Analysis
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Cudeck, Robert; Browne, Michael W. – Psychometrika, 1992
A method is proposed for constructing a population covariance matrix as the sum of a particular model plus a nonstochastic residual matrix, with the stipulation that the model holds with a prespecified lack of fit. The procedure is considered promising for Monte Carlo studies. (SLD)
Descriptors: Algorithms, Equations (Mathematics), Estimation (Mathematics), Factor Analysis
Jones, Patricia B.; And Others – 1987
In order to determine the effectiveness of multidimensional scaling (MDS) in recovering the dimensionality of a set of dichotomously-scored items, data were simulated in one, two, and three dimensions for a variety of correlations with the underlying latent trait. Similarity matrices were constructed from these data using three margin-sensitive…
Descriptors: Cluster Analysis, Correlation, Difficulty Level, Error of Measurement
Tucker, Ledyard R.; And Others – 1986
A Monte Carlo study of five indices of dimensionality of binary items used a computer model that allowed sampling of both items and people. Five parameters were systematically varied in a factorial design: (1) number of common factors from one to five; (2) number of items, including 20, 30, 40, and 60; (3) sample sizes of 125 and 500; (4) nearly…
Descriptors: Correlation, Difficulty Level, Educational Research, Expectancy Tables
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