arXiv subjects

Andre Beauducel

Publications and source records attributed to Andre Beauducel.

7 recordsLinked to original sources

arXiv2026

Purely analytic composites: Relative variance contributions of indicators corresponding to a priori indicator weights

Composites are often created to facilitate the work of decision-makers. Therefore, practical or theoretical considerations may lead to a priori weights of the indicators forming a composite. Composites that are created a weighted aggregates are not the result of data analysis and may therefore be termed 'analytic composites'. However, it has already been shown that the variance contributions of indicators within analytic composites are affected by the indicator variance and indicator inter-correlations. In the present study purely analytic composites are proposed, having exactly the variance contribution of indicators within the composites that are a priori defined by the indicator weights. An example based on simulated data illustrates the difference between analytic composites and purely analytic composites. As an application area, we propose that purely analytic composites could be of interest in the exchange-traded fund. An R-script for the computation of purely analytic composites is given in the Appendix.

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arXiv2017

Violation of the sphericity assumption and its effect on Type-I error rates in repeated measures ANOVA and multi-level linear models (MLM)

This study aims to investigate the effects of violations of the sphericity assumption on Type I error rates for different methodical approaches of repeated measures analysis using a simulation approach. In contrast to previous simulation studies on this topic, up to nine measurement occasions were considered. Therefore, two populations representing the conditions of a violation vs. a non-violation of the sphericity assumption without any between-group effect or within-subject effect were created and 5,000 random samples of each population were drawn. Finally, the mean Type I error rates for Multilevel linear models (MLM) with an unstructured covariance matrix (MLM-UN), MLM with compound-symmetry (MLM-CS) and for repeated measures analysis of variance (rANOVA) models (without correction, with Greenhouse-Geisser-correction, and Huynh-Feldt-correction) were computed. To examine the effect of both the sample size and the number of measurement occasions, sample sizes of n = 20, 40, 60, 80, and 100 were considered as well as measurement occasions of m = 3, 6 and 9. For MLM-UN, the results illustrate a massive progressive bias for small sample sizes (n =20) and m = 6 or more measurement occasions. This effect could not be found in previous simulation studies with a smaller number of measurement occasions. The mean Type I error rates for rANOVA with Greenhouse-Geisser-correction demonstrate a small conservative bias if sphericity was not violated, sample sizes were small (n = 20), and m = 6 or more measurement occasions were conducted. The results plead for a use of rANOVA with Huynh-Feldt-correction, especially when the sphericity assumption is violated, the sample size is rather small and the number of measurement occasions is large. MLM-UN may be used when the sphericity assumption is violated and when sample sizes are large.

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arXiv2016

Reliability estimates for three factor score predictors

Estimates for the reliability of Thurstone's regression factor score predictor, Bartlett's factor score predictor, and McDonald's factor score predictor were proposed. As in Kuder-Richardson's formula, the reliability estimates are based on a hypothetical set of equivalent items. The reliability estimates were compared by means of simulation studies. Overall, the reliability estimates were largest for the regression score predictor, so that the reliability estimates for Bartlett's and McDonald's factor score predictor should be compared with the reliability of the regression score predictor, whenever Bartlett's or McDonald's factor score predictor are to be computed. An R-script and an SPSS-script for the computation of the respective reliability estimates is presented.

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arXiv2015

A note on structured means analysis for a single group

The calculation of common factor means in structured means analysis (SMM) is considered. The SMM equations imply that the unique factors are defined as having zero means. It was shown within the one factor solution that this definition implies larger absolute common factor loadings to co-occur with larger absolute expectations of the observed variables in the single group case. This result was illustrated by means of a small simulation study. It is argued that the proportionality of factor loadings and observed means should be critically examined in the context of SMM. It is recommended that researchers should freely estimate the observed expectations, whenever, the proportionality of loadings and observed means does not make sense. It was also shown that for a given size of observed expectations, smaller common factor loadings result in larger common factor mean estimates. It should therefore be checked whether variables with very small factor loadings occur when SMM results in very large absolute common factor means.

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arXiv2015

Constraints for non-zero secondary loadings in confirmatory factor analysis

In the context of confirmatory factor analysis, the independent clusters model has been found to be overly restrictive in several research contexts. Therefore, a less restrictive criterion for parsimony of non-salient loadings in confirmatory factor analysis was proposed. The criterion is based on 'buffered scales', which have been introduced by Cattell and Tsujioka (1964) as optimal indicators of corresponding factors. Variables with positive and negative loadings on an unwanted factor are balanced out in a buffered scale, so that the variance of the unwanted factor is at minimum. It is proposed here to specify a balance of positive and negative secondary loadings by means of model constraints in order to achieve parsimony of loading patterns. The specification of buffered simple structure by means of model constraints was illustrated by means of a simulation study and an empirical example.

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arXiv2014

Extending the debate between Spearman and Wilson 1929: When do single variables optimally reproduce the common part of the observed covariances?

Because the covariances of observed variables reproduced from conventional factor score predictors are generally not the same as the covariances reproduced from the common factors, it is proposed to find a factor score predictor that optimally reproduces the common part of the observed covariances. It is shown that, under some conditions, the single observed variable with highest loading on a factor perfectly reproduces the non-diagonal observed covariances. This refers to Spearman's and Wilson's 1929 debate on the use of single variables as factor score predictors. The implications of this finding were investigated in a population based and in a sample based simulation study confirming that taking a single variable outperforms conventional factor score predictors in reproducing the observed covariances when the salient loading size and the number of salient loadings per factor are small. Implications of this finding for factor score predictors are discussed.

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arXiv2013

The factor paradox: Common factors can be correlated with the variance not accounted for by the common factors!

The case that the factor model does not account for all the covariances of the observed variables is considered. This is a quite realistic condition because some model error as well as some sampling error should usually occur with empirical data. It is shown that principal components representing covariances not accounted for by the factors of the model can have a non-zero correlation with the common factors of the factor model. Non-zero correlations of components representing variance not accounted for by the factor model with common factors were also found in a simulation study. Based on these results it should be concluded that common factors can be correlated with variance components representing model error as well as sampling error. In consequence, even when researchers decide not to represent some small or trivial variance by means of a common factor, these excluded variances can still be part of the model.

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