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This paper investigates how the major outcome of a confirmatory factor investigation is preserved when scaling the variance of a latent variable by the various scaling methods. A constancy framework, based upon the underlying factor analysis formula that enables scaling by modifying components through scalar multiplication, is described; a proof is included to demonstrate the constancy property of the framework. It provides the basis for a scaling method that enables the comparison of the contribution of different latent variables of the same confirmatory factor model to observed scores, as for example, the contributions of trait and method latent variables. Furthermore, it is shown that available scaling methods are in line with this constancy framework and that the criterion number included in some scaling methods enables modifications. The impact of the number of manifest variables on the scaled variance parameter can be modified and the range of possible values. It enables the adaptation of scaling methods to the requirements of the field of application.
The paper outlines a method for investigating the speed effect due to a time limit in testing. It is assumed that the time limit enables latent processing speed to influence responses by causing omissions in the case of insufficient speed. Because of processing speed as additional latent source, the customary confirmatory factor model is enlarged by a second latent variable representing latent processing speed. For distinguishing this effect from other method effects, the factor loadings are fixed according to the cumulative normal distribution. With the second latent variable added, confirmatory factor analysis of reasoning data (N=518) including omissions because of a time limit yielded good model fit and discriminated the speed effect from other possible effects due to the item difficulty, the homogeneity of an item subset and the item positions. Because of the crucial role of the cumulative normal distribution for fixing the factor loadings a check of the normality assumption is also reported.