Psychologie und Sportwissenschaften
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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.
We investigated whether dichotomous data showed the same latent structure as the interval-level data from which they originated. Given constancy of dimensionality and factor loadings reflecting the latent structure of data, the focus was on the variance of the latent variable of a confirmatory factor model. This variance was shown to summarize the information provided by the factor loadings. The results of a simulation study did not reveal exact correspondence of the variances of the latent variables derived from interval-level and dichotomous data but shrinkage. Since shrinkage occurred systematically, methods for recovering the original variance were fleshed out and evaluated.
Perfectionism nowadays is frequently understood as a multidimensional personality trait with two higher-order dimensions of perfectionistic strivings and perfectionistic concerns. While perfectionistic concerns are robustly found to correlate with negative outcomes and psychological malfunctioning, findings concerning the outcomes of perfectionistic strivings are inconsistent. There is evidence that perfectionistic strivings relate to psychological maladjustment on the one hand but to positive outcomes on the other hand as well. Moreover, perfectionistic strivings and perfectionistic concerns frequently showed substantial overlap. These inconsistencies of differential relations and the substantial overlap of perfectionistic strivings and perfectionistic concerns raise questions concerning the factorial structure of perfectionism and the meaning of its dimensions. In this study, several bifactor models were applied to disentangle the common variance of perfectionistic strivings and perfectionistic concerns at the item level using Hill et al.’s (2004) Perfectionism Inventory (PI). The PI measures a broad range of perfectionism dimensions by four perfectionistic strivings and four perfectionistic concerns subscales. The bifactor-(S – 1) model with one general factor defined by concern over mistakes as the reference facet, four specific perfectionistic strivings factors, and three specific perfectionistic concerns factors showed acceptable fit. The results revealed a clear separation between perfectionistic strivings and perfectionistic concerns, as the general factor represented concern over mistakes, while the perfectionistic strivings factors each explained a substantial amount of reliable variance independent of the general factor. As a result, factor scores of the specific perfectionistic strivings factors and the general factor had differential relationships with achievement motivation, neuroticism, conscientiousness, and self-efficacy that met with theoretical expectations, while results for manifest subscale scores were ambiguous. Our results question the existence of reliable sub-constructs of perfectionistic concerns independent of the general factor when defined by concern over mistakes.