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Numerous studies reported a strong link between working memory capacity (WMC) and fluid intelligence (Gf), although views differ in respect to how close these two constructs are related to each other. In the present study, we used a WMC task with five levels of task demands to assess the relationship between WMC and Gf by means of a new methodological approach referred to as fixed-links modeling. Fixed-links models belong to the family of confirmatory factor analysis (CFA) and are of particular interest for experimental, repeated-measures designs. With this technique, processes systematically varying across task conditions can be disentangled from processes unaffected by the experimental manipulation. Proceeding from the assumption that experimental manipulation in a WMC task leads to increasing demands on WMC, the processes systematically varying across task conditions can be assumed to be WMC-specific. Processes not varying across task conditions, on the other hand, are probably independent of WMC. Fixed-links models allow for representing these two kinds of processes by two independent latent variables. In contrast to traditional CFA where a common latent variable is derived from the different task conditions, fixed-links models facilitate a more precise or purified representation of the WMC-related processes of interest. By using fixed-links modeling to analyze data of 200 participants, we identified a non-experimental latent variable, representing processes that remained constant irrespective of the WMC task conditions, and an experimental latent variable which reflected processes that varied as a function of experimental manipulation. This latter variable represents the increasing demands on WMC and, hence, was considered a purified measure of WMC controlled for the constant processes. Fixed-links modeling showed that both the purified measure of WMC (β = .48) as well as the constant processes involved in the task (β = .45) were related to Gf. Taken together, these two latent variables explained the same portion of variance of Gf as a single latent variable obtained by traditional CFA (β = .65) indicating that traditional CFA causes an overestimation of the effective relationship between WMC and Gf. Thus, fixed-links modeling provides a feasible method for a more valid investigation of the functional relationship between specific constructs.
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 article reports three simulation studies conducted to find out whether the effect of a time limit for testing impairs model fit in investigations of structural validity, whether the representation of the assumed source of the effect prevents impairment of model fit and whether it is possible to identify and discriminate this method effect from another method effect. Omissions due to the time limit for testing were not considered as missing data but as information on the participants’ processing speed. In simulated data the presence of a time-limit effect impaired comparative fit index and nonnormed fit index whereas normed chi-square, root mean square error of approximation, and standardized root mean square residual indicated good model fit. The explicit consideration of the effect due to the time limit by an additional component of the model improved model fit. Effect-specific assumptions included in the model of measurement enabled the discrimination of the effect due to the time limit from another possible method effect.
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.
Can variances of latent variables be scaled in such a way that they correspond to eigenvalues?
(2017)
The paper reports an investigation of whether sums of squared factor loadings obtained in confirmatory factor analysis correspond to eigenvalues of exploratory factor analysis. The sum of squared factor loadings reflects the variance of the corresponding latent variable if the variance parameter of the confirmatory factor model is set equal to one. Hence, the computation of the sum implies a specific type of scaling of the variance. While the investigation of the theoretical foundations suggested the expected correspondence between sums of squared factor loadings and eigenvalues, the necessity of procedural specifications in the application, as for example the estimation method, revealed external influences on the outcome. A simulation study was conducted that demonstrated the possibility of exact correspondence if the same estimation method was applied. However, in the majority of realized specifications the estimates showed similar sizes but no correspondence.