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In modeling missing data, the missing data latent variable of the confirmatory factor model accounts for systematic variation associated with missing data so that replacement of what is missing is not required. This study aimed at extending the modeling missing data approach to tetrachoric correlations as input and at exploring the consequences of switching between models with free and fixed factor loadings. In a simulation study, confirmatory factor analysis (CFA) models with and without a missing data latent variable were used for investigating the structure of data with and without missing data. In addition, the numbers of columns of data sets with missing data and the amount of missing data were varied. The root mean square error of approximation (RMSEA) results revealed that an additional missing data latent variable recovered the degree-of-model fit characterizing complete data when tetrachoric correlations served as input while comparative fit index (CFI) results showed overestimation of this degree-of-model fit. Whereas the results for fixed factor loadings were in line with the assumptions of modeling missing data, the other results showed only partial agreement. Therefore, modeling missing data with fixed factor loadings is recommended.

Conceptualizing two-variable disturbances preventing good model fit in confirmatory factor analysis as item-level method effects instead of correlated residuals avoids violating the principle that residual variation is unique for each item. The possibility of representing such a disturbance by a method factor of a bifactor measurement model was investigated with respect to model identification. It turned out that a suitable way of realizing the method factor is its integration into a fixed-links, parallel-measurement or tau-equivalent measurement submodel that is part of the bifactor model. A simulation study comparing these submodels revealed similar degrees of efficiency in controlling the influence of two-variable disturbances on model fit. Perfect correspondence characterized the fit results of the model assuming correlated residuals and the fixed-links model, and virtually also the tau-equivalent model. [ABSTRACT FROM AUTHOR]

The item-position effect describes how an item's position within a test, that is, the number of previous completed items, affects the response to this item. Previously, this effect was represented by constraints reflecting simple courses, for example, a linear increase. Due to the inflexibility of these representations our aim was to examine whether adapted representations are more appropriate than the existing ones. Models of confirmatory factor analysis were used for testing the different representations. Analyses were conducted by means of simulated data that followed the covariance pattern of Raven's Advanced Progressive Matrices (APM) items. Since the item-position effect has been demonstrated repeatedly for the APM, it is a very suitable measure for our investigations. Results revealed no remarkable improvement by using an adapted representation. Possible reasons causing these results are discussed.

Rapid guessing is a test taking strategy recommended for increasing the probability of achieving a high score if a time limit prevents an examinee from responding to all items of a scale. The strategy requires responding quickly and without cognitively processing item details. Although there may be no omitted responses after participants' rapid guessing, an open question remains: do the data show unidimensionality, as is expected for data collected by a scale, or bi-dimensionality characterizing data collected with a time limit in testing, speeded data. To answer this question, we simulated speeded and rapid guessing data and performed confirmatory factor analysis using onefactor and two-factor models. The results revealed that speededness was detectable despite the presence of rapid guessing. However, detection may depend on the number of response options for a given set of items. [ABSTRACT FROM AUTHOR]

This paper presents the semi-hierarchical model for confirmatory factor analysis of speeded data. The semi-hierarchical model is achieved by integrating information from the second level of the hierarchical structure of speeded data into the customary confirmatory factor model. The second level of speeded data originates from subsets of participants responding on the basis of different sources. In the semi-hierarchical model, the contributions of the latent variables are modified to reflect characteristics of these subsets. Furthermore, the results of a simulation study comparing the semi-hierarchical model adapted to speeded data and the customary confirmatory factor model are reported. Whereas all the models yielded good model fit according to RMSEA and SRMR, differences between the models were signified by CFI and TLI. The semi-hierarchical model led to the better model fit in data showing noticeable speededness. [ABSTRACT FROM AUTHOR]

The paper reports an investigation on whether valid results can be achieved in analyzing the structure of datasets although a large percentage of data is missing without replacement. Two types of confirmatory factor analysis (CFA) models were employed for this purpose: the missing data CFA model with an additional latent variable for representing the missing data and the semi-hierarchical CFA model that also includes the additional latent variable and reflects the hierarchical structure assumed to underlie the data. Whereas, the missing data CFA model assumes that the model is equally valid for all participants, the semi-hierarchical CFA model is implicitly specified differently for subgroups of participants with and without omissions. The comparison of these models with the regular one-factor model in investigating simulated binary data revealed that the modeling of missing data prevented negative effects of missing data on model fit. The investigation of the accuracy in estimating the factor loadings yielded the best results for the semi-hierarchical CFA model. The average estimated factor loadings for items with and without omissions showed the expected equal sizes. But even this model tended to underestimate the expected values., Competing Interests: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest., (Copyright © 2020 Schweizer, Gold, Krampen and Wang.)