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Factor score regression (FSR) is widely used as a convenient alternative to traditional structural equation modeling (SEM) for assessing structural relations between latent variables. But when latent variables are simply replaced by factor scores, biases in the structural parameter estimates often have to be corrected, due to the measurement error in the factor scores. The method of Croon (MOC) is a well-known bias correction technique. However, its standard implementation can render poor quality estimates in small samples (e.g. less than 100). This article aims to develop a small sample correction (SSC) that integrates two different modifications to the standard MOC. We conducted a simulation study to compare the empirical performance of (a) standard SEM, (b) the standard MOC, (c) naive FSR, and (d) the MOC with the proposed SSC. In addition, we assessed the robustness of the performance of the SSC in various models with a different number of predictors and indicators. The results showed that the MOC with the proposed SSC yielded smaller mean squared errors than SEM and the standard MOC in small samples and performed similarly to naive FSR. However, naive FSR yielded more biased estimates than the proposed MOC with SSC, by failing to account for measurement error in the factor scores.

Exploratory graph analysis (EGA) is a commonly applied technique intended to help social scientists discover latent variables. Yet, the results can be influenced by the methodological decisions the researcher makes along the way. In this article, we focus on the choice regarding the number of factors to retain: We compare the performance of the recently developed EGA with various traditional factor retention criteria. We use both continuous and binary data, as evidence regarding the accuracy of such criteria in the latter case is scarce. Simulation results, based on scenarios resulting from varying sample size, communalities from major factors, interfactor correlations, skewness, and correlation measure, show that EGA outperforms the traditional factor retention criteria considered in most cases in terms of bias and accuracy. In addition, we show that factor retention decisions for binary data are preferably made using Pearson, instead of tetrachoric, correlations, which is contradictory to popular belief.

In this article, an overview is given of four methods to perform factor score regression (FSR), namely regression FSR, Bartlett FSR, the bias avoiding method of Skrondal and Laake, and the bias correcting method of Croon. The bias correcting method is extended to include a reliable standard error. The four methods are compared with each other and with structural equation modeling (SEM) by using analytic calculations and two Monte Carlo simulation studies to examine their finite sample characteristics. Several performance criteria are used, such as the bias using the unstandardized and standardized parameterization, efficiency, mean square error, standard error bias, type I error rate, and power. The results show that the bias correcting method, with the newly developed standard error, is the only suitable alternative for SEM. While it has a higher standard error bias than SEM, it has a comparable bias, efficiency, mean square error, power, and type I error rate.

Research indicates the need to further examine the dimensions of reading motivation. A clear theoretical basis is necessary for conceptualizing reading motivation and considering contextual differences therein. The present study develops and validates the SRQ-Reading Motivation, a questionnaire measuring recreational and academic reading motivation based on self-determination theory. The study clarifies the relation among reading motivation, reading self-concept, reading behavior (i.e., engagement and frequency), and reading performance (i.e., comprehension). Participants included 1,260 Flemish fifth-grade students and their 67 teachers. Exploratory and confirmatory factor analyses indicated that both recreational and academic reading motivation comprise 2 factors: autonomous and controlled motivation. This factor structure was found to be invariant across boys and girls. Comparisons of the SRQ-Reading Motivation with subscales of the Motivation for Reading Questionnaire provide evidence for the construct validity of the instrument. Structural equation modeling confirmed that recreational autonomous reading motivation is associated with more positive reading behavior and better performance. In the academic setting, only the equivalent relationship between autonomous reading motivation and leisure-time reading frequency could be corroborated. In this respect, the results confirm the independent contribution of recreational autonomous reading motivation and reading self-concept to reading behavior and performance. No significant indirect relationship between reading motivation and reading comprehension through reading frequency or reading engagement was found. The theoretical and practical significance of the present study is discussed. (Contains 5 tables, 4 figures and 3 footnotes.)

Systematic quantitative research on measuring distributed leadership is scarce. In this study, the Distributed Leadership Inventory (DLI) was developed and evaluated to investigate leadership team characteristics and distribution of leadership functions between formally designed leadership positions in large secondary schools. The DLI was presented to a sample of 2,198 respondents in 46 secondary schools. The input from a first subsample was used to perform exploratory factor analyses; the second subsample was used to verify the factor structure via confirmatory factor analysis. A one-factor structure for the leadership team characteristics (coherent leadership team) and a two-factor structure for the leadership functions (support and supervision) were confirmed. The results of the DLI underpin that leading schools involve multiple individuals, which differs by the type of function. (Contains 5 tables.)

The Beck Depression Inventory-II (BDI-II) is a frequently used scale for measuring depressive severity. BDI-II data (404 clinical; 695 nonclinical adults) were analyzed by means of confirmatory factor analysis to test whether the factor structure model with a somatic-affective and cognitive component of depression, formulated by Beck and colleagues, has a good fit. We also evaluated 10 alternative models. The fit of Beck's model was not good for all criteria. Three of the alternative models had a better fit in both samples, but none of these met all criteria for good fit. Of the alternatives with a better fit, we selected the only model with unidimensional subscales, which assesses a somatic, affective, and cognitive dimension. For this model, which we recommend, as well as for Beck's original model, a good fitting structure containing 15 and 16 items was developed with an item-deletion algorithm. (Contains 3 tables and 4 figures.)

The current study further validates the Quality of Relationships Inventory (QRI; G. R. Pierce, I. G. Sarason, & B. R. Sarason, 1991) by evaluating its factor structure in a sample of 572 partners from 286 couples. Confirmatory factor analysis was used to compare 3 different models of the QRI and to investigate the invariance of the factor structure of the QRI across gender and across relationship satisfaction. Analyses revealed that a 3-factor solution--consisting of 3 different but interrelated factors (a 7-item support factor, a 12-item conflict factor, and a 6-item depth factor)--best accounted for the data. The authors' findings suggest that full metric invariance holds across gender and across relationship satisfaction in the female subsample, whereas only partial metric invariance could be established for relationship satisfaction in the male subsample.

Psychological network approaches propose to see symptoms or questionnaire items as interconnected nodes, with links between them reflecting pairwise statistical dependencies evaluated on cross-sectional, time-series, or panel data. These networks constitute an established methodology to visualise and conceptualise the interactions and relative importance of nodes/indicators, providing an important complement to other approaches such as factor analysis. However, limiting the representation to pairwise relationships can neglect potentially critical information shared by groups of three or more variables (higher-order statistical interdependencies). To overcome this important limitation, here we propose an information-theoretic framework to assess these interdependencies and consequently to use hypergraphs as representations in psychometrics. As edges in hypergraphs are capable of encompassing several nodes together, this extension can thus provide a richer account on the interactions that may exist among sets of psychological variables. Our results show how psychometric hypergraphs can highlight meaningful redundant and synergistic interactions on either simulated or state-of-the-art, re-analysed psychometric datasets. Overall, our framework extends current network approaches while leading to new ways of assessing the data that differ at their core from other methods, enriching the psychometrics toolbox, and opening promising avenues for future investigation. [ABSTRACT FROM AUTHOR]

Factor score regression (FSR) is widely used as a convenient alternative to traditional structural equation modeling (SEM) for assessing structural relations between latent variables. But when latent variables are simply replaced by factor scores, biases in the structural parameter estimates often have to be corrected, due to the measurement error in the factor scores. The method of Croon (MOC) is a well-known bias correction technique. However, its standard implementation can render poor quality estimates in small samples (e.g. less than 100). This article aims to develop a small sample correction (SSC) that integrates two different modifications to the standard MOC. We conducted a simulation study to compare the empirical performance of (a) standard SEM, (b) the standard MOC, (c) naive FSR, and (d) the MOC with the proposed SSC. In addition, we assessed the robustness of the performance of the SSC in various models with a different number of predictors and indicators. The results showed that the MOC with the proposed SSC yielded smaller mean squared errors than SEM and the standard MOC in small samples and performed similarly to naive FSR. However, naive FSR yielded more biased estimates than the proposed MOC with SSC, by failing to account for measurement error in the factor scores. [ABSTRACT FROM AUTHOR]

We show that separable nonlinear least squares (SNLLS) estimation is applicable to all linear structural equation models (SEMs) that can be specified in RAM notation. SNLLS is an estimation technique that has successfully been applied to a wide range of models, for example neural networks and dynamic systems, often leading to improvements in convergence and computation time. It is applicable to models of a special form, where a subset of parameters enters the objective linearly. Recently, Kreiberg et al. (Struct Equ Model Multidiscip J 28(5):725–739, 2021. https://doi.org/10.1080/10705511.2020.1835484) have shown that this is also the case for factor analysis models. We generalize this result to all linear SEMs. To that end, we show that undirected effects (variances and covariances) and mean parameters enter the objective linearly, and therefore, in the least squares estimation of structural equation models, only the directed effects have to be obtained iteratively. For model classes without unknown directed effects, SNLLS can be used to analytically compute least squares estimates. To provide deeper insight into the nature of this result, we employ trek rules that link graphical representations of structural equation models to their covariance parametrization. We further give an efficient expression for the gradient, which is crucial to make a fast implementation possible. Results from our simulation indicate that SNLLS leads to improved convergence rates and a reduced number of iterations. [ABSTRACT FROM AUTHOR]

Late elementary education constitutes a critical period in the development of reading comprehension strategies, a key competence in today's society. However, to date, appropriate measurements to map late elementary students' reading strategies are lacking. In this respect, the present article first describes the development and validation of the 26-item reading comprehension strategies questionnaire (RCSQ). To this aim, exploratory (sample 1: n = 1585 students) and confirmatory (sample 2: n = 1585 students) factor analyses were conducted. These analyses resulted in the RCSQ, consisting of five subscales: (1) overt cognitive reading strategies, (2) covert cognitive reading strategies, (3) monitoring, and (4) evaluating. For non-native and bilingual students, a fifth subscale 'using home language in view of comprehending texts' emerged. Second, multilevel analyses were performed to explore individual differences in late elementary students' reading comprehension strategy use. Implications for practice and future research are discussed. [ABSTRACT FROM AUTHOR]

Exploratory graph analysis (EGA) is a commonly applied technique intended to help social scientists discover latent variables. Yet, the results can be influenced by the methodological decisions the researcher makes along the way. In this article, we focus on the choice regarding the number of factors to retain: We compare the performance of the recently developed EGA with various traditional factor retention criteria. We use both continuous and binary data, as evidence regarding the accuracy of such criteria in the latter case is scarce. Simulation results, based on scenarios resulting from varying sample size, communalities from major factors, interfactor correlations, skewness, and correlation measure, show that EGA outperforms the traditional factor retention criteria considered in most cases in terms of bias and accuracy. In addition, we show that factor retention decisions for binary data are preferably made using Pearson, instead of tetrachoric, correlations, which is contradictory to popular belief. [ABSTRACT FROM AUTHOR]

This study introduces the statistical theory of using the Standardized Root Mean Squared Error (SRMR) to test close fit in ordinal factor analysis. We also compare the accuracy of confidence intervals (CIs) and tests of close fit based on the SRMR with those obtained based on the Root Mean Squared Error of Approximation (RMSEA). The current (biased) implementation for the RMSEA never rejects that a model fits closely when data are binary and almost invariably rejects the model in large samples if data consist of five categories. The unbiased RMSEA produces better rejection rates, but it is only accurate enough when the number of variables is small and the degree of misfit is small. In contrast, across all simulated conditions, the tests of close fit based on the SRMR yield acceptable type I error rates. SRMR tests of close fit are also more powerful than those using the unbiased RMSEA. [ABSTRACT FROM AUTHOR]

Systematic quantitative research on measuring distributed leadership is scarce. In this study, the Distributed Leadership Inventory (DLI) was developed and evaluated to investigate leadership team characteristics and distribution of leadership functions between formally designed leadership positions in large secondary schools. The DLI was presented to a sample of 2,198 respondents in 46 secondary schools. The input from a first subsample was used to perform exploratory factor analyses; the second subsample was used to verify the factor structure via confirmatory factor analysis. A one-factor structure for the leadership team characteristics (coherent leadership team) and a two-factor structure for the leadership functions (support and supervision) were confirmed. The results of the DLI underpin that leading schools involve multiple individuals, which differs by the type of function. [ABSTRACT FROM AUTHOR]

The Beck Depression Inventory-II (BDI-II) is a frequently used scale for measuring depressive severity. BDI-II data (404 clinical; 695 nonclinical adults) were analyzed by means of confirmatory factor analysis to test whether the factor structure model with a somatic-affective and cognitive component of depression, formulated by Beck and colleagues, has a goodfit. We also evaluated 10 alternative models. The fit of Beck's model was not good for all criteria. Three of the alternative models had a better fit in both samples, but none of these met all criteria for good fit. Of the alternatives with a better fit, we selected the only model with unidimensional subscales, which assesses a somatic, affective, and cognitive dimension. For this model, which we recommend, as well as for Beck' original model, a good fitting structure containing 15 and 16 items was developed with an item-deletion algorithm. [ABSTRACT FROM AUTHOR]

This paper first examines the factorial validity of the Maslach Burnout Inventory for human services professions (MBI-HSS). The authors test the original 22-item version and a shortened 20-item version. Model fit is evaluated with confirmatory factor analysis starting with data collected from a sample of hospital nurses (n = 2515) and a sample of nurses and assistants working in residential welfare institutions (n = 1639). Only the fit of the 20-item MBI-HSS was good in both samples. Next the hypothesis of measurement invariance of the 20-item MBI-HSS across the samples is examined, but this hypothesis does not hold. Partial invariance at the level of the subscales also could not be confirmed. The authors conclude that for hospital nurses the MBI-HSS factors mean something other than what they mean for professionals working in welfare institutions, and suggest that future research could focus upon this difference. Copyright © 2006 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Highlights: [•] Based on exploratory factor analysis 79 self-report items were retained. [•] Factorial validity was supported by CFA for each component. [•] Factor invariance across gender after deletion of four items. [•] Final version contains 75 items across 15 subscales. [•] Advise to combine current instrument with on-line measures regarding SRL. [ABSTRACT FROM AUTHOR]

The current study further validates the Quality of Relationships Inventory (QRI; G. R. Pierce, I. G. Sarason, & B. R. Sarason, 1991) by evaluating its factor structure in a sample of 572 partners from 286 couples. Confirmatory factor analysis was used to compare 3 different models of the QRI and to investigate the invariance of the factor structure of the QRI across gender and across relationship satisfaction. Analyses revealed that a 3-factor solution-consisting of 3 different but interrelated factors (a 7-item support factor, a 12-item conflict factor, and a 6-item depth factor)-best accounted for the data. The authors' findings suggest that full metric invariance holds across gender and across relationship satisfaction in the female subsample, whereas only partial metric invariance could be established for relationship satisfaction in the male subsample. [ABSTRACT FROM AUTHOR]