A reciprocal effects model linking emotion and achievement over time is proposed. The model was tested using five annual waves of the Project for the Analysis of Learning and Achievement in Mathematics (PALMA) longitudinal study, which investigated adolescents’ development in mathematics (Grades 5–9; N = 3,425 German students; mean starting age = 11.7 years; representative sample). Structural equation modeling showed that positive emotions (enjoyment, pride) positively predicted subsequent achievement (math end-of-the-year grades and test scores), and that achievement positively predicted these emotions, controlling for students’ gender, intelligence, and family socioeconomic status. Negative emotions (anger, anxiety, shame, boredom, hopelessness) negatively predicted achievement, and achievement negatively predicted these emotions. The findings were robust across waves, achievement indicators, and school tracks, highlighting the importance of emotions for students’ achievement and of achievement for the development of emotions.

/pdf/achievement-emotions-and-academic-performance-longitudinal-2rlqdlli9p.pdf

Achievement emotions and academic performance: longitudinal models of reciprocal effects

In modern expectancy--value theory (EVT) in educational psychology, expectancy and value beliefs additively predict performance, persistence, and task choice. In contrast to earlier formulations of EVT, the multiplicative term Expectancy × Value in regression-type models typically plays no major role in educational psychology. The present study used latent moderated structural equation modeling to explore whether there is empirical support for a multiplicative effect in a sample of 2,508 students at the end of secondary education. Expectancy and four facets of value beliefs (attainment, intrinsic, and utility value as well as cost) predicted achievement when entered separately into a regression equation. Moreover, in models with both expectancy and value beliefs as predictor variables, the expectancy component as well as the multiplicative term Expectancy × Value were consistently found to predict achievement positively.

Probing for the multiplicative term in modern expectancy-value theory: a latent interaction modeling study

This study investigated the effect the number of observed variables (p) has on three structural equation modeling indices: the comparative fit index (CFI), the Tucker-Lewis index (TLI), and the root mean square error of approximation (RMSEA). The behaviors of the population fit indices and their sample estimates were compared under various conditions created by manipulating the number of observed variables, the types of model misspecification, the sample size, and the magnitude of factor loadings. The results showed that the effect of p on the population CFI and TLI depended on the type of specification error, whereas a higher p was associated with lower values of the population RMSEA regardless of the type of model misspecification. In finite samples, all three fit indices tended to yield estimates that suggested a worse fit than their population counterparts, which was more pronounced with a smaller sample size, higher p, and lower factor loading.

https://journals.sagepub.com/doi/pdf/10.1177/0013164418783530

Understanding the Model Size Effect on SEM Fit Indices

A latent variable study examined whether different classes of working-memory tasks measure the same general construct of working-memory capacity (WMC). Data from 270 subjects were used to examine the relationship between Binding, Updating, Recall-N-back, and Complex Span tasks, and the relations of WMC with secondary memory measures, indicators of cognitive control from two response-conflict paradigms (Simon task and Eriksen flanker task), and fluid intelligence. Confirmatory factor analyses support the concept of a general WMC factor. Results from structural-equation modeling show negligible relations of WMC with response-conflict resolution, and very strong relations of WMC with secondary memory and fluid intelligence. The findings support the hypothesis that individual differences in WMC reflect the ability to build, maintain and update arbitrary bindings.

/pdf/what-is-working-memory-capacity-and-how-can-we-measure-it-3tvcjxrsao.pdf

What is working memory capacity, and how can we measure it?

Despite clear evidence that manifest variable path analysis requires highly reliable measures, path analyses with fallible measures are commonplace even in premier journals. Using fallible measures in path analysis can cause several serious problems: (a) As measurement error pervades a given data set, many path coefficients may be either over- or underestimated. (b) Extensive measurement error diminishes power and can prevent invalid models from being rejected. (c) Even a little measurement error can cause valid models to appear invalid. (d) Differential measurement error in various parts of a model can change the substantive conclusions that derive from path analysis. (e) All of these problems become increasingly serious and intractable as models become more complex. Methods to prevent and correct these problems are reviewed. The conclusion is that researchers should use more reliable measures (or correct for measurement error in the measures they do use), obtain multiple measures for use in latent variable modeling, and test simpler models containing fewer variables.

/pdf/manifest-variable-path-analysis-potentially-serious-and-1oxjsysciw.pdf

Manifest variable path analysis: Potentially serious and misleading consequences due to uncorrected measurement error.

Fit indices are widely used in order to test the model fit for structural equation models. In a highly influential study, Hu and Bentler (1999) showed that certain cutoff values for these indices could be derived, which, over time, has led to the reification of these suggested thresholds as "golden rules" for establishing the fit or other aspects of structural equation models. The current study shows how differences in unique variances influence the value of the global chi-square model test and the most commonly used fit indices: Root-mean-square error of approximation, standardized root-mean-square residual, and the comparative fit index. Using data simulation, the authors illustrate how the value of the chi-square test, the root-mean-square error of approximation, and the standardized root-mean-square residual are decreased when unique variances are increased although model misspecification is present. For a broader understanding of the phenomenon, the authors used different sample sizes, number of observed variables per factor, and types of misspecification. A theoretical explanation is provided, and implications for the application of structural equation modeling are discussed.

Masking misfit in confirmatory factor analysis by increasing unique variances: a cautionary note on the usefulness of cutoff values of fit indices.

This paper is concerned with supplementing statistical tests for the Rasch model so that additionally to the probability of the error of the first kind (Type I probability) the probability of the error of the second kind (Type II probability) can be controlled at a predetermined level by basing the test on the appropriate number of observations. An approach to determining a practically meaningful extent of model deviation is proposed, and the approximate distribution of the Wald test is derived under the extent of model deviation of interest.

Sample size determination for rasch model tests

Recent detection methods for Differential Item Functioning (DIF) include approaches like Rasch Trees, DIFlasso, GPCMlasso and Item Focussed Trees, all of which - in contrast to well established methods - can handle metric covariates inducing DIF. A new estimation method shall address their downsides by mainly aiming at combining three central virtues: the use of conditional likelihood for estimation, the incorporation of linear influence of metric covariates on item difficulty and the possibility to detect different DIF types: certain items showing DIF, certain covariates inducing DIF, or certain covariates inducing DIF in certain items. Each of the approaches mentioned lacks in two of these aspects. We introduce a method for DIF detection, which firstly utilizes the conditional likelihood for estimation combined with group Lasso-penalization for item or variable selection and L1-penalization for interaction selection, secondly incorporates linear effects instead of approximation through step functions, and thirdly provides the possibility to investigate any of the three DIF types. The method is described theoretically, challenges in implementation are discussed. A dataset is analysed for all DIF types and shows comparable results between methods. Simulation studies per DIF type reveal competitive performance of cmlDIFlasso, particularly when selecting interactions in case of large sample sizes and numbers of parameters. Coupled with low computation times, cmlDIFlasso seems a worthwhile option for applied DIF detection.

Penalization approaches in the conditional maximum likelihood and Rasch modelling context.

The Rasch model is known in particular for its properties of parameter separability and specific objectivity. The extent to which this property is attained depends on the magnitude of the discrepancy between the data and the model. The use of reliable model fit tests which can detect model violations is therefore essential before a psychological test is used and inferences based on the requirements of the Rasch model are drawn. This paper provides a critical analysis of the performance of the parametric bootstrap model test (von Davier, 1997) in the presence of non-parallel item response functions as violations of a basic requirement of the dichotomous Rasch model. Based on results from simulated data it is shown that in general the bootstrap test leads too often to failures to reject non-fitting data.

/pdf/performance-of-the-bootstrap-rasch-model-test-under-1tvhac964y.pdf

Performance of the bootstrap Rasch model test under violations of non-intersecting item response functions

Action imagery describes a mental representation of an action and its consequences. Although it is widely recognized that people differ in their ability to imagine actions, objective validated tests to measure such differences are scarce. In search of an objective testing method for action imagery ability, the present study investigated whether solving mental paper-folding tasks involves action imagery. The stimuli were two-dimensional grids of six squares. A total of 99 participants mentally folded each grid into a three-dimensional cube to judge whether two highlighted lines in the grid overlapped in the imagined cube. This was done in two sessions of 214 judgements each, where the grids differed in overlaps, the least number of imagined folds, and the least number of imagined directional changes. Error rates and reaction times increased with the number of imagined folds and with the number of directional changes. Furthermore, more errors were committed with overlapping lines than with no overlaps. This was not reflected in the reaction times. Hence, the reaction times increased when the stepwise folding process was enlarged, but not when the final selection was more difficult. We concluded that the participants predominantly used action imagery as a task-solving strategy rather than for abstract problem-solving.

/pdf/mental-paper-folding-revisited-the-involvement-of-visual-2sgwsr4x.pdf

Clemens Draxler

Papers

Masking misfit in confirmatory factor analysis by increasing unique variances: a cautionary note on the usefulness of cutoff values of fit indices.

Sample size determination for rasch model tests

Penalization approaches in the conditional maximum likelihood and Rasch modelling context.

Performance of the bootstrap Rasch model test under violations of non-intersecting item response functions

Mental Paper Folding Revisited: The Involvement of Visual Action Imagery