On Modeling Missing Data in Structural Investigations Based on Tetrachoric Correlations With Free and Fixed Factor Loadings.

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.

Neural correlates of intelligence: ERP Components of temporary storage predict fluid intelligence over and above those of executive functions.

Previous research has revealed that individuals with different levels of intelligence exhibit distinct patterns of event-related potentials (ERPs) related to executive functions and temporary storage. However, there is a lack of studies investigating the relative contributions of these ERPs in predicting individual differences in fluid intelligence. This study aims to examine the extent to which ERPs associated with executive functions and temporary storage can predict individual differences in fluid intelligence. Special attention is given to determining whether electrophysiological activities of temporary storage can predict fluid intelligence after accounting for executive functions, and vice versa. Both executive attention and temporary storage were measured by two experimental tasks, while electroencephalographic data were collected simultaneously. Fluid intelligence was assessed by two established tests. To address previous inconsistencies due to small sample sizes, a relatively large sample of young adults (N = 136) was recruited. The results revealed that participants with lower fluid intelligence displayed larger P3 amplitudes in the executive functions and temporary storage tasks compared to those with higher fluid intelligence. Additionally, the amplitudes of frontal and parietal P3s elicited by both executive functions and temporary storage significantly predicted fluid intelligence. Interestingly, the frontal and parietal P3s associated with temporary storage predicted fluid intelligence beyond the contributions of executive functions, supporting the storage account of individual differences in fluid intelligence. This study provides an original and fresh understanding of how executive functions and temporary storage contribute to fluid intelligence, offering new insights into the neurocognitive mechanisms underlying intelligence.

The dual mechanisms of cognitive control and their relation to reasoning and the item-position effect.

Braver's (2012) dual mechanisms of cognitive control differentiate between proactive control (PMC; i.e. early selection and maintenance of goal-relevant information) and reactive control (RMC; i.e. a late mobilization of attention when required). It has been suggested that higher cognitive capacities (as indicated by reasoning ability as a major characteristic of fluid intelligence) facilitate using the more resource-demanding PMC. We propose the following alternative explanation: engagement in PMC during the completion of reasoning tests leads to better test performance because gained knowledge (i.e. rules learned) during completion of early items is better maintained and transferred to later items. This learning of rules during the completion of a reasoning test results in an item-position effect (IPE) as an additional source of individual differences besides reasoning ability. We investigated this idea in a sample of 210 young adults who completed the AX-Continuous Performance Task (AX-CPT) and the Vienna Matrices Test (VMT). Using fixed-links modeling, we separated an IPE from reasoning ability in the VMT. Based on reaction time (RT) patterns across AX-CPT conditions, we identified three different groups by means of latent-profile analysis. RT patterns indicated engagement in PMC for Group A, mixed PMC and RMC for Group B, and RMC for Group C. With the consideration of the IPE, groups did not differ in their reasoning abilities. However, Group A (engaging in PMC) had a more pronounced IPE than Group C (engaging in RMC). Therefore, we conclude that PMC contributes to a stronger IPE, which in turn leads to higher scores in reasoning tests as measures of fluid intelligence.

How Executive Processes Explain the Overlap between Working Memory Capacity and Fluid Intelligence: A Test of Process Overlap Theory.

Working memory capacity (WMC) and fluid intelligence (Gf) are highly correlated, but what accounts for this relationship remains elusive. Process-overlap theory (POT) proposes that the positive manifold is mainly caused by the overlap of domain-general executive processes which are involved in a battery of mental tests. Thus, executive processes are proposed to explain the relationship between WMC and Gf. The current study aims to (1) achieve a relatively purified representation of the core executive processes including shifting and inhibition by a novel approach combining experimental manipulations and fixed-links modeling, and (2) to explore whether these executive processes account for the overlap between WMC and Gf. To these ends, we reanalyzed data of 215 university students who completed measures of WMC, Gf, and executive processes. Results showed that the model with a common factor, as well as shifting and inhibition factors, provided the best fit to the data of the executive function (EF) task. These components explained around 88% of the variance shared by WMC and Gf. However, it was the common EF factor, rather than inhibition and shifting, that played a major part in explaining the common variance. These results do not support POT as underlying the relationship between WMC and Gf.

On Modeling Missing Data of an Incomplete Design in the CFA Framework.

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.

An Investigation on How Inhibition in Cognitive Processing Contributes to Fluid Reasoning.

This article reports an investigation of how inhibition contributes to fluid reasoning when it is decomposed into the reasoning ability, item-position, and speed components to control for possible method effects. Working memory was also taken into consideration. A sample of 223 university students completed a fluid reasoning scale, two tasks tapping prepotent response inhibition, and two working memory tasks. Fixed-links modeling was used to separate the effect of reasoning ability from the effects of item-position and speed. The goodness-of-fit results confirmed the necessity to consider the reasoning ability, item-position, and speed components simultaneously. Prepotent response inhibition was only associated with reasoning ability. This association disappeared when working memory served as a mediator. Taken together, these results reflect the inhomogeneity of what is tapped by the fluid reasoning scale on one hand and, on the other, suggest inhibition as an important component of working memory.

Higher-order processing and change-to-automaticity as explanations of the item-position effect in reasoning tests.

Higher-order processing and learning are two alternative explanations of the item-position effect. Whereas higher-order processing as explanation emphasizes the recruitment of executive processes, learning as explanation highlights the improvement in performance due to repetition and is specified as change-to-automaticity. In a sample of 287 participants the item-position effect was captured by means of Advanced Progressive Matrices. Higher-order processing was inferred from rule acquisition, and change-to-automaticity was derived from sustained attention data. The results of independent investigations revealed that both higher-order processing and change-to-automaticity contributed to the occurrence of the item-position effect.

Scaling the Variance of a Latent Variable While Assuring Constancy of the Model.

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.

Speed Effect Analysis Using the CFA Framework.

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.

Does the Effect of a Time Limit for Testing Impair Structural Investigations by Means of Confirmatory Factor Models?

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.

Executive Control in Learning: Evidence for the Dissociation of Rule Learning and Associative Learning.

The dual-process account and the propositional account of learning hold opposite views regarding the recruitment of higher-level processes in rule learning and associative learning. Taking an individual differences perspective, the current study focused on the relationship between rule learning and associative learning and investigated to what extent executive control accounts for rule learning and associative learning. Two studies were conducted. In Study 1, a sample of 184 university students completed paired associative learning and rule learning tasks, as well as measures of working memory capacity, short-term storage, and executive control. Theory-based bifactor models were used to achieve a purified representation of executive control. The results showed that the latent correlation between associative learning and rule learning was rather small. Executive control showed a substantial relationship with rule learning, whereas no significant link was found with associative learning. In Study 2, a sample of 211 university students completed a three-term contingency learning task and an executive control task. The results replicated the finding that executive control was not significantly related to associative learning. Taken together, these results suggest a dissociation between rule learning and associative learning in terms of their underlying processes, which supports the dual-process account of learning.

Is the Factor Observed in Investigations on the Item-Position Effect Actually the Difficulty Factor?

In confirmatory factor analysis quite similar models of measurement serve the detection of the difficulty factor and the factor due to the item-position effect. The item-position effect refers to the increasing dependency among the responses to successively presented items of a test whereas the difficulty factor is ascribed to the wide range of item difficulties. The similarity of the models of measurement hampers the dissociation of these factors. Since the item-position effect should theoretically be independent of the item difficulties, the statistical ex post manipulation of the difficulties should enable the discrimination of the two types of factors. This method was investigated in two studies. In the first study, Advanced Progressive Matrices (APM) data of 300 participants were investigated. As expected, the factor thought to be due to the item-position effect was observed. In the second study, using data simulated to show the major characteristics of the APM data, the wide range of items with various difficulties was set to zero to reduce the likelihood of detecting the difficulty factor. Despite this reduction, however, the factor now identified as item-position factor, was observed in virtually all simulated datasets.

On the relationship between executive functions of working memory and components derived from fluid intelligence measures.

The aim of the current study is to provide new insights into the relationship between executive functions and intelligence measures in considering the item-position effect observed in intelligence items. Raven's Advanced Progressive Matrices (APM) and Horn's LPS reasoning test were used to assess fluid intelligence which served as criterion in investigating the relationship between intelligence and executive functions. A battery of six experimental tasks measured the updating, shifting, and inhibition processes of executive functions. Data were collected from 205 university students. Fluid intelligence showed substantial correlations with the updating and inhibition processes and no correlation with the shifting process without considering the item-position effect. Next, the fixed-link model was applied to APM and LPS data separately to decompose them into an ability component and an item-position component. The results of relating the components to executive functions showed that the updating and shifting processes mainly contributed to the item-position component whereas the inhibition process was mainly associated with the ability component of each fluid intelligence test. These findings suggest that improvements in the efficiency of updating and shifting processes are likely to occur during the course of completing intelligence measures and inhibition is important for intelligence in general.

Do Adaptive Representations of the Item-Position Effect in APM Improve Model Fit? A Simulation Study.

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.

Models for the Detection of Deviations from the Expected Processing Strategy in Completing the Items of Cognitive Measures.

This paper presents confirmatory factor models with fixed factor loadings that enable the identification of deviations from the expected processing strategy. The instructions usually define the expected processing strategy to a considerable degree. Simplification is a deviation from instructions that is likely to occur in complex cognitive measures. Since simplification impairs the validity of the measure, its identification is important. Models representing simplicity and instruction-based processing strategies were considered in investigating the data of 345 participants obtained by a working memory measure in order to find out whether and how the use of these strategies influences model-data fit. As expected, the consideration of simplicity strategies improved the model-data fit achieved for the instruction-based strategy.

The Prediction of Students' Academic Performance With Fluid Intelligence in Giving Special Consideration to the Contribution of Learning.

The present study provides a new account of how fluid intelligence influences academic performance. In this account a complex learning component of fluid intelligence tests is proposed to play a major role in predicting academic performance. A sample of 2, 277 secondary school students completed two reasoning tests that were assumed to represent fluid intelligence and standardized math and verbal tests assessing academic performance. The fluid intelligence data were decomposed into a learning component that was associated with the position effect of intelligence items and a constant component that was independent of the position effect. Results showed that the learning component contributed significantly more to the prediction of math and verbal performance than the constant component. The link from the learning component to math performance was especially strong. These results indicated that fluid intelligence, which has so far been considered as homogeneous, could be decomposed in such a way that the resulting components showed different properties and contributed differently to the prediction of academic performance. Furthermore, the results were in line with the expectation that learning was a predictor of performance in school.

The contribution of temporary storage and executive processes to category learning.

Three distinctly different working memory processes, temporary storage, mental shifting and inhibition, were proposed to account for individual differences in category learning. A sample of 213 participants completed a classic category learning task and two working memory tasks that were experimentally manipulated for tapping specific working memory processes. Fixed-links models were used to decompose data of the category learning task into two independent components representing basic performance and improvement in performance in category learning. Processes of working memory were also represented by fixed-links models. In a next step the three working memory processes were linked to components of category learning. Results from modeling analyses indicated that temporary storage had a significant effect on basic performance and shifting had a moderate effect on improvement in performance. In contrast, inhibition showed no effect on any component of the category learning task. These results suggest that temporary storage and the shifting process play different roles in the course of acquiring new categories.

A fixed-links modeling approach to assess individual differences in the attentional blink: Analysis of behavioral and psychophysiological data.

The attentional blink (AB) is a fundamental limitation of the ability to select relevant information from irrelevant information. It can be observed with the detection rate in an AB task as well as with the corresponding P300 amplitude of the event-related potential. In previous research, however, correlations between these two levels of observation were weak and rather inconsistent. A possible explanation of this finding might be that multiple processes underlie the AB and, thus, obscure a possible relationship between AB-related detection rate and the corresponding P300 amplitude. The present study investigated this assumption by applying a fixed-links modeling approach to represent behavioral individual differences in the AB as a latent variable. Concurrently, this approach enabled us to control for additional sources of variance in AB performance by deriving two additional latent variables. The correlation between the latent variable reflecting behavioral individual differences in AB magnitude and a corresponding latent variable derived from the P300 amplitude was high (r=.70). Furthermore, this correlation was considerably stronger than the correlations of other behavioral measures of the AB magnitude with their psychophysiological counterparts (all rs<.40). Our findings clearly indicate that the systematic disentangling of various sources of variance by utilizing the fixed-links modeling approach is a promising tool to investigate behavioral individual differences in the AB and possible psychophysiological correlates of these individual differences.

Elucidating the functional relationship between working memory capacity and psychometric intelligence: a fixed-links modeling approach for experimental repeated-measures designs.

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 (ß = .48) as well as the constant processes involved in the task (ß = .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 (ß = .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.