The Trade-Off Between Factor Score Determinacy and the Preservation of Inter-Factor Correlations.

Regression factor score predictors have the maximum factor score determinacy, that is, the maximum correlation with the corresponding factor, but they do not have the same inter-correlations as the factors. As it might be useful to compute factor score predictors that have the same inter-correlations as the factors, correlation-preserving factor score predictors have been proposed. However, correlation-preserving factor score predictors have smaller correlations with the corresponding factors (factor score determinacy) than regression factor score predictors. Thus, higher factor score determinacy goes along with bias of the inter-correlations and unbiased inter-correlations go along with lower factor score determinacy. The aim of the present study was therefore to investigate the size and conditions of the trade-off between factor score determinacy and bias of inter-correlations by means of algebraic considerations and a simulation study. It turns out that under several conditions very small gains of factor score determinacy of the regression factor score predictor go along with a large bias of inter-correlations. Instead of using the regression factor score predictor by default, it is proposed to check whether substantial bias of inter-correlations can be avoided without substantial loss of factor score determinacy using a correlation-preserving factor score predictor. A syntax that allows to compute correlation-preserving factor score predictors from regression factor score predictors, and to compare factor score determinacy and inter-correlations of the factor score predictors is given in the Appendix.

Robust oblique Target-rotation for small samples.

Introduction: Oblique Target-rotation in the context of exploratory factor analysis is a relevant method for the investigation of the oblique simple structure. It was argued that minimizing single cross-loadings by means of target rotation may lead to large effects of sampling error on the target rotated factor solutions. Method: In order to minimize effects of sampling error on results of Target-rotation we propose to compute the mean cross-loadings for each block of salient loadings of the independent clusters model and to perform Target-rotation for the block-wise mean cross-loadings. The resulting transformation-matrix is than applied to the complete unrotated loading matrix in order to produce mean Target-rotated factors. Results: A simulation study based on correlated independent clusters model and zero-mean cross-loading models revealed that mean oblique Target-rotation resulted in smaller bias of factor inter-correlations than conventional Target-rotation based on single loadings, especially when sample size was small and when the number of factors was large. An empirical example revealed that the similarity of Target-rotated factors computed for small subsamples with Target-rotated factors of the total sample was more pronounced for mean Target-rotation than for conventional Target-rotation. Discussion: Mean Target-rotation can be recommended in the context of oblique factor models based on simple structure, especially for small samples. An R-script and an SPSS-script for this form of Target-rotation are provided in the Supplementary Material.

Intra-Subject Variability, Intelligence, and ADHD Traits in a Community-Based Sample.

OBJECTIVE: The present study investigates the predictive validity of intra-subject variability (ISV) for ADHD traits in a community-based sample and the stability of the relationship between ISV and fluid intelligence (gf) across the continuum of ADHD traits. METHOD: Age-residualized data from 426 participants (8-18 years, 6% ADHD) was used to investigate whether ex-Gaussian and DDM parameters derived from simple choice-reaction-time tasks can predict continuously assessed ADHD traits. Multiple-Group-Analyses and Latent-Moderated-Structural-Equations were used to test whether ADHD traits moderate the relationship between ISV and gf. RESULTS: σ and µ of the ex-Gaussian model as well as DDM parameters drift rate (v) and boundary separation (a) significantly predicted general ADHD traits, while τ predicted attention difficulties specifically. Across the ADHD continuum, σ and v were significant predictors of gf. CONCLUSION: The results confirm the link between ISV and ADHD. The relationship between ISV and gf appears stable across the ADHD continuum.

Coefficients of Factor Score Determinacy for Mean Plausible Values of Bayesian Factor Analysis.

In the context of Bayesian factor analysis, it is possible to compute plausible values, which might be used as covariates or predictors or to provide individual scores for the Bayesian latent variables. Previous simulation studies ascertained the validity of mean plausible values by the mean squared difference of the mean plausible values and the generating factor scores. However, the mean correlation of sets of single plausible values of different factors were shown to be an adequate estimator of the correlation between factors. Using sets of single plausible values to compute a mean prediction in secondary analysis implies that their determinacy should be known. Therefore, a plausible value-based determinacy coefficient allowing for estimation of the determinacy of single plausible values was proposed and evaluated by means of two simulation studies. The first simulation study demonstrated that the plausible value-based determinacy coefficient is an adequate estimate of the correlation of single plausible values with the population factor. It is also shown that the plausible value-based determinacy coefficient of mean plausible values approaches the conventional, model parameter-based determinacy coefficient with increasing number of imputations. The second simulation study revealed that the plausible value-based determinacy coefficient and the model parameter-based determinacy coefficient yield similar results even for misspecified models in small samples. It also revealed that for small sample sizes and a small salient loading size, the coefficients of determinacy overestimate the validity, so that it is recommended to report the determinacy coefficients together with a bias-correction to estimate the validity of plausible values in empirical settings.

Evidence towards a continuum of impairment across neurodevelopmental disorders from basic ocular-motor tasks.

Findings of genetic overlap between Schizophrenia, Attention-Deficit/Hyperactivity Disorder (ADHD) and Autism Spectrum Disorder (ASD) contributed to a renewed conceptualization of these disorders as laying on a continuum based on aetiological, pathophysiological and neurodevelopmental features. Given that cognitive impairments are core to their pathophysiology, we compared patients with schizophrenia, ADHD, ASD, and controls on ocular-motor and manual-motor tasks, challenging crucial cognitive processes. Group comparisons revealed inhibition deficits common to all disorders, increased intra-subject variability in schizophrenia and, to a lesser extent, ADHD as well as slowed processing in schizophrenia. Patterns of deviancies from controls exhibited strong correlations, along with differences that posited schizophrenia as the most impaired group, followed by ASD and ADHD. While vector correlations point towards a common neurodevelopmental continuum of impairment, vector levels suggest differences in the severity of such impairment. These findings argue towards a dimensional approach to Neurodevelopmental Disorders' pathophysiological mechanisms.

Conditions affecting the association of general trait-anxiety with the ERN-Ne.

The ERN-Ne of the event-related potential indicates error monitoring. Even though enlarged ERN-Ne amplitudes have often been related to higher anxiety scores, a recent meta-analysis provided very small effect sizes for the association of trait-anxiety with the ERN-Ne. Conditions modulating this association were investigated in the present study: (1) The generality of the trait-anxiety factor, (2) gender, and (3) experimental conditions, i.e., worry induction and error aversiveness. Participants (48% men) completed a flanker task. Worries were induced before the task by giving participants (n = 61) a bogus feedback claiming their responses were slower than the average responses of participants, whereas other participants (n = 61) got the feedback that they responded as fast as other participants. Aversiveness of errors was varied by playing sinus tones after too slow responses in one part of the task (no-scream condition) and aversive screams after too slow responses in another part (scream condition). Increased ERN-Ne amplitudes of response time errors occurred for individuals higher on trait-anxiety in the condition with induced worries and screams. A multiple group model for women and men indicated that women are more sensitive to conditions altering the association of trait-anxiety with the ERN-Ne.

Visual search in neurodevelopmental disorders: evidence towards a continuum of impairment.

Disorders with neurodevelopmental aetiology such as Attention-Deficit/Hyperactivity Disorder (ADHD), Autism Spectrum Disorder (ASD) and Schizophrenia share commonalities at many levels of investigation despite phenotypic differences. Evidence of genetic overlap has led to the concept of a continuum of neurodevelopmental impairment along which these disorders can be positioned in aetiological, pathophysiological and developmental features. This concept requires their simultaneous comparison at different levels, which has not been accomplished so far. Given that cognitive impairments are core to the pathophysiology of these disorders, we provide for the first time differentiated head-to-head comparisons in a complex cognitive function, visual search, decomposing the task with eye movement-based process analyses. N = 103 late-adolescents with schizophrenia, ADHD, ASD and healthy controls took a serial visual search task, while their eye movements were recorded. Patients with schizophrenia presented the greatest level of impairment across different phases of search, followed by patients with ADHD, who shared with patients with schizophrenia elevated intra-subject variability in the pre-search stage. ASD was the least impaired group, but similar to schizophrenia in post-search processes and to schizophrenia and ADHD in pre-search processes and fixation duration while scanning the items. Importantly, the profiles of deviancy from controls were highly correlated between all three clinical groups, in line with the continuum idea. Findings suggest the existence of one common neurodevelopmental continuum of performance for the three disorders, while quantitative differences appear in the level of impairment. Given the relevance of cognitive impairments in these three disorders, we argue in favour of overlapping pathophysiological mechanisms.

Bayesian and Maximum-Likelihood Modeling and Higher-Level Scores of Interpersonal Problems With Circumplex Structure.

Difficulties in interpersonal behavior are often measured by the circumplex-based Inventory of Interpersonal Problems. Its eight scales can be represented by a three-factor structure with two circumplex factors, Dominance and Love, and a general problem factor, Distress. Bayesian confirmatory factor analysis is well-suited to evaluate the higher-level structure of interpersonal problems because circumplex loading priors allow for data-driven adjustments and a more flexible investigation of the ideal circumplex pattern than conventional maximum likelihood confirmatory factor analysis. Using a non-clinical sample from an online questionnaire study (N = 822), we replicated the three-factor structure of the IIP by maximum likelihood and Bayesian confirmatory factor analysis and found great proximity of the Bayesian loadings to perfect circumplexity. We found additional support for the validity of the three-factor model of the IIP by including external criteria-Agreeableness, Extraversion, and Neuroticism from the Big Five and subclinical grandiose narcissism-in the analysis. We also investigated higher-level scores for Dominance, Love, and Distress using traditional regression factor scores and weighted sum scores. We found excellent reliability (with R tt ≥ 0.90) for Dominance, Love, and Distress for the two scoring methods. We found high congruence of the higher-level scores with the underlying factors and good circumplex properties of the scoring models. The correlational pattern with the external measures was in line with theoretical expectations and similar to the results from the factor analysis. We encourage the use of Bayesian modeling when dealing with circumplex structure and recommend the use of higher-level scores for interpersonal problems as parsimonious, reliable, and valid measures.

Psychometric Properties of a German Online Version of the Gudjonsson Suggestibility Scale 1.

Suggestibility is a trait dimension that has been differentiated into Yield and Shift dimensions. Yield refers to the susceptibility to suggestive item content in a first question series (Yield 1) and a second question series following negative feedback (Yield 2). Shift describes the tendency to change answers over the two series of questions depending on social pressure. This study aimed at investigating the psychometric properties and the factor structure of a German online version of the Gudjonsson Suggestibility Scale 1 (GSS 1) and measurement invariance of suggestibility scores for gender and research institution. A total of N=560 (n=287 female; age: M=24.20, SD=4.60years) students participated in the study. We present Stanine norms for the application of the online GSS 1. Results supported the theoretical basis of the GSS by revealing the two expected suggestibility factors: Yield and Shift. As expected, a leading factor and a non-leading factor were identified for Yield 1 and Yield 2 and a single factor for Shift. We report psychometric properties (e.g., item difficulty, part-whole corrected item-total correlations, reliability coefficients). We compare the factorial structure of the German online GSS 1 with former versions of the GSS 1. Our data suggest widely measurement invariance for gender and research institution on Yield 1 and Yield 2.

On the Detection of the Correct Number of Factors in Two-Facet Models by Means of Parallel Analysis.

Methods for optimal factor rotation of two-facet loading matrices have recently been proposed. However, the problem of the correct number of factors to retain for rotation of two-facet loading matrices has rarely been addressed in the context of exploratory factor analysis. Most previous studies were based on the observation that two-facet loading matrices may be rank deficient when the salient loadings of each factor have the same sign. It was shown here that full-rank two-facet loading matrices are, in principle, possible, when some factors have positive and negative salient loadings. Accordingly, the current simulation study on the number of factors to extract for two-facet models was based on rank-deficient and full-rank two-facet population models. The number of factors to extract was estimated from traditional parallel analysis based on the mean of the unreduced eigenvalues as well as from nine other rather traditional versions of parallel analysis (based on the 95th percentile of eigenvalues, based on reduced eigenvalues, based on eigenvalue differences). Parallel analysis based on the mean eigenvalues of the correlation matrix with the squared multiple correlations of each variable with the remaining variables inserted in the main diagonal had the highest detection rates for most of the two-facet factor models. Recommendations for the identification of the correct number of factors are based on the simulation results, on the results of an empirical example data set, and on the conditions for approximately rank-deficient and full-rank two-facet models.

The P300 and MFN as indicators of concealed knowledge in situations with negative and positive moral valence.

Many studies on concealed knowledge involve mock-thefts. The present study compares ERPs of participants concealing knowledge of a morally negative behavior (mock-theft) with ERPs of participants concealing knowledge of a morally positive behavior. Some participants (n= 33) stole a candy box out of an office, whereas others (n= 28) put the candy box into an office as a present. During a concealed information test, participants concealed knowledge of the candy box and a key they had seen in the office (probe stimuli) and honestly indicated not knowing similar irrelevant stimuli. P300s were enlarged for probe, compared to irrelevant stimuli in both conditions, revealing that probe stimuli were more salient than irrelevant stimuli regardless of their moral valence. Likewise, medial frontal negativities were enlarged for probe versus irrelevant stimuli in both conditions, indicating response conflicts when answering deceptively to probe items in both situations.

Identification of Facet Models by Means of Factor Rotation: A Simulation Study and Data Analysis of a Test for the Berlin Model of Intelligence Structure.

We investigated by means of a simulation study how well methods for factor rotation can identify a two-facet simple structure. Samples were generated from orthogonal and oblique two-facet population factor models with 4 (2 factors per facet) to 12 factors (6 factors per facet). Samples drawn from orthogonal populations were submitted to factor analysis with subsequent Varimax, Equamax, Parsimax, Factor Parsimony, Tandem I, Tandem II, Infomax, and McCammon's minimum entropy rotation. Samples drawn from oblique populations were submitted to factor analysis with subsequent Geomin rotation and a Promax-based Tandem II rotation. As a benchmark, we investigated a target rotation of the sample loadings toward the corresponding faceted population loadings. The three conditions were sample size (n = 400, 1,000), number of factors (q = 4-12), and main loading size (l = .40, .50, .60). For less than six orthogonal factors Infomax and McCammon's minimum entropy rotation and for six and more factors Tandem II rotation yielded the highest congruence of sample loading matrices with faceted population loading matrices. For six and more oblique factors Geomin rotation and a Promax-based Tandem II rotation yielded the highest congruence with faceted population loadings. Analysis of data of 393 participants that performed a test for the Berlin Model of Intelligence Structure revealed that the faceted structure of this model could be identified by means of a Promax-based Tandem II rotation of task aggregates corresponding to the cross-products of the facets. Implications for the identification of faceted models by means of factor rotation are discussed.

Individual differences of conflict monitoring and feedback processing during reinforcement learning in a mock forensic context.

This study investigated individual differences of conflict monitoring (N2 component), feedback processing (feedback negativity component), and reinforcement learning in a discrimination learning task using a mock (fictitious) forensic scenario to set participants in a semantic task context. We investigated individual differences of anxiety-related, impulsivity-related traits and reasoning ability during trial-and-error learning of mock suspect and nonsuspect faces. Thereby, we asked how the differential investment of cognitive-motivational processes facilitates learning in a mock forensic context. As learning can be studied by means of time-on-task effects (i.e., variations of cognitive processes across task blocks), we investigated the differential investment of cognitive-motivational processes block-wise in N = 100 participants. By performing structural equation modeling, we demonstrate that conflict monitoring decreased across task blocks, whereas the percentage of correct responses increased across task blocks. Individuals with higher reasoning scores and higher impulsivity-related traits relied rather on feedback processing (i.e., external indicators) during reinforcement learning. Individuals with higher anxiety-related traits intensified their conflict monitoring throughout the task to learn successfully. Observation by relevant others intensified conflict monitoring more than nonobservation. Our data highlight that individual differences and social context modulate the intensity of information processing in a discrimination learning task using a mock forensic task scenario. We discuss our data with regard to recent cognitive-motivational approaches and in terms of reinforcement learning.

Individual differences in ERPs during deception: Observing vs. demonstrating behavior leading to a small social conflict.

The present study investigated individual differences modulating P300 and MFN amplitudes in a concealed information test (CIT). Some participants were offered candy and either denied (n = 41) or ate it (n = 31), while others witnessed an examiner eating it (informed condition; n = 34). Afterwards it was suggested that the candy was not meant for them. During the CIT, participants saw the candy (probe) and similar unknown items (irrelevants) and indicated that they did not know them. P300 and MFN amplitudes differed for probe and irrelevant items, revealing that known items were more salient and deception was accompanied by response conflicts. Larger differences between P300s for probe versus irrelevant items occurred for women. Furthermore, especially for women, response conflicts diminished when being in the informed condition. Different patterns of MFN amplitudes appeared for informed women depending on the Machiavellianism score, suggesting that gender and Machiavellianism could be related to different cognitive processing during deception.

Score Predictor Factor Analysis: Reproducing Observed Covariances by Means of Factor Score Predictors.

The non-diagonal elements of the observed covariances are more exactly reproduced by the factor loadings than by the model implied by the corresponding factor score predictors. This is a limitation to the validity of factor score predictors. It is therefore investigated whether it is possible to estimate factor loadings for which the model implied by the factor score predictors optimally reproduces the non-diagonal elements of the observed covariance matrix. Accordingly, loading estimates are proposed for which the model implied by the factor score predictors allows for a least-squares approximation of the non-diagonal elements of the observed covariance matrix. This estimation method is termed score predictor factor analysis and algebraically compared with Minres factor analysis as well as principal component analysis. A population-based and a sample-based simulation study was performed in order to compare score predictor factor analysis, Minres factor analysis, and principal component analysis. It turns out that the non-diagonal elements of the observed covariance matrix can more exactly be reproduced from the factor score predictors computed from score predictor factor analysis than from the factor score predictors computed from Minres factor analysis and from principal components.

A meta-analysis of the P3 amplitude in tasks requiring deception in legal and social contexts.

In deception tasks the parietal P3 amplitude of the event-related potential indicates either recognition of salient stimuli (larger P3 following salient information) or mental effort (smaller P3 following demanding information). This meta-analysis (k = 77) investigated population effect sizes (δ) for conceptual and methodological a-priori moderators (study design, pre-task scenario, context of deception tasks, and P3 quantification). Within-subject designs show evidence of the underlying cognitive processes, between-subject designs allow for comparisons of cognitive processes in culprits vs. innocents. Committed vs. imagined mock crime scenarios yield larger δ. Deception tasks with a legal context result in almost twice as large δ than deception tasks with social-evaluative and social-biographical contexts. Peak-to-peak P3 quantification resulted in larger δ than other quantifications. Counter-measure techniques in 3-stimulus protocols reduce the discriminability of concealed vs. truthful P3 amplitudes. Depending on stimulus knowledge, deception tasks provide evidence for the salience hypothesis and the mental effort hypothesis, respectively.

Varimax Rotation Based on Gradient Projection Is a Feasible Alternative to SPSS.

Gradient projection rotation (GPR) is an openly available and promising tool for factor and component rotation. We compare GPR toward the Varimax criterion in principal component analysis to the built-in Varimax procedure in SPSS. In a simulation study, we tested whether GPR-Varimax yielded multiple local solutions by creating population simple structure with a single optimum and with two optima, a global and a local one (double-optimum condition). The other conditions comprised the number of components (k = 3, 6, 9, and 12), the number of variables per component (m/k = 4, 6, and 8), the number of iterations per rotation (i = 25 and 250), and whether loadings were Kaiser normalized before rotation or not. GPR-Varimax was conducted with unrotated and multiple (q = 1, 10, 50, and 100) random start loadings. We found equal results for GPR-Varimax and SPSS-Varimax in most conditions. The few very small differences in favor of SPSS-Varimax were eliminated when Kaiser-normalized loadings and 250 iterations per rotation were used. Selecting the best solution out of multiple random starts in GPR-Varimax increased proximity to population components in the double-optimum condition with Kaiser normalized loadings, for which GPR-Varimax recovered population structure better than SPSS-Varimax. We also included an empirical example and found that GPR-Varimax and SPSS-Varimax yielded highly similar solutions for orthogonal simple structure in a real data set. We suggest that GPR-Varimax can be used as an alternative to Varimax rotation in SPSS. Users of GPR-Varimax should allow for at least 250 iterations, normalize loadings before rotation, and select the best solution from at least 10 random starts to ensure optimal results.

ADHD Traits in German School-Aged Children: Validation of the German Strengths and Weaknesses of ADHS Symptoms and Normal Behavior (SWAN-DE) Scale.

OBJECTIVE: The Strengths and Weaknesses of ADHS-Symptoms and Normal Behavior (SWAN) Scale has been developed to support the dimensional assessment of ADHD symptoms by capturing variance on both poles of the ADHD continuum. The present study provides the first validation of the German version of SWAN (SWAN-DE). METHOD: Based on a sample of N1 = 343 children from the general population and N2 = 62 children with ADHD, both aged between 8 and 18 years, normality, internal consistency, test-retest reliability, and different validity indices were examined. RESULTS: SWAN was characterized by normally distributed scores, good to excellent reliability, and factorial validity. It showed high diagnostic utility in discriminating between patients with ADHD and healthy controls and significant correlations to related clinical scales and neuropsychological constructs, such as intra-subject variability. CONCLUSION: The present study reveals the excellent psychometric properties of SWAN-DE, which can now be usefully applied in the German-speaking countries as well as in cross-national studies.

Does concealing familiarity evoke other processes than concealing untrustworthiness? - Different forms of concealed information modulate P3 effects.

It was investigated whether concealing learned stimulus attributes (i.e., trustworthiness vs. untrustworthiness) has similar effects on the P3 amplitude than concealing stimulus familiarity. According to salience hypothesis, known, deceptive stimuli (probe) are (perceived) more relevant than truthful, unknown stimuli (irrelevant) evoking a more positive probe P3 amplitude. When all stimuli are known, concealing information is more cognitively demanding than non-concealing information evoking a less positive P3 amplitude according to the mental effort account. Ninety-seven participants concealed knowledge of previously learned faces in the familiarity condition (probe vs. irrelevant stimuli). In the trustworthiness condition, participants concealed untrustworthiness to previously learned faces and responded truthfully to previously learned trustworthy and untrustworthy faces (known, concealed vs. known, truthful stimuli). The parietal mean P3 amplitude was more positive for probe stimuli than for irrelevant stimuli in the familiarity condition providing evidence for the salience hypothesis. In the trustworthiness condition, concealing untrustworthiness showed the smallest parietal mean P3 amplitude suggesting evidence for the mental effort hypothesis. Individual differences of perpetrator's sensitivity to injustice modulated the P3 amplitude in the trustworthiness condition.

The N2 component in a go-nogo learning task: Motivation, behavioral activation, and reasoning.

Although the association of the N2 component with behavioral inhibition (BIS) has regularly been investigated, its association with other personality characteristics remains widely unknown. We investigated the association of the N2 with the sensitivity of the behavioral activation system (BAS). The aim was not to show that the N2 is linked to trait BAS instead of trait BIS, but that a motivating setting may alter its association with those traits. Furthermore, we aimed at replicating results indicating that the association between reasoning ability and the N2 depends on the matching of the content of the reasoning tasks and the go-nogo task. The electroencephalogram (64 electrodes, P9/P10 offline reference, Biosemi) was recorded in a sample of 117 healthy participants (60 females; age: M = 24.79, SD = 3.98), who performed a numerical learning task. At the beginning of each trial, participants heard motivating or neutral words. Participants completed Carver and White's BIS/BAS scales (1994) and the Intelligence-Structure-Test 2000R (Liepmann et al., 2007). The N2 was identified by a temporospatial principal component analysis. Structural equation models revealed that higher trait BAS scores were associated with larger N2s especially when hearing motivating words. Solely higher numerical reasoning scores were associated with larger N2s in the neutral condition. Moreover, the interaction of trait BAS with verbal reasoning ability predicted an increased negativity of the N2 with time-on-task in the motivating condition, suggesting that motivating words yielded an increase of conflict monitoring with time-on-task for participants with higher verbal reasoning ability and higher trait BAS.