Ordinary Least Squares Estimation of Parameters in Exploratory Factor Analysis With Ordinal Data

Exploratory factor analysis (EFA) is often conducted with ordinal data (e.g., items with 5-point responses) in the social and behavioral sciences. These ordinal variables are often treated as if they were continuous in practice. An alternative strategy is to assume that a normally distributed continuous variable underlies each ordinal variable. The EFA model is specified for these underlying continuous variables rather than the observed ordinal variables. Although these underlying continuous variables are not observed directly, their correlations can be estimated from the ordinal variables. These correlations are referred to as polychoric correlations. This article is concerned with ordinary least squares (OLS) estimation of parameters in EFA with polychoric correlations. Standard errors and confidence intervals for rotated factor loadings and factor correlations are presented. OLS estimates and the associated standard error estimates and confidence intervals are illustrated using personality trait ratings from 228 college students. Statistical properties of the proposed procedure are explored using a Monte Carlo study. The empirical illustration and the Monte Carlo study showed that (a) OLS estimation of EFA is feasible with large models, (b) point estimates of rotated factor loadings are unbiased, (c) point estimates of factor correlations are slightly negatively biased with small samples, and (d) standard error estimates and confidence intervals perform satisfactorily at moderately large samples.     

The Contributions of Memory and Attention Processes to Cognitive Abilities

In two experiments, the contributions of memory and attention processes to the cognitive abilities of reasoning and perceptual speed were investigated. Two measures of speed of information retrieval from long-term and short-term memory (Posner paradigm, Sternberg paradigm) and two attention measures (continuous attention test, attention switching test) were included in the first experiment (N = 220). The memory tests led to correlations with the measures of cognitive abilities, whereas the attention test did not. The same tests as well as one additional memory test and one attention test (working memory test, test of covert orientation) were administered in the second experiment (N = 116). Again, the memory tests led to the larger correlations with the measures of cognitive abilities. Two components were obtained in components analysis, of which the first was characterized by high loadings of the memory tests and the second by high loadings of the attention tests. Only the memory component contributed to the prediction of cognitive abilities.     

Comparing subtest profiles of g loadings and correlations with RT measures

It is argued that if a response time (RT) measure correlates with psychometric test (PT) scores because it shares variance in common with general intelligence, g, then the profile of g loadings for a set of PTs would be predictable from the profile of correlations between the RT measure and the PT scores. On the other hand, if an RT correlates with PTs through variance not shared with g, the g loadings of the PTs should be unrelated to the correlations between RT and PTs. The profiles of g loadings and correlations with RT were compared for a set of 6 RT measures and 8 PT scores from Smith and Stanley (1983). To demonstrate statistical significance, standard errors of the statistics were generated by Efron's bootstrap technique (Efron, 1979). It was clearly shown that the profile of the PT's g loadings could be well predicted from the RT-PT correlations for four of the RT measures. It can be concluded that RT tasks do measure general intelligence. Analysis of the errors in prediction suggested that the RTs may correlate more with fluid than crystallized intelligence.     

Perceived Weight of Other Persons

Abstract

On the basis of photographs, students (N = 258) evaluated the weights of 77 male executives or 50 businesswomen. Women students were expected to be less likely than men, and non-American students (mostly ethnic Chinese) to be less likely than Americans, to assign thin ratings to the people in the photographs. No differences in ratings were found between the responses of male and female students, but some significant differences in ratings were found between the American and non-American students. The results suggest that studies of other persons' body images may yield limited insights into the eating disorders that can accompany body self-image distortions.     

A General Factor of Personality (GFP) from two meta-analyses of the Big Five: and

In two studies, we used structural equation models to test the hypothesis that a General Factor of Personality (GFP) occupies the apex of the hierarchy of personality. In Study 1, we found a GFP that explained 45% of the reliable variance in a model that went from the Big Five to the Big Two to the Big One in the 14 studies of inter-scale correlations (N = 4496) assembled by Digman (1997). A higher order factor of Alpha/Stability was defined by Conscientiousness, Emotional Stability, and Agreeableness, with loadings of from 0.61 to 0.70, while Beta/Plasticity was defined by Openness and Extraversion with loadings of 0.55 and 0.77. In turn, the GFP was defined by Alpha and Beta with loadings of 0.67. In Study 2, a GFP explained 44% of the reliable variance in a similar model using data from a published meta-analysis of the Big Five (N = 4000) by Mount, Barrick, Scullen, and Rounds (2005). Strong general factors such as these, based on large data sets with good model fits that cross validate perfectly, are unlikely to be due to artifacts and response sets.     

The ministry of silly walks’ report: representational momentum sensitive to awkwardness following action,not single posture

ABSTRACT

Completing a representational momentum (RM) task, participants viewed animations of a human cartoon or a robot figure with three levels of awkwardness in the walk and indicated if the final posture was identical to the final frame of the animation. Animations were shown forward and backward, and the level of awkwardness influenced the extent of RM (Experiment 1: N?=?30). Positive distortions decreased with increased awkwardness for forward actions. Negative distortions for the backward animations meant either participants were falling behind the depicted action, or that continuing familiar actions forward is a stronger bias than continuing presented (backward) actions. Following a single posture (Experiment 2: N?=?19), positive distortions were observed, but no pattern regarding awkwardness. A single posture is sufficient to elicit forward distortions, but the awkwardness effect requires viewing the action.     

Experimental comparison of dyspnea and pain

Dyspnea and pain are similarly unpleasant, alarming physical sensations, but studies examining both sensations in combination are lacking. In the present study, dyspnea was induced in 7 healthy volunteers by breathing through inspiratory resistive loads and the effects were compared with those of a heat pain stimulus. End-tidal partial pressures of carbon dioxide (PET_CO2), inspiratory time (Ti), breathing frequency (f), experienced unpleasantness, and intensity were measured. No difference was observed between dyspnea and pain in experienced intensity and unpleasantness (p >.05). During dyspneic stimulation, slightly higherTi was found than for pain (p<.08). PET_CO2 showed slight increases during the dyspneic versus the baseline and painful conditions (ΔPET_CO2=1.5 and 1.3 mmHg, respectively;p<.01 andp<.05). This study shows that the effects of dyspnea and heat pain can be compared within one experiment; both stimuli can be presented with similar intensity and unpleasantness, which is a prerequisite for comparing responses to them. The changes in PET_CO2 between our conditions were minimal, allowing an application of the present design to future fMRI studies.     

The Italian version of the Social Comparison Rating Scale and the Submissive Behaviour Scale: Reliability and validity in a sample of adolescents

Social rank theory argues that social comparison and submissive behaviour are mechanisms by which humans and animals form themselves into social ranks. Design: this study assesses the psychometric properties of Italian versions of the Social Comparison Rating Scale—SCRS and Submissive Behaviour Scale—SBS in a sample of adolescents. The samples consisted of a clinical group (N = 200) and a non-clinical group (N = 1991). The non-clinical group allowed us to obtain two random samples used for the EFA and the CFA; moreover, we also extracted a Retest sample consisting of 219 subjects. Internal consistency was satisfactory and the factor structures were similar to the original version of the measures. The SBS and SCRS were significantly correlated with all the symptom profiles on the SCL-90-R, in both populations. Clinical populations had higher correlations with these measures. Statistical analyses showed a good fit to the data, replicating the constructs of the original scales. These results confirm that submissive behaviour and social comparison are associated with mental health problems.     

Specified Meet Contraction

Specified meet contraction is the operation ?\div defined by the identity K ?p = K   ~  f(p)K \div p = K \,{\sim}\, f(p) where ∼ is full meet contraction and f is a sentential selector, a function from sentences to sentences. With suitable conditions on the sentential selector, specified meet contraction coincides with the partial meet contractions that yield a finite-based contraction outcome if the original belief set is finite-based. In terms of cognitive realism, specified meet contraction has an advantage over partial meet contraction in that the selection mechanism operates on sentences rather than on temporary infinite structures (remainders) that are cognitively inaccessible. Specified meet contraction provides a versatile framework in which other types of contraction, such as severe withdrawal and base-generated contraction, can be expressed with suitably chosen properties of the sentential selector.     

Exploratory Factor Analysis With Small Samples and Missing Data

Exploratory factor analysis (EFA) is an extremely popular method for determining the underlying factor structure for a set of variables. Due to its exploratory nature, EFA is notorious for being conducted with small sample sizes, and recent reviews of psychological research have reported that between 40% and 60% of applied studies have 200 or fewer observations. Recent methodological studies have addressed small size requirements for EFA models; however, these models have only considered complete data, which are the exception rather than the rule in psychology. Furthermore, the extant literature on missing data techniques with small samples is scant, and nearly all existing studies focus on topics that are not of primary interest to EFA models. Therefore, this article presents a simulation to assess the performance of various missing data techniques for EFA models with both small samples and missing data. Results show that deletion methods do not extract the proper number of factors and estimate the factor loadings with severe bias, even when data are missing completely at random. Predictive mean matching is the best method overall when considering extracting the correct number of factors and estimating factor loadings without bias, although 2-stage estimation was a close second.     

On the maximum number of folds of a piece of paper

We argue that a piece of paper, of thickness T and width W, can be folded a maximum number N?=?0.962 ln(f W/T) times, where f is a factor of order unity, determined by mechanical constraints. N typically takes a value of around six.     

Monte Carlo tests of the Rasch model based on scalability coefficients

For item responses fitting the Rasch model, the assumptions underlying the Mokken model of double monotonicity are met. This makes non‐parametric item response theory a natural starting‐point for Rasch item analysis. This paper studies scalability coefficients based on Loevinger's H coefficient that summarizes the number of Guttman errors in the data matrix. These coefficients are shown to yield efficient tests of the Rasch model using p‐values computed using Markov chain Monte Carlo methods. The power of the tests of unequal item discrimination, and their ability to distinguish between local dependence and unequal item discrimination, are discussed. The methods are illustrated and motivated using a simulation study and a real data example.     

Quantifying the Strength of General Factors in Psychopathology: A Comparison of CFA with Maximum Likelihood Estimation,BSEM, and ESEM/EFA Bifactor Approaches

Whether or not importance should be placed on an all-encompassing general factor of psychopathology (or p factor) in classifying, researching, diagnosing, and treating psychiatric disorders depends (among other issues) on the extent to which comorbidity is symptom-general rather than staying largely within the confines of narrower transdiagnostic factors such as internalizing and externalizing. In this study, we compared three methods of estimating p factor strength. We compared omega hierarchical and explained common variance calculated from confirmatory factor analysis (CFA) bifactor models with maximum likelihood (ML) estimation, from exploratory structural equation modeling/exploratory factor analysis models with a bifactor rotation, and from Bayesian structural equation modeling (BSEM) bifactor models. Our simulation results suggested that BSEM with small variance priors on secondary loadings might be the preferred option. However, CFA with ML also performed well provided secondary loadings were modeled. We provide two empirical examples of applying the three methodologies using a normative sample of youth (z-proso, n = 1,286) and a university counseling sample (n = 359).     

Empirically Corrected Rescaled Statistics for SEM with Small N and Large p

Survey data often contain many variables. Structural equation modeling (SEM) is commonly used in analyzing such data. With typical nonnormally distributed data in practice, a rescaled statistic T_rml proposed by Satorra and Bentler was recommended in the literature of SEM. However, T_rml has been shown to be problematic when the sample size N is small and/or the number of variables p is large. There does not exist a reliable test statistic for SEM with small N or large p, especially with nonnormally distributed data. Following the principle of Bartlett correction, this article develops empirical corrections to T_rml so that the mean of the empirically corrected statistics approximately equals the degrees of freedom of the nominal chi-square distribution. Results show that empirically corrected statistics control type I errors reasonably well even when N is smaller than 2p, where T_rml may reject the correct model 100% even for normally distributed data. The application of the empirically corrected statistics is illustrated via a real data example.     

How Accurate Is the Pearson r-from-Z Approximation? A Monte Carlo Simulation Study

The Pearson r-from-Z approximation estimates the sample correlation (as an effect size measure) from the ratio of two quantities: the standard normal deviate equivalent (Z-score) corresponding to a one-tailed p-value divided by the square root of the total (pooled) sample size. The formula has utility in meta-analytic work when reports of research contain minimal statistical information. Although simple to implement, the accuracy of the Pearson r-from-Z approximation has not been empirically evaluated. To address this omission, we performed a series of Monte Carlo simulations. Results indicated that in some cases the formula did accurately estimate the sample correlation. However, when sample size was very small (N = 10) and effect sizes were small to small-moderate (ds of 0.1 and 0.3), the Pearson r-from-Z approximation was very inaccurate. Detailed figures that provide guidance as to when the Pearson r-from-Z formula will likely yield valid inferences are presented.     

Contemporary theories of 1/f noise in motor control

1/f noise has been discovered in a number of time series collected in psychological and behavioral experiments. This ubiquitous phenomenon has been ignored for a long time and classical models were not designed for accounting for these long-range correlations. The aim of this paper is to present and discuss contrasted theoretical perspectives on 1/f noise, in order to provide a comprehensive overview of current debates in this domain. In a first part, we propose a formal definition of the phenomenon of 1/f noise, and we present some commonly used methods for measuring long-range correlations in time series. In a second part, we develop a theoretical position that considers 1/f noise as the hallmark of system complexity. From this point of view, 1/f noise emerges from the coordination of the many elements that compose the system. In a third part, we present a theoretical counterpoint suggesting that 1/f noise could emerge from localized sources within the system. In conclusion, we try to draw some lines of reasoning for going beyond the opposition between these two approaches.     

Copper and iron precipitates in thermochemically reduced yttria-stabilized zirconia crystals

We identify a 2D chain cluster, which consists of a periodic single row of bubbles of equal area with unequal pressures in alternate bubbles (C-cluster with curved inter-bubble films), existing in a finite interval of the period in which a normal configuration with equal pressures and straight inter-bubble films (N-cluster) also exists. For the same number of bubbles per unit length of the chain, the C-cluster has lower energy per bubble than the N-cluster of uniform pressure.     

Development and psychometric examination of a German video‐based situational judgment test for social competencies in medical school applicants

The present study describes the development and validation of a video‐based situational judgment test (SJT) assessing social competencies in applicants to medical school. Study 1 explored the psychometric properties of the SJT based on two applicant cohorts (N₁ = 769, N₂ = 787). Study 2 compared SJT data from applicants and 90 medical students. Tests for mean differences, correlation and factor analyses were used. In Study 1, the supposed two‐factor model for the SJT must be rejected. According to the minimum average partial test a single factor solution explaining 19–21% of the variance was suggested. The SJT showed satisfactory psychometric properties and stronger correlations to personality than to cognition as well as high acceptance. In study 2, applicants reached higher SJT scores than students.     

Job Experience and Big Five Personality Dimensions

Using a sample of engineers (N=80), the correlation between job experience and the personality dimensions was estimated. The results showed very small correlations. Based on these results, we suggest that composites created with job experience and personality measures can be useful for personnel selection.