Structural equations and causation: six counterexamples

Hall [(2007), Philosophical Studies, 132, 109–136] offers a critique of structural equations accounts of actual causation, and then offers a new theory of his own. In this paper, I respond to Hall’s critique, and present some counterexamples to his new theory. These counterexamples are then diagnosed.

Structural equations and causation

Structural equations have become increasingly popular in recent years as tools for understanding causation. But standard structural equations approaches to causation face deep problems. The most philosophically interesting of these consists in their failure to incorporate a distinction between default states of an object or system, and deviations therefrom. Exploring this problem, and how to fix it, helps to illuminate the central role this distinction plays in our causal thinking.

Effect size, power, and sample size determination for structured means modeling and mimic approaches to between-groups hypothesis testing of means on a single latent construct

While effect size estimates, post hoc power estimates, and a priori sample size determination are becoming a routine part of univariate analyses involving measured variables (e.g., ANOVA), such measures and methods have not been articulated for analyses involving latent means. The current article presents standardized effect size measures for latent mean differences inferred from both structured means modeling and MIMIC approaches to hypothesis testing about differences among means on a single latent construct. These measures are then related to post hoc power analysis, a priori sample size determination, and a relevant measure of construct reliability.I wish to convey my appreciation to the reviewers and Associate Editor, whose suggestions extended and strengthened the article's content immensely, and to Ralph Mueller of The George Washington University for enhancing the clarity of its presentation.     

The Influence of Number of Categories and Threshold Values on Fit Indices in Structural Equation Modeling with Ordered Categorical Data

This study examines the unscaled and scaled root mean square error of approximation (RMSEA), comparative fit index (CFI), and Tucker–Lewis index (TLI) of diagonally weighted least squares (DWLS) and unweighted least squares (ULS) estimators in structural equation modeling with ordered categorical data. We show that the number of categories and threshold values for categorization can unappealingly impact the DWLS unscaled and scaled fit indices, as well as the ULS scaled fit indices in the population, given that analysis models are misspecified and that the threshold structure is saturated. Consequently, a severely misspecified model may be considered acceptable, depending on how the underlying continuous variables are categorized. The corresponding CFI and TLI are less dependent on the categorization than RMSEA but are less sensitive to model misspecification in general. In contrast, the number of categories and threshold values do not impact the ULS unscaled fit indices in the population.     

Structural model of acculturation attitudes and related psychosocial variables: Empirical evidence in native Spaniards

This work falls within the framework of the study of acculturation processes of natives and immigrants. Its goal is to test an explanatory multi‐group model of natives' acculturation attitudes as a function of diverse psychosocial variables: Prejudice and natives' appraisal of their own culture (in a direct way) and inter‐group contact and perceived inter‐group similarity (in an indirect way). Participants were 499 Spaniards surveyed for their attitude towards Romanian immigrants and 493 towards Ecuadorian immigrants. The indicators used took into account three socio‐cultural spheres: peripheral, intermediate and central areas. This multi‐group model shows an adequate fit to the data.     

The Problem with Having Two Watches: Assessment of Fit When RMSEA and CFI Disagree

The root mean square error of approximation (RMSEA) and the comparative fit index (CFI) are two widely applied indices to assess fit of structural equation models. Because these two indices are viewed positively by researchers, one might presume that their values would yield comparable qualitative assessments of model fit for any data set. When RMSEA and CFI offer different evaluations of model fit, we argue that researchers are likely to be confused and potentially make incorrect research conclusions. We derive the necessary as well as the sufficient conditions for inconsistent interpretations of these indices. We also study inconsistency in results for RMSEA and CFI at the sample level. Rather than indicating that the model is misspecified in a particular manner or that there are any flaws in the data, the two indices can disagree because (a) they evaluate, by design, the magnitude of the model's fit function value from different perspectives; (b) the cutoff values for these indices are arbitrary; and (c) the meaning of “good” fit and its relationship with fit indices are not well understood. In the context of inconsistent judgments of fit using RMSEA and CFI, we discuss the implications of using cutoff values to evaluate model fit in practice and to design SEM studies.     

Effect size,statistical power,and sample size for assessing interactions between categorical and continuous variables

The reporting and interpretation of effect size estimates are widely advocated in many academic journals of psychology and related disciplines. However, such concern has not been adequately addressed for analyses involving interactions between categorical and continuous variables. For the purpose of improving current practice, this article presents fundamental features and theoretical developments for the variance of standardized slopes as a desirable standardized effect size measure for the degree of disparity between several slope coefficients. To estimate the effect size, a consistent and nearly unbiased estimator is described and a simple refinement is emphasized for extreme situations whenever appropriate. The essential problems of power and sample size calculations for testing the equality of slope coefficients are also considered. According to the analytic justification and empirical assessment, the exact approach has a clear advantage over the approximate methods. Both SAS and R computer codes are provided to facilitate practical accessibility of the proposed techniques in interaction studies.     

Religious obsessions and compulsions in a non-clinical sample: the Penn Inventory of Scrupulosity (PIOS)

The present investigation reports on the development and psychometric evaluation of the Penn Inventory of Scrupulosity (PIOS), a 19-item self-report scale measuring religious obsessive-compulsive symptoms. Factor analysis yielded a two factor solution with the first subscale measuring fears about having committed sin, and the second measuring fears concerning punishment from God. Using a sample of college students, the PIOS was shown to be internally consistent and possess good convergent and discriminant validity. Highly devout participants evidenced higher scores on both PIOS subscales, but devout Jews evidenced fewer fears of sin and punishment from God compared to devout Protestants or Catholics. The PIOS has utility both as a research and clinical tool.     

Religion and the five factor model of personality: An exploratory investigation using a Canadian university sample

The purpose of the present study was to examine the relation of religion, defined in terms of religious affiliation, religious involvement and religious orientation, to the five factor model of personality as measured by the NEO Personality Inventory-Revised using a religiously heterogeneous sample of 1129 Canadian university students. Results indicate that NEO-PI-R Agreeableness and Conscientiousness domains are significantly related to and affected by religion as measured across all three operationalizations of the construct used, though some sex differences were observed. Contrary to expectation, Neuroticism was found to differ as a function of religious affiliation with persons, particularly females, reporting No Religion obtaining significantly higher scores than those persons reporting a formal religious institution for their affiliation. Findings involving Extraversion were also inconsistent with hypotheses; Extraversion did not significantly relate to any form of religion measured. Openness was found to be largely unassociated with religion except for a significant negative correlation with a measure of extrinsic religious orientation. The article concludes with a discussion of the implications of the findings in relation to existing literature and Eysenck's hypothesis that religiousness is a function of conditionability and tender-minded attitudes. Limitations of the study and suggestions for future research are also overviewed.     

The Infant Behavior Questionnaire-Revised: Factor structure in a culturally and sociodemographically diverse sample in the United States

The recommended factor structure for the Infant Behavior Questionnaire-Revised (IBQ-R), a widely used parent-report measure of infant temperament, has limited empirical support. Moreover, the recommended factors were developed using homogenous samples not representative of current United States (U.S.) sociodemographics. The objective of this study was to examine the factor structure of the IBQ-R in a culturally and sociodemographically diverse U.S. cohort (N = 380 mother-infant dyads). Mothers were assessed during pregnancy on a range of cultural and sociodemographic characteristics and completed the IBQ-R when their infants were 6 months of age. The sample was diverse on maternal marital status, educational attainment, household income, race/ethnicity, primary language spoken, and country of birth. Initial confirmatory factor analysis for the recommended three-factor model yielded a poor fit. Modifications employed in other studies failed to improve model fit. An exploratory factor analysis revealed an acceptable model fit for a three-factor solution that showed similarities to as well as differences from the originally proposed factor structure. Additional analyses suggested lack of invariance on several factor and scale scores by maternal country of birth, race/ethnicity, and household income. The findings suggest that the commonly used IBQ-R factor structure may need to be adjusted for diverse samples and deserves further study.     

Methods matter: A review of Scientific Method: How Science Works,Fails to Work,and Pretends to Work by John Staddon,Routledge Press, 2018

The short and engaging book, How Science Works by John Staddon, reviews ways in which social and behavioral sciences arrive at decisions and how those decisions can best influence public policy. It is a provocative book that takes on controversial topics, including a critique of null hypothesis statistical testing, classical economic theories of supply and demand, limitations of Prospect Theory and behavioral economics, and evidence behind the health effects of smoking. A key theme running throughout is the idea that the theories and quantitative models used in the social sciences capture behavior and attitudes as fixed in time and fail to address the important issue of how behavior arose and how pliable it might be. The book will be of interest to scientists of all types as well as advanced students of psychology and other behavioral scientists.     

Point-biserial correlation: Interval estimation,hypothesis testing,meta-analysis,and sample size determination

The point-biserial correlation is a commonly used measure of effect size in two-group designs. New estimators of point-biserial correlation are derived from different forms of a standardized mean difference. Point-biserial correlations are defined for designs with either fixed or random group sample sizes and can accommodate unequal variances. Confidence intervals and standard errors for the point-biserial correlation estimators are derived from the sampling distributions for pooled-variance and separate-variance versions of a standardized mean difference. The proposed point-biserial confidence intervals can be used to conduct directional two-sided tests, equivalence tests, directional non-equivalence tests, and non-inferiority tests. A confidence interval for an average point-biserial correlation in meta-analysis applications performs substantially better than the currently used methods. Sample size formulas for estimating a point-biserial correlation with desired precision and testing a point-biserial correlation with desired power are proposed. R functions are provided that can be used to compute the proposed confidence intervals and sample size formulas.     

A closer look at moral dilemmas: Latent dimensions of morality and the difference between trolley and footbridge dilemmas

Although a distinction between moral-personal and moral-impersonal dilemmas (Greene, Sommerville, Nystrom, Darley, & Cohen, 2001 Greene, J. D., Sommerville, R. B., Nystrom, L. E., Darley, J. M. and Cohen, J. D. 2001. An fMRI investigation of emotional engagement in moral judgement. Science, 293: 2105–2108. doi:10.1126/science.1062872.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) has been widely accepted as an explanation for a difference between the trolley and footbridge dilemmas (Thomson, 1985 Thomson, J. J. 1985. “The trolley problem”. In Ethics: Problems and principles, Edited by: Fischer, J. M. and Ravizza, M. Fort Worth, TX: Harcourt Brace Jovanovich.  [Google Scholar]), its psychometric properties remain a mystery. In this study 219 participants completed 62 moral dilemma tasks used in Greene et al. (2001 Greene, J. D., Sommerville, R. B., Nystrom, L. E., Darley, J. M. and Cohen, J. D. 2001. An fMRI investigation of emotional engagement in moral judgement. Science, 293: 2105–2108. doi:10.1126/science.1062872.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]), and the correlation structure among the dilemmas was analysed through factor analysis and structural equation modelling. Findings suggest that, first, moral-personal dilemmas are composed of one factor, indicating that the assumption in Greene et al. (2001 Greene, J. D., Sommerville, R. B., Nystrom, L. E., Darley, J. M. and Cohen, J. D. 2001. An fMRI investigation of emotional engagement in moral judgement. Science, 293: 2105–2108. doi:10.1126/science.1062872.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]) was supported. Second, moral-impersonal dilemmas are explained by two factors that reflect procedural and consequential aspects of decision making. Third, the trolley and footbridge dilemmas fall under the same factor category; therefore the difference between the two dilemmas cannot be attributed to emotional involvement. Additionally, the results of the structural equation modelling suggest that they differ in the engagement of rational processing.     

Model Fit and Item Factor Analysis: Overfactoring,Underfactoring, and a Program to Guide Interpretation

In exploratory item factor analysis (IFA), researchers may use model fit statistics and commonly invoked fit thresholds to help determine the dimensionality of an assessment. However, these indices and thresholds may mislead as they were developed in a confirmatory framework for models with continuous, not categorical, indicators. The present study used Monte Carlo simulation methods to investigate the ability of popular model fit statistics (chi-square, root mean square error of approximation, the comparative fit index, and the Tucker–Lewis index) and their standard cutoff values to detect the optimal number of latent dimensions underlying sets of dichotomous items. Models were fit to data generated from three-factor population structures that varied in factor loading magnitude, factor intercorrelation magnitude, number of indicators, and whether cross loadings or minor factors were included. The effectiveness of the thresholds varied across fit statistics, and was conditional on many features of the underlying model. Together, results suggest that conventional fit thresholds offer questionable utility in the context of IFA.     

Multivariate modelling and personality organization: A comparative study of the Defense Mechanism Test and linguistic expressions

The main aim of the study is to establish an empirical connection between perceptual defences as measured by the Defense Mechanism Test (DMT)–a projective percept-genetic method–and manifest linguistic expressions based on word pattern analyses. The subjects were 25 psychiatric patients with the diagnoses neurotic personality organization (NPO), borderline personality organization (BPO) and psychotic personality organization (PPO) in accordance with Kernberg's theory. A set of 130 DMT variables and 40 linguistic variables were analyzed by means of partial least squares (PLS) discriminant analysis separately and then pooled together. The overall hypothesis was that it would be possible to define the personality organization of the patients in terms of an amalgam of perceptual defences and word patterns, and that these two kinds of data would confirm each other. The result of the combined PLS analysis revealed a very good separation between the diagnostic groups as measured by the pooled variable sets. Among other things, it was shown that NPO patients are principally characterized by linguistic variables, whereas BPO and PPO patients are better defined by perceptual defences as measured by the DMT method.     

Exploratory structural equation modeling,bifactor models,and standard confirmatory factor analysis models: Application to the BASC-2 Behavioral and Emotional Screening System Teacher Form

Several psychological assessment instruments are based on the assumption of a general construct that is composed of multiple interrelated domains. Standard confirmatory factor analysis is often not well suited for examining the factor structure of such scales. This study used data from 1885 elementary school students (mean age = 8.77 years, SD = 1.47 years) to examine the factor structure of the Behavioral Assessment System for Children, Second Edition (BASC-2) Behavioral and Emotional Screening System (BESS) Teacher Form that was designed to assess general risk for emotional/behavioral difficulty among children. The modeling sequence included the relatively new exploratory structural equation modeling (ESEM) approach and bifactor models in addition to more standard techniques. Findings revealed that the factor structure of the BASC-2 BESS Teacher Form is multidimensional. Both ESEM and bifactor models showed good fit to the data. Bifactor models were preferred on conceptual grounds. Findings illuminate the hypothesis-generating power of ESEM and suggest that it might not be optimal for instruments designed to assess a predominant general factor underlying the data.     

Humanizing autonomous vehicle driving: Understanding,modeling and impact assessment

The advent of autonomous vehicles brings major changes in the transportation systems influencing the infrastructure design, the network performance, as well as driving functions and habits. The penetration rate of this new technology highly depends on the acceptance of the automated driving services and functions, as well as on their impacts on various traffic, user oriented and environmental aspects. This research aims to present a methodological framework aiming to facilitate the modelling of the behaviour of new AV driving systems and their impacts on traffic, safety and environment. This framework introduces a stepwise approach, which will be leveraged by stakeholders in order to evaluate the new technology and its components at the design or implementation phase in order to increase acceptance and favor the adoption of the new technology. The proposed framework consists of four sequential steps: i. conceptual design, ii. data collection, processing and mining, iii. modelling and iv. autonomous vehicles impact assessment. The connection between these steps is illustrated and various Key Performance Indicators are specified for each impact area. The paper ends with highlighting some conceptual and modeling challenges that may critically affect the study of acceptance of autonomous vehicles in future mobility scenarios.     

Confirmatory Factor Analysis (CFA), Exploratory Structural Equation Modeling (ESEM), and Set-ESEM: Optimal Balance Between Goodness of Fit and Parsimony

Abstract

CFAs of multidimensional constructs often fail to meet standards of good measurement (e.g., goodness-of-fit, measurement invariance, and well-differentiated factors). Exploratory structural equation modeling (ESEM) represents a compromise between exploratory factor analysis’ (EFA) flexibility, and CFA/SEM’s rigor and parsimony, but lacks parsimony (particularly in large models) and might confound constructs that need to be kept separate. In Set-ESEM, two or more a priori sets of constructs are modeled within a single model such that cross-loadings are permissible within the same set of factors (as in Full-ESEM) but are constrained to be zero for factors in different sets (as in CFA). The different sets can reflect the same set of constructs on multiple occasions, and/or different constructs measured within the same wave. Hence, Set-ESEM that represents a middle-ground between the flexibility of traditional-ESEM (hereafter referred to as Full-ESEM) and the rigor and parsimony of CFA/SEM. Thus, the purposes of this article are to provide an overview tutorial on Set-ESEM, juxtapose it with Full-ESEM, and to illustrate its application with simulated data and diverse “real” data applications with accessible, heuristic explanations of best practice.