The Factor Structure and Measurement Invariance of the Daily Spiritual Experiences Scale

The current study has two main goals: (a) to identify a factor structure of the Daily Spiritual Experiences Scale (DSES) on a large archival data, collected from 1,325 adults in the United States (709 women, 616 men) by the U.S. General Social Survey in 2004 and (b) to examine the measurement invariance of the 16 DSES items between women and men in the same data to see whether any of the items are favoring or biased toward either women or men. The one-factor confirmatory factor analysis (CFA) model fit our data better than the two-factor CFA models because of high correlations between the two factors (r > .90). The fit of the one-factor CFA to our sample data was improved when we specified seven correlated residuals suggested by overlapping item content and large modification indices. The ensuing measurement invariance testing of the one-factor CFA model with seven correlated residuals supported full measurement invariance of factor loadings, thresholds, and residual variances, as well as factor variances between the women and the men. Yet the factor mean for the women was .841 units (Cohen’s d = .496) higher than it was for the men, indicating that higher levels of daily spiritual experiences for women reported in gender comparison studies in the United States are not likely to be an artifact of bias in the questionnaire.     

A survey of residual analysis and a new test of residual trend

A survey of residual analysis in behavior‐analytic research reveals that existing methods are problematic in one way or another. A new test for residual trends is proposed that avoids the problematic features of the existing methods. It entails fitting cubic polynomials to sets of residuals and comparing their effect sizes to those that would be expected if the sets of residuals were random. To this end, sampling distributions of effect sizes for fits of a cubic polynomial to random data were obtained by generating sets of random standardized residuals of various sizes, n. A cubic polynomial was then fitted to each set of residuals and its effect size was calculated. This yielded a sampling distribution of effect sizes for each n. To test for a residual trend in experimental data, the median effect size of cubic‐polynomial fits to sets of experimental residuals can be compared to the median of the corresponding sampling distribution of effect sizes for random residuals using a sign test. An example from the literature, which entailed comparing mathematical and computational models of continuous choice, is used to illustrate the utility of the test.     

When fit indices and residuals are incompatible

Standard chi-square-based fit indices for factor analysis and related models have a little known property: They are more sensitive to misfit when unique variances are small than when they are large. Consequently, very small correlation residuals indicating excellent fit can be accompanied by indications of bad fit by the fit indices when unique variances are small. An empirical example of this incompatibility between residuals and fit indices is provided. For illustrative purposes, an artificial example is provided that yields exactly the same correlation residuals as the empirical example but has larger unique variances. For this example, the fit indices indicate excellent fit. A theoretical explanation for this phenomenon is provided using relationships between unique variances and eigenvalues of the fitted correlation matrix.     

Psychological validation of the Rosenberg Self-Esteem Scale (RSES) in South Africa: Method effects and dimensionality in black African and white university students

The study examined the factor structure and cross-cultural validity of the Rosenberg Self-esteem Scale (RSES) in a sample of South African students (N = 862; black African = 67%, female = 71.5%). Alternative a priori CFA models (unidimensional, bi-dimensional and unidimensional models comprising either latent method factor or correlated residuals) were evaluated. Results indicated that the RSES in black and white South African university students is represented by a unidimensional model with correlated residuals of negatively and positively phrased items. Findings also suggested method effects on black African students to be significantly associated with negatively worded items compared to white students. Method bias effects appear to show for some RSES items and this may have important implications for the cross-cultural utility of the RSES in South Africa.     

Assessing Item Fit for Unidimensional Item Response Theory Models Using Residuals from Estimated Item Response Functions

Residual analysis (e.g. Hambleton & Swaminathan, Item response theory: principles and applications, Kluwer Academic, Boston, 1985; Hambleton, Swaminathan, & Rogers, Fundamentals of item response theory, Sage, Newbury Park, 1991) is a popular method to assess fit of item response theory (IRT) models. We suggest a form of residual analysis that may be applied to assess item fit for unidimensional IRT models. The residual analysis consists of a comparison of the maximum-likelihood estimate of the item characteristic curve with an alternative ratio estimate of the item characteristic curve. The large sample distribution of the residual is proved to be standardized normal when the IRT model fits the data. We compare the performance of our suggested residual to the standardized residual of Hambleton et al. (Fundamentals of item response theory, Sage, Newbury Park, 1991) in a detailed simulation study. We then calculate our suggested residuals using data from an operational test. The residuals appear to be useful in assessing the item fit for unidimensional IRT models.     

Bayesian latent variable models for the analysis of experimental psychology data

In this paper, we address the use of Bayesian factor analysis and structural equation models to draw inferences from experimental psychology data. While such application is non-standard, the models are generally useful for the unified analysis of multivariate data that stem from, e.g., subjects’ responses to multiple experimental stimuli. We first review the models and the parameter identification issues inherent in the models. We then provide details on model estimation via JAGS and on Bayes factor estimation. Finally, we use the models to re-analyze experimental data on risky choice, comparing the approach to simpler, alternative methods.     

Correspondence analysis used complementary to loglinear analysis

Loglinear analysis and correspondence analysis provide us with two different methods for the decomposition of contingency tables. In this paper we will show that there are cases in which these two techniques can be used complementary to each other. More specifically, we will show that often correspondence analysis can be viewed as providing a decomposition of the difference between two matrices, each following a specific loglinear model. Therefore, in these cases the correspondence analysis solution can be interpreted in terms of the difference between these loglinear models. A generalization of correspondence analysis, recently proposed by Escofier, will also be discussed. With this decomposition, which includes classical correspondence analysis as a special case, it is possible to use correspondence analysis complementary to loglinear analysis in more instances than those described for classical correspondence analysis. In this context correspondence analysis is used for the decomposition of the residuals of specific restricted loglinear models.     

A meta-analytic approach to growth curve analysis

A meta-analytic approach to growth curve analysis is described and illustrated by applying it to the evaluation of the Arizona Pilot Project, an experimental project for financing the treatment of the severely mentally ill. In this approach to longitudinal data analysis, each individual subject for which repeated measures are obtained is initially treated as a separate case study for analysis. This approach has at least two distinct advantages. First, it does not assume a balanced design (equal numbers of repeated observations) across all subjects; to accommodate a variable number of observations for each subject, individual growth curve parameters are differentially weighted by the number of repeated measures on which they are based. Second, it does not assume homogeneity of treatment effects (equal slopes) across all subjects. Individual differences in growth curve parameters representing potentially unequal developmental rates through time are explicitly modeled. A meta-analytic approach to growth curve analysis may be the optimal analytical strategy for longitudinal studies where either (1) a balanced design is not feasible or (2) an assumption of homogeneity of treatment effects across all individuals is theoretically indefensible. In our evaluation of the Arizona Pilot Project, individual growth curve parameters were obtained for each of the 13 rationally derived subscales of the New York Functional Assessment Survey, over time, by linear regression analysis. The slopes, intercepts, and residuals obtained for each individual were then subjected to meta-analytic causal modeling. Using factor analytic models and then general linear models for the latent constructs, the growth curve parameters of all individuals were systematically related to each other via common factors and predicted based on hypothesized exogenous causal factors. The same two highly correlated common factors were found for all three growth curve parameters analyzed, a general psychological factor and a general functional factor. The factor patterns were found to be nearly identical across the separate analyses of individual intercepts, slopes, and residuals. Direct effects on the unique factors of each subscale of the New York Functional Assessment Survey were tested for each growth curve parameter by including the common factors as hierarchically prior predictors in the structural model for each of the indicator variables, thus statistically controlling for any indirect effect produced on the indicator through the common factors. The exogenous predictors modeled were theoretically specified orthogonal contrasts for Method of Payment (comparing Arizona Pilot Project treatment or "capitation" to traditional or "fee-for-service" care as a control), Treatment Administration Site (comparing various locations within treatment or control groups), Pretreatment Assessment (comparing general functional level at intake as assigned by an Outside Assessment Team), and various interactions among these main effects. The intercepts, representing the initial status of individual subjects on both the two common factors and the 13 unique factors of the subscales of the New York Functional Assessment Survey, were found to vary significantly across many of the various different treatment conditions, treatment administration sites, and pretreatment functional levels. This indicated a severe threat to the validity of the originally intended design of the Arizona Pilot Project as a randomized experiment. When the systematic variations were statistically controlled by including intercepts as hierarchically prior predictors in the structural models for slopes, recasting the experiment as a nonequivalent groups design, the effects of the intercepts on the slopes were found to be both statistically significant and substantial in magnitude. (ABSTRACT TRUNCATED)     

Decomposing person and occasion-specific effects: an extension of latent state-trait (LSI) theory to hierarchical LST models

An extension of latent state-trait (LST) theory to hierarchical LST models is presented. In hierarchical LST models, the covariances between 2 or more latent traits are explained by a general 3rd-order factor, and the covariances between latent state residuals pertaining to different traits measured on the same measurement occasion are explained by 2nd-order latent occasion-specific factors. Analogous to recent developments in multitrait-multimethod methodology, all factors are interpreted in relation to factors taken as comparison standards. An empirical example from test anxiety research illustrates how estimates of additive variance components due to general trait, specific trait, occasion, state residual, method, and measurement error can be obtained using confirmatory factor analysis. Advantages and limitations of these models are discussed.     

Examining the Cross-National Measurement Invariance of the Extended Satisfaction with Life Scale in the United States and Hungary

The measurement invariance properties of four domains from the Extended Satisfaction with Life Scale (ESWLS) were examined in samples of young adults from the United States and Hungary. The four domains (scales) were general life satisfaction, social life satisfaction, family life satisfaction, and satisfaction with one’s self. For both countries, confirmatory factor analyses supported a correlated four-factor model, with each ESWLS domain constituting a single independent factor. Multigroup invariance testing provided support for both configural invariance and metric invariance, suggesting that across the U.S. and Hungarian samples the four ESWLS scales evidenced the same pattern of factor loadings as well as largely equivalent regression weights. These results suggest that respondents in both countries attributed the same meaning to the ESWLS constructs and that associations between the four ESWLS scales and other variables can be meaningfully compared across the two nations. Latent factor analyses indicated that with the exception of the correlation between general- and self-satisfaction, which was higher for the U.S., the magnitudes of the correlations between ESWLS domains were similar for the U.S. and Hungary. Possible explanations for the lack of measurement invariance across all of the nested models (i.e., item intercepts through residuals) are discussed.     

Modeling Common Traits and Method Effects in Multitrait-Multimethod Analysis

Method effects often occur when constructs are measured by different methods. In traditional multitrait-multimethod (MTMM) models method effects are regarded as residuals, which implies a mean method effect of zero and no correlation between trait and method effects. Furthermore, in some recent MTMM models, traits are modeled to be specific to a certain method. However, often we are not interested in a method-specific trait but in a trait that is common to all methods. Here we present the Method Effect model with common trait factors, which allows modeling “common” trait factors and method factors that represent method “effects” rather than residuals. The common trait factors are defined as the mean of the true-score variables of all variables measuring the same trait and the method factors are defined as differences between true-score variables and means of true-score variables. Because the model allows estimating mean method effects, correlations between method factors, and correlations between trait and method factors, new research questions may be investigated. The application of the model is demonstrated by 2 examples studying the effect of negative, as compared with positive, item wording for the measurement of mood states.     

Contextualized Personality Questionnaires: A Case for Copulas in Structural Equation Models for Categorical Data

For structural equation models (SEMs) with categorical data, correlated measurement residuals are not easily implemented. The problem lies mainly in the absence of a categorical analogue to the multivariate normal distribution and the absence of closed form formulas in SEMs for categorical data. We present a novel technique to handle measurement residuals that keeps the attractive SEM mainframe intact yet adds flexibility in dependence modeling without excessive computational burden. The technique is based upon the concept of copula functions and is introduced with a data set of ordinal responses originating from a contextualized personality study on aggression. Focus is on models arising in a multitrait-multimethod context, where the flexibility in dependence structures allows for method effects that can vary across the latent trait dimension. The empirical application illustrates that ignoring design-implied correlated measurement residuals can potentially influence study results and conclusions in both a quantitative as well as a qualitative way. Model parameter estimates can be biased, but more important, model inferences can be heavily distorted.     

Extending Dynamical Systems Theory to Model Embodied Cognition

We define a mathematical formalism based on the concept of an ‘‘open dynamical system” and show how it can be used to model embodied cognition. This formalism extends classical dynamical systems theory by distinguishing a ‘‘total system’’ (which models an agent in an environment) and an ‘‘agent system’’ (which models an agent by itself), and it includes tools for analyzing the collections of overlapping paths that occur in an embedded agent's state space. To illustrate the way this formalism can be applied, several neural network models are embedded in a simple model environment. Such phenomena as masking, perceptual ambiguity, and priming are then observed. We also use this formalism to reinterpret examples from the embodiment literature, arguing that it provides for a more thorough analysis of the relevant phenomena.     

Democracy in Education

The point of departure in this article is the Danish debate about democracyin schools. This article presents a first step in a study of how the relationshipbetween democracy and education can be understood. A juxtaposition of thetwo concepts requires, first of all, an analysis of how the concept of democracyis used in the educational debate. In this article three models of democracy areapplied as an analytical framework: a liberal model (Hobbes, Locke, Kant, Rawls,Dworkin), a communitarian model (MacIntyre, Sandel, Nussbaum) and a communicative/deliberativemodel (Walzer, Benhabib, Taylor, Habermas). Numerous contradictions and tensionsbetween concepts of democracy and education can be found in such a juxtaposition,depending on which conception of democracy one chooses to apply. In this articleI discuss which conception affords us the most meaningful concept of democraticteaching. As an introduction, a brief historical overview of the interplay betweendemocracy and education in Danish school is provided.     

Models as icons: modeling models in the semiotic framework of Peirce’s theory of signs

In this paper, we try to shed light on the ontological puzzle pertaining to models and to contribute to a better understanding of what models are. Our suggestion is that models should be regarded as a specific kind of signs according to the sign theory put forward by Charles S. Peirce, and, more precisely, as icons, i.e. as signs which are characterized by a similarity relation between sign (model) and object (original). We argue for this (1) by analyzing from a semiotic point of view the representational relation which is characteristic of models. We then corroborate our hypothesis (2) by discussing the conceptual differences between icons, i.e. models, and indexical and symbolic signs and (3) by putting forward a general classification of all icons into three functional subclasses (images, diagrams, and metaphors). Subsequently, we (4) integratively refine our results by resorting to two influential and, as can be shown, complementary philosophy of science approaches to models. This yields the following result: models are determined by a semiotic structure in which a subject intentionally uses an object, i.e. the model, as a sign for another object, i.e. the original, in the context of a chosen theory or language in order to attain a specific end by instituting a representational relation in which the syntactic structure of the model, i.e. its attributes and relations, represents by way of a mapping the properties of the original, which hence are regarded as similar in a relevant manner.     

The Rhetoric of Deliberation: Some Problems in Kantian Theories of Deliberative Democracy

Deliberative or discursive models of democracy have recently enjoyed a revival in both political theory and policy practice. Against the picture of democracy as a procedure for aggregating and effectively meeting the given preference of individuals, deliberative theory offers a model of democracy as a forum through which judgements and preferences are formed and altered through reasoned dialogue between free and equal citizens. Much in the recent revival of deliberative democracy, especially that which comes through Habermas and Rawls, has Kantian roots. Deliberative institutions are embodiments of the free public use of reason that Kant takes to define the enlightenment project. Within the Kantian model the public use of reason is incompatible with the use of rhetoric. While this paper rejects strong rhetorical criticisms of deliberative democracy which render all communication strategic, it argues that rhetorical studies of deliberation have highlighted features of deliberation which point to significant weaknesses in Kantian approaches to it. Two features are of particular importance: the role of testimony and judgements of credibility in deliberation; and the role of appeal to emotions in public discourse. Both from the Kantian perspective are potential sources of heteronomy. However, the appeal to testimony and emotion are features of public deliberation that cannot and should not be eliminated. For those committed to the enlightenment values that underlie the deliberative model of democracy the question is whether these rhetorical features of deliberation are incompatible with those values. The paper argues that they are compatible. It does so by defending an Aristotelian account of rhetoric in public deliberation which denies the Platonic contrast between reasoned discourse and rhetoric which the Kantian model inherits. This revised version was published online in August 2006 with corrections to the Cover Date.     

Nonlinear Regime-Switching State-Space (RSSS) Models

Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases—namely, latent “regimes” or classes—during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsumes regime-switching nonlinear dynamic factor analysis models as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman filter and the Kim filter is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well-known discrete change models in the literature are discussed briefly.     

A New “Essential Tension” for Rationality and Culture. What Happens if Politics Tries to Encounter Science Again

My intention is not to get into specific, detailed historical observation about the ways that led the term ‘democracy’ to take on its current meaning, in science as much as in politics, but rather to establish a comparison between the models that political science proposes and interprets as important for the existence of democracy and those that science illustrates as indicators of scientific knowledge constructed in a democratic form. The debate about the contemporary meaning of democracy has generated an extraordinary diversification of models of democracy: from technocratic conceptions of government to conceptions of social life that include widespread political participation. And it is exactly for this reason that the assumption of a specific point of view on the question we are dealing with inevitably brings with it the choice of a model suitable to describe democratic form as a form of politics without further explanation, that is, as a political system with which science measures itself as a cultural category. In this sense, we can consider the passage from the concept of democracy to that of politics and generally of science to be a peaceful one, since politics has been appointed with that set of behaviours and democratic practices (including science) that political culture demands for the social benefit. This demand can be met only on condition that structural obstacles are removed and new cultural and epistemological mediators are introduced.     

Direct Schmid–Leiman Transformations and Rank-Deficient Loadings Matrices

The Schmid–Leiman (S–L; Psychometrika 22: 53–61, 1957) transformation is a popular method for conducting exploratory bifactor analysis that has been used in hundreds of studies of individual differences variables. To perform a two-level S–L transformation, it is generally believed that two separate factor analyses are required: a first-level analysis in which k obliquely rotated factors are extracted from an observed-variable correlation matrix, and a second-level analysis in which a general factor is extracted from the correlations of the first-level factors. In this article, I demonstrate that the S–L loadings matrix is necessarily rank deficient. I then show how this feature of the S–L transformation can be used to obtain a direct S–L solution from an unrotated first-level factor structure. Next, I reanalyze two examples from Mansolf and Reise (Multivar Behav Res 51: 698–717, 2016) to illustrate the utility of ‘best-fitting’ S–L rotations when gauging the ability of hierarchical factor models to recover known bifactor structures. Finally, I show how to compute direct bifactor solutions for non-hierarchical bifactor structures. An online supplement includes R code to reproduce all of the analyses that are reported in the article.     

On the relations among regular, equal unique variances, and image factor analysis models

We investigate under what conditions the matrix of factor loadings from the factor analysis model with equal unique variances will give a good approximation to the matrix of factor loadings from the regular factor analysis model. We show that the two models will give similar matrices of factor loadings if Schneeweiss' condition, that the difference between the largest and the smallest value of unique variances is small relative to the sizes of the column sums of squared factor loadings, holds. Furthermore, we generalize our results and discus the conditions under which the matrix of factor loadings from the regular factor analysis model will be well approximated by the matrix of factor loadings from Jöreskog's image factor analysis model. Especially, we discuss Guttman's condition (i.e., the number of variables increases without limit) for the two models to agree, in relation with the condition we have shown, and conclude that Schneeweiss' condition is a generalization of Guttman's condition. Some implications for practice are discussed.Kentaro Hayashi is a visiting Assistant Professor, Department of Mathematics, Bucknell University, Lewisburg PA 17837, and Peter M. Bentler is Professor, Departments of Psychology and Statistics, University of California, Los Angeles CA 90095-1563. (Emails: Khayashi@bucknell.edu, bentler@ucla.edu) Parts of this paper were discussed in a session on Factor Analysis (J. ten Berge, Chair) at the IFCS-98 International Conference, Rome, July, 1998. This work was supported by National Institute on Drug Abuse grant DA 01070. The authors thank Professors Hans Schneeweiss and Ke-Hai Yuan, and four anonymous referees, for their invaluable comments which led to an improved version of this paper.