The statistical tests used in the analysis of structural equation models with unobservable variables and measurement error are examined. A drawback of the commonly applied chi square test, in addit...

Evaluating Structural Equation Models with Unobservable Variables and Measurement Error

In this article, we provide guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development. We present a comprehensive, two-step modeling approach that employs a series of nested models and sequential chi-square difference tests. We discuss the comparative advantages of this approach over a one-step approach. Considerations in specification, assessment of fit, and respecification of measurement models using confirmatory factor analysis are reviewed. As background to the two-step approach, the distinction between exploratory and confirmatory analysis, the distinction between complementary approaches for theory testing versus predictive application, and some developments in estimation methods also are discussed.

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Structural equation modeling in practice: a review and recommended two-step approach

Factor analysis, path analysis, structural equation modeling, and related multivariate statistical methods are based on maximum likelihood or generalized least squares estimation developed for covariance structure models. Large-sample theory provides a chi-square goodness-of-fit test for comparing a model against a general alternative model based on correlated variables. This model comparison is insufficient for model evaluation: In large samples virtually any model tends to be rejected as inadequate, and in small samples various competing models, if evaluated, might be equally acceptable. A general null model based on modified independence among variables is proposed to provide an additional reference point for the statistical and scientific evaluation of covariance structure models. Use of the null model in the context of a procedure that sequentially evaluates the statistical necessity of various sets of parameters places statistical methods in covariance structure analysis into a more complete framework. The concepts of ideal models and pseudo chi-square tests are introduced, and their roles in hypothesis testing are developed. The importance of supplementing statistical evaluation with incremental fit indices associated with the comparison of hierarchical models is also emphasized. Normed and nonnormed fit indices are developed and illustrated.

Significance tests and goodness of fit in the analysis of covariance structures

In this chapter a theory of motivation and emotion developed from an attributional perspective is presented Before undertaking this central task, it might be beneficial to review the progression of the book In Chapter 1 it was suggested that causal attributions have been prevalent throughout history and in disparate cultures Studies reviewed in Chapter 2 revealed a large number of causal ascriptions within motivational domains, and different ascriptions in disparate domains Yet some attributions, particularly ability and effort in the achievement area, dominate causal thinking To compare and contrast causes such as ability and effort, their common denominators or shared properties were identified Three causal dimensions, examined in Chapter 3, are locus, stability, and controllability, with intentionality and globality as other possible causal properties As documented in Chapter 4, the perceived stability of a cause influences the subjective probability of success following a previous success or failure; causes perceived as enduring increase the certainty that the prior outcome will be repeated in the future And all the causal dimensions, as well as the outcome of an activity and specific causes, influence the emotions experienced after attainment or nonattainment of a goal The affects linked to causal dimensions include pride (with locus), hopelessness and resignation (with stability), and anger, gratitude, guilt, pity, and shame (with controllability)

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An attributional theory of achievement motivation and emotion.

A review of the literature suggests that few studies use formative indicator measurement models, even though they should. Therefore, the purpose of this research is to (a) discuss the distinction between formative and reflective measurement models, (b) develop a set of conceptual criteria that can be used to determine whether a construct should be modeled as having formative or reflective indicators, (c) review the marketing literature to obtain an estimate of the extent of measurement model misspecification in the field, (d) estimate the extent to which measurement model misspecification biases estimates of the relationships between constructs using a Monte Carlo simulation, and (e) provide recommendations for modeling formative indicator constructs.

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A Critical Review of Construct Indicators and Measurement Model Misspecification in Marketing and Consumer Research

An interdependent multivariate linear relations model based on manifest, measured variables as well as unmeasured and unmeasurable latent variables is developed. The latent variables include primary or residual common factors of any order as well as unique factors. The model has a simpler parametric structure than previous models, but it is designed to accommodate a wider range of applications via its structural equations, mean structure, covariance structure, and constraints on parameters. The parameters of the model may be estimated by gradient and quasi-Newton methods, or a Gauss-Newton algorithm that obtains least-squares, generalized least-squares, or maximum likelihood estimates. Large sample standard errors and goodness of fit tests are provided. The approach is illustrated by a test theory model and a longitudinal study of intelligence.

Linear structural equations with latent variables

Research on loneliness has been hampered by its strong association with depression. The two states frequently co-occur, and measures of the two states are substantially correlated. Inability to manipulate experimentally loneliness or depression makes it difficult to untangle the causal influence of one on the other. The combination of longitudinal design and structural equation methodology is proposed as a solution to this general problem. Measures of loneliness and depression were administered to undergraduates at two points 5 weeks apart. Data from 333 subjects were correlated and analyzed under a succession of structural equation models. Results indicated that loneliness and depression were correlated but clearly different constructs; neither was a direct cause of the other, though both probably share some common origins; both were highly stable over to 5-week-period.

Relation between loneliness and depression: a structural equation analysis.

Washington University School of Medicine This study examined the applicability of Weiner's model of causal attributions to lay explanations for the causes of loneliness. Weiner posits three dimensions (Internality, Stability, and Controllability) along which causes vary and links each dimension to distinct consequences for the actor. To test the salience of these dimensions in lay perceptions of causality, 180 college students made judgments about the causes of loneliness. As predicted, both exploratory and confirmatory multidimensional scaling analyses found that dimensions of Internality and Stability were perceived by respondents. Contrary to recent theorizing, Controllability was not independent of the other two dimensions; instead, controllable causes were both internal and unstable. Confirmation of Internality and Stability as dimensions underlying attributions for loneliness supported the extension of Weiner's model to the domain of affiliative behavior. Attribution theorists have emphasized that the perceived causes of events are central features in social perception (Kelley & Michela, 1980). Researchers have sought to identify the general properties or dimensions underlying specific causal attributions and the psychological consequences o f causal attributions. The model of causal attributions developed b y Weiner and his colleagues (Weiner, 1974, 1979; Weiner et al., 1972) identifies basic causal dimensions of Internality, Stability and, more tentatively, Controllability. In research primarily on achievement behavior, these dimensions have been linked to particular consequences involving expectancies, affect, evaluation, and behavior. Recently, Weiner (1979) suggested that this model applies beyond the achievement context and -that i t constitutes a general model of motivation. We gratefully acknowledge the contributions of Mar

Perceived dimensions of attributions for loneliness.

ureI encodes an inner membrane protein of Helicobacter pylori The role of the bacterial inner membrane and UreI in acid protection and regulation of cytoplasmic urease activity in the gastric microorganism was studied The irreversible inhibition of urease when the organism was exposed to a protonophore (3,3',4', 5-tetrachlorsalicylanide; TCS) at acidic pH showed that the inner membrane protected urease from acid Isogenic ureI knockout mutants of several H pylori strains were constructed by replacing the ureI gene of the urease gene cluster with a promoterless kanamycin resistance marker gene (kanR) Mutants carrying the modified ureAB-kanR-EFGH operon all showed wild-type levels of urease activity at neutral pH in vitro The mutants resisted media of pH > 40 but not of pH < 40 Whereas wild-type bacteria showed high levels of urease activity below pH 40, this ability was not retained in the ureI mutants, resulting in inhibition of metabolism and cell death Gene complementation experiments with plasmid-derived H pylori ureI restored wild-type properties The activation of urease activity found in structurally intact but permeabilized bacteria treated with 001% detergent (polyoxy-ethylene-8-laurylether; C12E8), suggested a membrane-limited access of urea to internal urease at neutral pH Measurement of 14C-urea uptake into Xenopus oocytes injected with ureI cRNA showed acid activation of uptake only in injected oocytes Acceleration of urea uptake by UreI therefore mediates the increase of intracellular urease activity seen under acidic conditions This increase of urea permeability is essential for H pylori survival in environments below pH 40 ureI-independent urease activity may be sufficient for maintenance of bacterial viability above pH 40

https://www.onlinelibrary.wiley.com/doi/pdf/10.1046/j.1365-2958.2000.01835.x

David G. Weeks

Papers

Linear structural equations with latent variables

Relation between loneliness and depression: a structural equation analysis.

Perceived dimensions of attributions for loneliness.

Acid resistance of Helicobacter pylori depends on the UreI membrane protein and an inner membrane proton barrier

Restricted multidimensional scaling models