Measurement invariance is usually tested using Multigroup Confirmatory Factor Analysis, which examines the change in the goodness-of-fit index (GFI) when cross-group constraints are imposed on a measurement model. Although many studies have examined the properties of GFI as indicators of overall model fit for single-group data, there have been none to date that examine how GFIs change when between-group constraints are added to a measurement model. The lack of a consensus about what constitutes significant GFI differences places limits on measurement invariance testing. We examine 20 GFIs based on the minimum fit function. A simulation under the two-group situation was used to examine changes in the GFIs (ΔGFIs) when invariance constraints were added. Based on the results, we recommend using Δcomparative fit index, ΔGamma hat, and ΔMcDonald's Noncentrality Index to evaluate measurement invariance. These three ΔGFIs are independent of both model complexity and sample size, and are not correlated with the overall fit measures. We propose critical values of these ΔGFIs that indicate measurement invariance.

The fit between a structural equation model and a data set is operationalized as the value of goodness-of-fit indices. The discrepancy between the estimated value and the value indicating perfect fit has three sources: misspecification, error arising from theoretical parsimony in the description of the model (parsimony error), and sampling error. Misspecification, which represents a disparity between “realworld” relationships and relationships in the model, is the most important source of error for researchers. It cannot be accurately assessed, however, unless parsimony error and sampling error are taken into account. Parsimony error occurs in measurement models when secondary relationships are excluded. Secondary relationships are defined here as secondary factor loadings and error term correlations that have small values, no theoretical bases, and no substantive meaning. A simulation was conducted to examine the effects of parsimony error on perfect measurement models and to establish appropriate criteria for model fit when parsimony error is present.

Extreme response styles (ERS) and acquiescence response styles (ARS) may constitute important sources of cross-cultural differences on survey-type instruments. Differences in ERS and ARS, if undetected, may give rise to spurious results that do not reflect genuine differences in attitudes or perceptions. Multiple-group confirmatory factor analysis is recommended as the most effective method of testing for ERS and ARS and determining whether cultural groups can be meaningfully compared on the basis of factor (latent) means. A detailed numerical example is provided.

Many cross-cultural researchers are concerned with factorial invariance; that is, with whether or not members of different cultures associate survey items, or similar measures, with similar constructs. Researchers usually test items for factorial invariance using confirmatory factor analysis (CFA). CFA, however, poses certain problems that must be dealt with. Primary among them is standardization, the process that assigns units of measurement to the constructs (latent variables). Two standardization procedures and several minor variants have been reported in the literature, but using these procedures when testing for factorial invariance can lead to inaccurate results. In this paper we review basic theory, and propose an extension of Byrne, Shavelson, and Muthgn’s (1989) procedure for identifying non-invariant items. The extended procedure solves the standardization problem by performing a systematic comparison of all pairs of factor loadings across groups. A numerical example based upon a large published data set is presented to illustrate the utility of the new procedure, particularly with regard to partial factorial invariance.

Relatively little attention has been given to detecting influential cases (ICs) when estimating structural equation models (SEMs). Most techniques examine individual cases using covariance-based techniques such as the Mahalanobis distance, which examine the distributional characteristics of the cases but ignore the model. Cases identified using such model-free techniques are usually referred to as out-liers. In SEM, however, the model is of central importance. The characteristics of the model (number of latent variables, etc.) have an effect on which cases are influential. The authors propose applying the well-known jackknife procedure to detect model-based ICs, which may be influential with respect to overall fit, particular model parameters, or both. The procedure is illustrated by two studies-one using simulated data, the other empirical data.

This study examined computer ethical perceptions and computer use attitudes (operationalized as computer aversion) among subjects from the United States, Singapore and Hong Kong. The purpose of the...

Comparing different groups (e.g., cultures, age cohorts) using survey-type instruments raises the question of factorial invariance, that is, whether or not members of different groups ascribe the same meanings to survey items. This article attempts to advance multi-group research by (a) providing a concise summary of the factorial invariance problem, (b) proposing a simplified notation intended to facilitate discussion of the problem, and (c) suggesting a structured approach for testing large models. This procedure is illustrated using an extended example. Two computer programs designed to make the recommended procedures less laborious are offered.

This article describes the development of three domain-specific measures of individual differences in feedback propensities. In a series of studies, the authors identify the primary dimensions, psychometric characteristics, and construct validation evidence for internal ability, internal propensity, and external propensity for feedback. Confirmatory factor analysis supports the three dimensional representation. Correlations between the new scales and existing measures of personality are consistent with theoretical predictions. Theoretical and practical extensions of the current work are discussed.