Configural Equivalence

This study is focused on the construction of a cross-national comparable measurement instrument for attitude variables in comparative surveys. Multi-group measurement models for latent variables (LISREL), taking method effects into account, are applied. The measurements of the 'outgroup' dimension of ethnocentrism (variables q42, q44, q45, q47-q52) in the 1995 ISSP dataset are used. Nearly all the items in the quasi balanced set are written in a Likert format in which respondents are asked how strongly they agree or disagree with each attitude statement. There is considerable evidence that such a response format can be susceptible to an agreeingresponse bias called acquiescence (Billiet and McClendon, 2000). It is shown that in all countries, models with a method or style factor (acquiescence) always fit the data better than models without a style factor. It is investigated to what extent the measurement instrument with a content and a method factor is equivalent over the cultural groups. In a first step the factor loadings of the groups are explored by cluster analysis. After the detection of two subsets of groups that are likely to share equivalent measurement instruments, a stepwise procedure was performed starting with the measurement model for one group, and then looking for equivalent groups (countries) only accepting minor changes in the measurement model. The introduction of a style factor allows us to control for a possible source of measurement non-equivalence, namely method bias. Moreover, the inclusion of a method factor gives the opportunity to investigate the differences in method effects between the groups (countries). However, it is found that both, the variance of the style factor and its factor loadings do not differ between the groups in the first subset of countries, but there are

This article reports new methodology for cross-cultural exploration of psychometric properties of a four-dimensional hierarchical love scale. We collected data from 2831 participants from nine regional locations from six countries and assessed their responses to the love scale as well as several other love feelings. We applied a new methodological approach using recently advanced statistical methods to the comparison of forty love attitudes underscoring four distinct latent attitudes associated with love to another person in romantic relationships across these samples. The results demonstrate the importance of measurement invariance tests for cross-cultural comparison of scores on love scales. To properly assess measurement invariance, we suggest five statistical procedures, which we investigated in this study: (1) making corrections for acquiescence and extreme response biases; (2) taking into consideration cultural uniqueness in how participants respond to the measures, which may ...

Empirical models of spatial voting allow legislators' locations in a policy or ideological space to be inferred from their roll call votes. These are typically random utility models where the features of the utility functions other than the ideal points are assumed rather than estimated. In this paper, we first consider a model in which legislators' utility functions are allowed to be a mixture of the two most commonly assumed utility functions: the quadratic function and the Gaussian function assumed by NOMINATE. Across many roll call data sets, we find that legislators' utility functions are estimated to be very nearly Gaussian. We then relax the usual assumption that each legislator is equally sensitive to policy change and find that extreme legislators are generally more sensitive to policy change than their more centrally located counterparts. This result suggests that extremists are more often ideologically rigid while moderates are more likely to consider influences that arise outside liberal-conservative conflict.

This article reports new methodology for cross-cultural exploration of psychometric properties of a four-dimensional hierarchical love scale. We collected data from 2831 participants from nine regional locations from six countries and assessed their responses to the love scale as well as several other love feelings. We applied a new methodological approach using recently advanced statistical methods to the comparison of forty love attitudes underscoring four distinct latent attitudes associated with love to another person in romantic relationships across these samples. The results demonstrate the importance of measurement invariance tests for cross-cultural comparison of scores on love scales. To properly assess measurement invariance, we suggest five statistical procedures, which we investigated in this study: (1) making corrections for acquiescence and extreme response biases; (2) taking into consideration cultural uniqueness in how participants respond to the measures, which may ...

Assessing measurement equivalence in the framework of the common factor linear models (CFL) is known as factorial invariance. This methodology is used to evaluate the equivalence among the parameters of a measurement model among different groups. However, when dichotomous, Likert, or ordered responses are used, one of the assumptions of the CFL is violated: the continuous nature of the observed variables. The common factor analysis of ordered-categorical data (CFO) has been described in several works, but none evaluate its power and Type I error rate in the evaluation of measurement equivalence (ME). In this simulation study, we evaluated ME under four different conditions: size of group (300, 500 and 1000), type of DIF (thresholds, loadings), amount of DIF (0.25, 0.40), and equality/impact of the distributions. The parameters used for the data generation came from one scale with nine items with three ordered categories. The results were evaluated according to three decision rules: a) the significance of the difference in chi-square values obtained in two nested models, b) the significance of the difference in chi-square values between two nested models with Bonferroni corrections, and c) the difference between the values of the Comparative Fix Index (CFI) obtained in two nested models. The results showed good power as well as good control of the false positives for both the chi-square Bonferroni correction and CFI difference index.

This article reports new methodology for cross-cultural exploration of psychometric properties of a four-dimensional hierarchical love scale. We collected data from 2831 participants from nine regional locations from six countries and assessed their responses to the love scale as well as several other love feelings. We applied a new methodological approach using recently advanced statistical methods to the comparison of forty love attitudes underscoring four distinct latent attitudes associated with love to another person in romantic relationships across these samples. The results demonstrate the importance of measurement invariance tests for cross-cultural comparison of scores on love scales. To properly assess measurement invariance, we suggest five statistical procedures, which we investigated in this study: (1) making corrections for acquiescence and extreme response biases; (2) taking into consideration cultural uniqueness in how participants respond to the measures, which may ...

Given the increasing importance of international business, cross-cultural research becomes more and more relevant to marketing academics and practitioners. This paper illustrates the difficulties in achieving equivalence when conducting marketing research across borders. It opens with a general typology of equivalence issues in cross-cultural research and, subsequently, focuses specifically on data equivalence. Recent studies either disregard data equivalence at all or they predominantly suggest the use of simultaneous confirmatory factor analysis (CFA) for establishing data equivalence. The Latent Trait Theory (LTT), based on a different measurement paradigm, offers an alternative which promises to overcome many of the problems inherent in CFA. This paper contrasts the advantages and disadvantages of both approaches and illustrates their application by means of a simulated data set. In conclusion, a call is made for the incorporation of equivalence issues in scale development by qu...

With the growing interest of consumer researchers to test measures and theories in an international context, the cross-national invariance of measurement instruments has become an important issue. At least two issues still need to be addressed. First, the ordinal nature of the rating scale is ignored. Second, when few or no items in the confirmatory factor analysis (CFA) exhibit metric and scalar invariance across all countries, comparison of results across countries is difficult. We solve these problems using a hierarchical IRT model. An empirical application is provided for susceptibility to normative influence, using a sample of 5,484 respondents from 11 countries on four continents. C onsumer researchers are becoming increasingly interested in testing their measures and theories in an international context (Bagozzi 1994; Durvasula et al. 1993; Wong, Rindfleisch, and Burroughs 2003). It is in this vein that Monroe (1993, v) urges consumer behavior researchers "to move beyond the relative security of our own backyards and investigate issues relative to consumption on an international basis." Consider the following substantive questions that consumer researchers may want to address: • A consumer researcher is interested in testing whether materialism is largely a U.S. construct ("emic") or a pancultural construct ("etic"). To address this question, s/he wants to test the nomological relations between this construct and antecedents, consequences, and con

This article reports new methodology for cross-cultural exploration of psychometric properties of a four-dimensional hierarchical love scale. We collected data from 2831 participants from nine regional locations from six countries and assessed their responses to the love scale as well as several other love feelings. We applied a new methodological approach using recently advanced statistical methods to the comparison of forty love attitudes underscoring four distinct latent attitudes associated with love to another person in romantic relationships across these samples. The results demonstrate the importance of measurement invariance tests for cross-cultural comparison of scores on love scales. To properly assess measurement invariance, we suggest five statistical procedures, which we investigated in this study: (1) making corrections for acquiescence and extreme response biases; (2) taking into consideration cultural uniqueness in how participants respond to the measures, which may ...

This article reports new methodology for cross-cultural exploration of psychometric properties of a four-dimensional hierarchical love scale. We collected data from 2831 participants from nine regional locations from six countries and assessed their responses to the love scale as well as several other love feelings. We applied a new methodological approach using recently advanced statistical methods to the comparison of forty love attitudes underscoring four distinct latent attitudes associated with love to another person in romantic relationships across these samples. The results demonstrate the importance of measurement invariance tests for cross-cultural comparison of scores on love scales. To properly assess measurement invariance, we suggest five statistical procedures, which we investigated in this study: (1) making corrections for acquiescence and extreme response biases; (2) taking into consideration cultural uniqueness in how participants respond to the measures, which may ...

This article reports new methodology for cross-cultural exploration of psychometric properties of a four-dimensional hierarchical love scale. We collected data from 2831 participants from nine regional locations from six countries and assessed their responses to the love scale as well as several other love feelings. We applied a new methodological approach using recently advanced statistical methods to the comparison of forty love attitudes underscoring four distinct latent attitudes associated with love to another person in romantic relationships across these samples. The results demonstrate the importance of measurement invariance tests for cross-cultural comparison of scores on love scales. To properly assess measurement invariance, we suggest five statistical procedures, which we investigated in this study: (1) making corrections for acquiescence and extreme response biases; (2) taking into consideration cultural uniqueness in how participants respond to the measures, which may ...

Empirical models of spatial voting allow legislators' locations in a policy or ideological space to be inferred from their roll call votes. These are typically random utility models where the features of the utility functions other than the ideal points are assumed rather than estimated. In this paper, we first consider a model in which legislators' utility functions are allowed to be a mixture of the two most commonly assumed utility functions: the quadratic function and the Gaussian function assumed by NOMINATE. Across many roll call data sets, we find that legislators' utility functions are estimated to be very nearly Gaussian. We then relax the usual assumption that each legislator is equally sensitive to policy change and find that extreme legislators are generally more sensitive to policy change than their more centrally located counterparts. This result suggests that extremists are more often ideologically rigid while moderates are more likely to consider influences that arise outside liberal-conservative conflict.

Comparing solidarity attitudes of European citizen is highly relevant in the context of European integration and unification. Such comparisons, however, are only valid if responses to attitude questions reflect true differences in solidarity and, hence, the measurement of latent solidarity attitudes is comparable. Often comparability is assumed, rarely is it tested. We argue that establishing equivalence in measurement across cultures is as important as testing the reliability and validity of the measurement since lack of comparability may result in biased or misleading conclusions. This research presents a multiple-group latent-class factor analysis of a set of questions concerning solidarity towards different social groups, taken from the 1999/2000 wave of European Value Study. This multiple-group comparison revealed that homogeneity in attitude measurement is not established. Countries can only be compared if particular direct effects of country on items are estimated. Country ranking on solidarity factors substantially changed when this source of construct inequivalence was taken into account.

This article introduces a multilevel growth mixture model (MGMM) for classifying both the individuals and the groups they are nested in. Nine variations of the general model are described that differ in terms of categorical and continuous latent variable specification within and between groups. An application in the context of school effectiveness research is presented. Schools are classified into three Type B effectiveness categories based on their mean student mathematics achievement growth trajectories, controlling for differences in students' backgrounds across schools. The classification outcome is regressed on a set of school practice variables to investigate the association between practices and cognitive development. Various issues related to model specification are discussed, including the use of covariates to identify substantively meaningful classes.

IntroductIon and Background "Globalization of business highlights the need to understand the management of organizations that span different nations and cultures" (Srite et al., 2003, p. 31). In these multinational and transcultural organizations, there is a growing call for utilizing information technology (IT) to achieve efficiencies, coordination, and communication. However, cultural differences between countries may have an impact on the effectiveness and efficiency of IT deployment. Despite its importance, the effect of cultural factors has received limited attention from information systems' (IS) researchers. In a review of cross-cultural research specifically focused on the MIS area (Evaristo, Karahanna, & Srite, 2000), a very limited number of studies were found that could be classified as cross-cultural. Additionally, even though many of the studies found provided useful insights, raised interesting questions, and generally contributed toward the advancement of the state of the art in its field, with few exceptions, no study specifically addressed equivalency issues central to measurement in cross-cultural research. It is this methodological issue of equivalency that is the focus of this article. Transcultural Organization: A firm that operates across multiple cultures.

This paper presents a discussion of methodological issues that are relevant and idiosyncratic to cross-cultural research. One characteristic that typifies cross-cultural studies is their comparative nature, i.e., they involve a comparison across two separate cultures on a focal phenomenon. When differences across cultures are observed, the question arises as to whether the results are true cultural differences or merely measurement artifacts. Methodological considerations in cross-cultural research focus on ruling out alternative explanations for these differences and thus enhancing the interpretability of the results. The paper presents an overview of key methodological issues in cross-cultural research and reviews methods of preventing or detecting methodological problems. METHODOLOGICAL ISSUES Cross-cultural research has some unique methodological idiosyncrasies that are not pertinent to intracultural research. One characteristic that typifies cross-cultural studies is their comparative nature, i.e., they involve a comparison across two or more separate cultures on a focal phenomenon. Any observed differences across cultures give rise to many alternative explanations. Particularly when results are different than expected (e.g., no statistical significance, factor analysis items do not load as expected, or reliability assessment is low), researchers may question whether results are true differences due to culture or merely measurement artifacts (Mullen, 1995). Methodological considerations in carrying out crosscultural research attempt to rule out alternative explanations for these differences and enhance the interpretability of results (van de Vijver and Leung, 1997). Clearly, the choice

Empirical models of spatial voting allow legislators' locations in a policy or ideological space to be inferred from their roll call votes. These are typically random utility models where the features of the utility functions other than the ideal points are assumed rather than estimated. In this paper, we first consider a model in which legislators' utility functions are allowed to be a mixture of the two most commonly assumed utility functions: the quadratic function and the Gaussian function assumed by NOMINATE. Across many roll call data sets, we find that legislators' utility functions are estimated to be very nearly Gaussian. We then relax the usual assumption that each legislator is equally sensitive to policy change and find that extreme legislators are generally more sensitive to policy change than their more centrally located counterparts. This result suggests that extremists are more often ideologically rigid while moderates are more likely to consider influences that arise outside liberal-conservative conflict.

Purpose -The paper presents a framework for establishing equivalence of international marketing data. The framework is meant to reduce confusion about equivalence issues, and guide the design of international studies and data analysis. Design/methodology/approach -A short overview is given of the two main approaches to equivalence in the literature. These are integrated and used to distinguish sources of cultural bias in the various stages of the research process. Findings -The highest levels of equivalence most often established are construct equivalence and partial measurement equivalence, implying that distributions of scores obtained in various countries cannot be interpreted at face value. To understand cross-cultural differences better, researchers should investigate why higher levels of equivalence could not be established; this can be done best by including elements from both the conceptual and the measurement approach to equivalence. Practical implications -This study can help marketing managers to establish the extent to which consumer perceptions can be considered equal across countries. Moreover, it helps researchers to determine causes of unequivalence and relate these to concrete stages in the research process. Originality/value -Integration of the two main approaches to equivalence will lead to a better understanding of the validity of cross-cultural differences and similarities. This should lead to improved decision making in international marketing.

Multiple group confirmatory factor analysis has become the most common technique for assessing measurement invariance. However, higher-order factor modeling is less frequently discussed in this context. In particular, the literature provides only very general guidelines for testing measurement invariance of second-order factor models, which is a prerequisite for conducting meaningful comparative research using higher-order factors. The current paper attempts to fill this gap. First, we explicate the constraints required for identification of the invariance levels in a multiple group second-order factor model. Second , in addition to the conventional interpretation of the results of this assessment, we suggest an alternative view on the invariance properties of a second-order factor as evidence of structural rather than measurement invariance. Third, we present an empirical application of the test which builds on Seeman's alienation scale and utilizes data from eight countries collected in 2008-2009. We found empirical support for metric invariance of both the first-and second-order factors, but no support for scalar invariance of the first-and second-order factors. However, we find pairs of countries where scalar invariance for both the first-and second-order factors is supported by the data. We finalize with a discussion of the results and their interpretation.

Response bias continues to be a perennial challenges for social scientist, including educators, who depend considerably on non-cognitive instrument to generate data in their attempt to provide solution to educational challenges and knowledge advancement. Response bias, a generic term for the tendency to respond to questionnaire items on some basis other than the specific items in the questionnaire has generate concerns, yet few attempt has been made to measure and control it. In this paper, attempt was made in discussing two common response bias namely social desirability bias and extreme response biases. Also presented were some procedural steps to ameliorate its impact during the process of instrument development and some statistical techniques that have been developed to measure and control them in data analysis and interpretation. This work concludes by recommending the best possible approach for controlling response style within the context of a developing country like Nigeria.

The purpose of the present study was to compare the Type I error rate and power of two model-based procedures, the mean and covariance structure model (MACS) and the item response theory (IRT), and an observed-score based procedure, ordinal logistic regression, for detecting differential item functioning (DIF) in polytomous items. A simulation study was employed in which polytomous data with five ordered categories were generated using Samejima's graded response model under three crossed factors: sample size per group (300-, 500-, and 1,000-examinees), type of DIF (b-parameter, aparameter, and a-and b-parameter DIF), and magnitude of DIF (small and large magnitudes of DIF). The Type I error rate was inflated for IRT based tests and ordinal logistic regression when some of the items contained DIF. For the uniform DIF conditions, MACS and IRT exhibited similar power rates; however, ordinal logistic regression exhibited slightly higher power compared to the other two methods for smaller sample sizes. Lastly, for nonuniform DIF, IRT exhibited much more power compared to MACS and ordinal logistic regression.

With the growing interest of consumer researchers to test measures and theories in an international context, the cross-national invariance of measurement instruments has become an important issue. At least two issues still need to be addressed. First, the ordinal nature of the rating scale is ignored. Second, when few or no items in the confirmatory factor analysis (CFA) exhibit metric and scalar invariance across all countries, comparison of results across countries is difficult. We solve these problems using a hierarchical IRT model. An empirical application is provided for susceptibility to normative influence, using a sample of 5,484 respondents from 11 countries on four continents.

Surveys increasingly use mixed mode data collection (e.g., combining face-to-face and web) because this controls costs and helps to maintain good response rates. However, a combination of different survey modes in one study, be it cross-sectional or longitudinal, can lead to different kinds of measurement errors. For example, respondents in a face-to-face survey or a web survey may interpret the same question differently, and might give a different answer, just because of the way the question is presented. This effect of survey mode on the question-answer process is called measurement mode effect. This study develops methodological and statistical tools to identify the existence and size of mode effects in a mixed mode survey. In addition, it assesses the size and importance of mode effects in measurement instruments using a specific mixed mode panel survey (Netherlands Kinship Panel Study). Most measurement instruments in the NKPS are multi-item scales, therefore confirmatory factor analysis (CFA) will be used as the main analysis tool, using propensity score methods to correct for selection effects. The results show that the NKPS scales by and large have measurement equivalence, but in most cases only partial measurement equivalence. Controlling for respondent differences on demographic variables, and on scale scores from the previous uni-mode measurement occasion, tends to improve measurement equivalence, but not for all scales. The discussion ends with a review of the implications of our results for analyses employing these scales.

This study is focused on the construction of a cross-national comparable measurement instrument for attitude variables in comparative surveys. Multi-group measurement models for latent variables (LISREL), taking method effects into account, are applied. The measurements of the 'outgroup' dimension of ethnocentrism (variables q42, q44, q45, q47-q52) in the 1995 ISSP dataset are used. Nearly all the items in the quasi balanced set are written in a Likert format in which respondents are asked how strongly they agree or disagree with each attitude statement. There is considerable evidence that such a response format can be susceptible to an agreeingresponse bias called acquiescence . It is shown that in all countries, models with a method or style factor (acquiescence) always fit the data better than models without a style factor. It is investigated to what extent the measurement instrument with a content and a method factor is equivalent over the cultural groups. In a first step the factor loadings of the groups are explored by cluster analysis. After the detection of two subsets of groups that are likely to share equivalent measurement instruments, a stepwise procedure was performed starting with the measurement model for one group, and then looking for equivalent groups (countries) only accepting minor changes in the measurement model. The introduction of a style factor allows us to control for a possible source of measurement non-equivalence, namely method bias. Moreover, the inclusion of a method factor gives the opportunity to investigate the differences in method effects between the groups (countries). However, it is found that both, the variance of the style factor and its factor loadings do not differ between the groups in the first subset of countries, but there are 54 Jaak Billiet et al.

With the growing interest of consumer researchers to test measures and theories in an international context, the cross-national invariance of measurement instruments has become an important issue. At least two issues still need to be addressed. First, the ordinal nature of the rating scale is ignored. Second, when few or no items in the confirmatory factor analysis (CFA) exhibit metric and scalar invariance across all countries, comparison of results across countries is difficult. We solve these problems using a hierarchical IRT model. An empirical application is provided for susceptibility to normative influence, using a sample of 5,484 respondents from 11 countries on four continents.

This paper presents a discussion of methodological issues that are relevant and idiosyncratic to cross-cultural research. One characteristic that typifies cross-cultural studies is their comparative nature, i.e., they involve a comparison across two separate cultures on a focal phenomenon. When differences across cultures are observed, the question arises as to whether the results are true cultural differences or merely measurement artifacts. Methodological considerations in cross-cultural research focus on ruling out alternative explanations for these differences and thus enhancing the interpretability of the results. The paper presents an overview of key methodological issues in cross-cultural research and reviews methods of preventing or detecting methodological problems.

"The greatest social benefit will come from applied research if we can find for each individual the
treatment to which he can most easily adapt. This calls for the joint application of experimental and
correlational methods” (Cronbach as cited by Witcherts, 2007). Recent developments in experimental
industrial psychology concerning the effects of individual differences on test performance and efforts
to increase validity, reliability and minimise bias have contributed to the understanding of the nature of
group differences in achievement and intelligence test scores. This has been made possible by the
introduction of measurement equivalence (ME) techniques that are used in psychometric evaluation.

Minorities’ attitudes can be compared to attitudes of fellow citizen within the host country as well as to attitudes of the motherland. Given the heterogeneity of Luxembourg’s minority groups, this country is a relevant example case in which the comparison needs to involve answering a two-folded question. First we analyze the level of measurement equivalence, i.e. the extent to which different groups can be compared. Secondly, we examine whether ethnic-cultural groups within Luxembourg resemble citizens from their native country more than their country of residence. Using EVS-data from 2008 we demonstrate different types of outcomes. Results indicate that cultural background is more important than national context in the case of culturally more distant minorities to Luxembourg’s resident population, and that national setting is the prevailing factor when minorities are from neighboring countries. The effect of a common national setting is also important with regards to the issue of measurement equivalence, where it contributes to greater comparability of intra-national, cross-ethnic comparisons.

Empirical models of spatial voting allow legislators’ locations in an abstract policy or ideological space to be inferred from their roll call votes. These are typically random utility models of Euclidean spatial voting, where voters assign utility to each of two alternatives associated with each roll call. The specific functional forms of the utility functions are generally assumed rather than estimated. In this paper, we attempt to infer important features of these utility functions. We first consider a model in which legislators’ utility functions are assumed to be a mixture of the two most commonly assumed utility functions (the Gaussian function assumed by NOMINATE and the quadratic function assumed by IDEAL and many other estimators). Applying this estimator to large number of roll call data sets, we find that in nearly every case legislators’ utility functions are estimated to be very nearly Gaussian. We then relax the usual assumption that each legislator is equally sensitive to policy change and find that extreme legislators are generally more sensitive to policy change than their more centrally located counterparts. This result is substantively important to the formation and interpretation of law, because it suggests that extremists are ideologically rigid whereas moderates are more likely to consider influences that arise outside liberal–conservative conflict. Finally, we considered a third model extension examining the possibility that legislators have asymmetric utility functions. Our results tentatively suggest that, conditional on party, as legislators become more conservative their sensitivity to policy alternatives on the right increases.

Cross-national comparisons of the prevalence of depression in general populations are hampered by the absence of comparable data. Using information on the frequency and severity of depressive symptoms from the third wave of the European Social Survey (ESS-3), we are able to fill this gap. In the ESS-3, depression is measured with an eight-item version of the Center for Epidemiological Studies-Depression (CES-D 8) scale. Using multigroup confirmatory factor analysis, we assess configural, metric, and scalar measurement invariance of the CES-D 8. Next, best-fitting factor models are used for latent mean comparisons of women and men in the 25 participating European countries. The present study is the first to present highly comparable data on the prevalence of depression in women and men in Europe. Results show that, after eliminating measurement bias, the gender difference in depression stays significant and regional clustering can be noted.

In cross-cultural comparative studies it is essential to establish equivalent measurement of relevant constructs across cultures. If this equivalence is not confirmed it is difficult if not impossible to make meaningful comparison of results across countries. This work presents concept of measurement equivalence, its relationship with other related concepts, different equivalence levels and causes of inequivalence in cross-cultural research. It also reviews three main approaches to the analysis of measurement equivalence – multigroup confirmatory factor analysis, differential item functioning, and multigroup latent class analysis – with special emphasis on their similarities and differences, as well as comparative advantages.

Three distinctive methods of assessing measurement equivalence of ordinal items, i.e. confirmatory factor analysis, differential item functioning using item response theory and latent class factor analysis, make different modeling assumptions and adopt different procedures. Simulation data are used to compare the performance of these three approaches in detecting the sources of measurement inequivalence. For this purpose, we simulated Likert-type data using two non-linear models, one with categorical and one with continuous latent variables. Inequivalence was set up in the slope parameters (loadings) as well as in the item intercept parameters in a form resembling agreement and extreme response styles. Results indicate that the item response theory and latent class factor models can relatively accurately detect and locate inequivalence in the intercept and slope parameters both at the scale and the item level. Confirmatory factor analysis performs well when inequivalence is located in the slope parameters, but wrongfully indicates inequivalence in the slope parameters when inequivalence is located in the intercept parameters. Influences of sample size, number of inequivalent items in a scale, and model fit criteria on the performance of the three methods are also analysed.