Sociological Methods & Research

This article reviews and compares recently proposed factor analytic and item response theory approaches to the study of invariance across groups. Two methods are described and contrasted. The alignment method considers the groups as a fixed mode of variation, while the random-intercept, random-loading two-level method considers the groups as a random mode of variation. Both maximum likelihood and Bayesian analyses are applied. A survey of close to 50,000 subjects in 26 countries is used as an illustration. In addition, the two methods are studied by Monte Carlo simulations. A list of considerations for choosing between the two methods is presented.

Measurement invariance is a necessary precondition for meaningful cross-country comparisons, and three levels have been differentiated: configural, metric, and scalar. Unfortunately, establishing the most stringent form, that is, scalar measurement invariance, across groups is difficult. Recently, Muthén and Asparouhov proposed testing for approximate rather than exact measurement invariance, as this may be sufficient for meaningful comparisons. Following their strategy, the results of cross-country approximate measurement invariance tests of the 21-item Portrait Value Questionnaire (PVQ-21) scale to measure values in the European Social Survey are presented (N = 274,447 respondents from 15 countries participating in all six rounds). Applying the new approximate method for the test of measurement invariance allows both using more moderate constraints of approximate equality of parameters across groups and exploring the extent of noninvariance. Approximate measurement invariance was established in almost all rounds for two higher-order values: openness to change and self-enhancement. In the case of the two other higher-order values, self-transcendence and conservation, approximate measurement invariance was established across a subset of countries.

This study applies the alignment method, a technique for assessing measurement equivalence across many groups, to the analysis of adolescents’ support for immigrants’ rights in a pooled data set from the 1999 International Association for the Evaluation of Educational Achievement (IEA) Civic Education Study and the 2009 IEA International Civics and Citizenship Education Study. We examined measurement invariance across 92 groups (country by cohort by gender), finding that a five-item scale was statistically well-grounded for unbiased group comparisons despite the presence of significant noninvariance in some groups. Using the resulting group mean scores, we compared European youth’s attitudes finding that female students had more positive attitudes than did male students across countries and cohorts. An analysis of countries participating in both studies revealed that students in most countries demonstrated more positive attitudes in 2009 than in 1999. The alignment methodology makes it feasible to comprehensively assess measurement invariance in large data sets and to compute aligned factor scores for the full sample that can update existing databases for more efficient further secondary analysis and with metainformation concerning measurement invariance.

It is necessary to test for equivalence of measurements across groups to guarantee that comparisons of regression coefficients or mean scores of a latent factor are meaningful. Unfortunately, when tested, many scales display nonequivalence. Several researchers have suggested that nonequivalence may be used as a useful source of information as to why equivalence is biased and proposed employing a multilevel structural equation modeling (MLSEM) approach to explain why equivalence is not given. This method can consider a latent between-level factor and/or single contextual variables and use them to explain items’ nonequivalence. In the current study, we show that this method may also be useful for social science studies in general and for survey research and sociological comparative studies in particular when one fails to establish cross-group equivalence. We utilize data from the International Social Survey Program national identity module (2003) to test for the cross-country equivalence of a scale measuring attitudes toward granting citizenship rights to immigrants. As expected, the scale fails to achieve scalar equivalence. However, we explain a significant part of the most nonequivalent intercept by a latent between-level factor and one contextual variable, namely, the percentage of foreigners in the country relying on group threat theory. We show that the method does not necessarily rectify nonequivalence, but it can help to explain why it is absent.

The article outlines a methodology for systematically observing collective violence (and public order policing in relation to it). Specific attention is given to matters of sampling and measurement and to the way in which observational challenges have been met in comparison with participant observational studies of demonstrations and football matches. The article shows that it is possible to conduct meaningful systematic observations of episodes of collective violence in a reliable way (more complete and more detailed than police records or newspaper reports) without compromising the physical safety of the observer. Even though violence at these types of events is relatively rare, it is also possible specifically to sample events with an increased likelihood for collective violence. Direct systematic observation of collective violence yields data that cannot be obtained by other means (surveys, interviews, participant observation) and that are crucial to an understanding of the initiation and escalation of collective violence.

This article distinguishes three measures of intergenerational economic mobility that emerge when the population is divided into groups: overall individual mobility, within-group mobility, and between-group mobility. We clarify their properties and the relationship between them. We then evaluate Clark’s use of surname between-group persistence as a preferred measure of intergenerational mobility in the book The Son Also Rises: Surnames and the History of Social Mobility. We show that aggregate surname-level intergenerational persistence cannot be compared with individual persistence because group-level income averages captures diverse individual-level and group-level factors impossible to disentangle without additional identifying information. Furthermore, measures of group persistence do not address the problem of measurement error leading to attenuation bias, which is Clark’s rationale to study surname mobility. An empirical example partitioning the population into groups based on racial/ethnic origins and a simulation clarify the relationship between these different measures of mobility.

Development and refinement of self-report measures generally involves selecting a subset of indicators from a larger set. Despite the importance of this task, methods applied to accomplish this are often idiosyncratic and ad hoc, or based on incomplete statistical criteria. We describe a structural equation modeling (SEM)-based technique, based on the standardized residual variance–covariance matrix, which subsumes multiple traditional psychometric criteria: item homogeneity, reliability, convergent, and discriminant validity. SEMs with a fixed structure, but with substituted candidate items, can be used to evaluate the relative performance of those items. Using simulated data sets, we demonstrate a simple progressive elimination algorithm, which demonstrably optimizes item choice across multiple psychometric criteria. This method is then applied to the task of short-form development of the multidimensional “4Es” (Excitement, Esteem, Escape, Excess) scale, which are understood as indicators of psychological vulnerability to gambling problems. It is concluded that the proposed SEM-based algorithm provides an automatic and efficient approach to the item-reduction stage of scale development and should be similarly useful for the development of short forms of preexisting scales. Broader use of such an algorithm would promote more transparent, consistent, and replicable scale development.

The last decade has witnessed resurgence in the interest in studying the causal mechanisms linking causes and effects. This article games through the methodological consequences that adopting a systems understanding of mechanisms has for what types of cases we should select when using in-depth case study methods like process tracing. The article proceeds in three steps. We first expose the assumptions that underpin the study of causal mechanisms as systems that have methodological implications for case selection. In particular, we take as our point of departure the case-based position, where: causation is viewed in deterministic and asymmetric terms, the focus is ensuring causal homogeneity in case-based research to enable cross-case inferences to be made, and finally where mechanisms are understood as more than just intervening variables but instead a system of interacting parts that transfers causal forces from causes to outcomes. We then develop a set of case selection guidelines that are in methodological alignment with these underlying assumptions. We then develop guidelines for research where the mechanism is the primary focus, contending that only typical cases where both X, Y, and the requisite contextual conditions are present should be selected. We compare our guidelines with the existing, finding that practices like selecting most/least-likely cases are not compatible with the underlying assumptions of tracing mechanisms. We then present guidelines for deviant cases, focusing on tracing mechanisms until they breakdown as a tool to shed light on omitted contextual and/or causal conditions.

Analyzing relationships of necessity is important for both scholarly and applied research questions in the social sciences. An often-used technique for identifying such relationships—fuzzy set Qualitative Comparative Analysis (fsQCA)—has limited ability to make the most out of the data used. The set-theoretical technique fsQCA makes statements in kind (e.g., “a condition or configuration is necessary or not for an outcome”), thereby ignoring the variation in degree. We propose to apply a recently developed technique for identifying relationships of necessity that can make both statements in kind and in degree, thus making full use of variation in the data: Necessary Condition Analysis (NCA). With its ability to also make statements in degree (“a specific level of a condition is necessary or not for a specific level of the outcome”), NCA can complement the in kind analysis of necessity with fsQCA.