Latent variable model

About: Latent variable model is a research topic. Over the lifetime, 3589 publications have been published within this topic receiving 235061 citations.

Complex working memory span tasks and higher-order cognition: A latent-variable analysis of the relationship between processing and storage

Abstract: Complex span tasks, assumed by many to measure an individual’s working memory capacity, are predictive of several aspects of higher-order cognition. However, the underlying cause of the relationships between ‘‘processing-and-storage’’ tasks and cognitive abilities is still hotly debated nearly 30 years after the tasks were first introduced. The current study utilised latent constructs across verbal, numerical, and spatial content domains to examine a number of questions regarding the predictive power of complex span tasks. In particular, the relations among processing time, processing accuracy, and storage accuracy from the complex span tasks were examined, in combination with their respective relationships with fluid intelligence. The results point to a complicated pattern of unique and shared variance among the constructs. Implications for various theories of working memory are discussed.

Modeling Uncertainty in Latent Class Membership: A Case Study in Criminology

Abstract: Social scientists are commonly interested in relating a latent trait (e.g., criminal tendency) to measurable individual covariates (e.g., poor parenting) to understand what defines or perhaps causes the latent trait. In this article we develop an efficient and convenient method for answering such questions. The basic model presumes that two types of variables have been measured: Response variables (possibly longitudinal) that partially determine the latent class membership, and covariates or risk factors that we wish to relate to these latent class variables. The model assumes that these observable variables are conditionally independent, given the latent class variable. We use a mixture model for the joint distribution of the observables. We apply this model to a longitudinal dataset assembled as part of the Cambridge Study of Delinquent Development to test a fundamental theory of criminal development. This theory holds that crime is committed by two distinct groups within the population: Adoles...

Finite-Mixture Structural Equation Models for Response-Based Segmentation and Unobserved Heterogeneity

Abstract: Two endemic problems face researchers in the social sciences e.g., Marketing, Economics, Psychology, and Finance: unobserved heterogeneity and measurement error in data. Structural equation modeling is a powerful tool for dealing with these difficulties using a simultaneous equation framework with unobserved constructs and manifest indicators which are error-prone. When estimating structural equation models, however, researchers frequently treat the data as if they were collected from a single population Muthen [Muthen, Bengt O. 1989. Latent variable modeling in heterogeneous populations. Psychometrika54 557--585.]. This assumption of homogeneity is often unrealistic. For example, in multidimensional expectancy value models, consumers from different market segments can have different belief structures Bagozzi [Bagozzi, Richard P. 1982. A field investigation of causal relations among cognitions, affect, intentions, and behavior. J. Marketing Res.19 562--584.]. Research in satisfaction suggests that consumer decision processes vary across segments Day [Day, Ralph L. 1977. Extending the concept of consumer satisfaction. W. D. Perreault, ed. Advances in Consumer Research, Vol. 4. Association for Consumer Research, Atlanta, 149--154.]. This paper shows that aggregate analysis which ignores heterogeneity in structural equation models produces misleading results and that traditional fit statistics are not useful for detecting unobserved heterogeneity in the data. Furthermore, sequential analyses that first form groups using cluster analysis and then apply multigroup structural equation modeling are not satisfactory. We develop a general finite mixture structural equation model that simultaneously treats heterogeneity and forms market segments in the context of a specified model structure where all the observed variables are measured with error. The model is considerably more general than cluster analysis, multigroup confirmatory factor analysis, and multigroup structural equation modeling. In particular, the model subsumes several specialized models including finite mixture simultaneous equation models, finite mixture confirmatory factor analysis, and finite mixture second-order factor analysis. The finite mixture structural equation model should be of interest to academics in a wide range of disciplines e.g., Consumer Behavior, Marketing, Economics, Finance, Psychology, and Sociology where unobserved heterogeneity and measurement error are problematic. In addition, the model should be of interest to market researchers and product managers for two reasons. First, the model allows the manager to perform response-based segmentation using a consumer decision process model, while explicitly allowing for both measurement and structural error. Second, the model allows managers to detect unobserved moderating factors which account for heterogeneity. Once managers have identified the moderating factors, they can link segment membership to observable individual-level characteristics e.g., socioeconomic and demographic variables and improve marketing policy. We applied the finite mixture structural equation model to a direct marketing study of customer satisfaction and estimated a large model with 8 unobserved constructs and 23 manifest indicators. The results show that there are three consumer segments that vary considerably in terms of the importance they attach to the various dimensions of satisfaction. In contrast, aggregate analysis is misleading because it incorrectly suggests that except for price all dimensions of satisfaction are significant for all consumers. Methodologically, the finite mixture model is robust; that is, the parameter estimates are stable under double cross-validation and the method can be used to test large models. Furthermore, the double cross-validation results show that the finite mixture model is superior to sequential data analysis strategies in terms of goodness-of-fit and interpretability. We performed four simulation experiments to test the robustness of the algorithm using both recursive and nonrecursive model specifications. Specifically, we examined the robustness of different model selection criteria e.g., CAIC, BIC, and GFI in choosing the correct number of clusters for exactly identified and overidentified models assuming that the distributional form is correctly specified. We also examined the effect of distributional misspecification i.e., departures from multivariate normality on model performance. The results show that when the data are heterogeneous, the standard goodness-of-fit statistics for the aggregate model are not useful for detecting heterogeneity. Furthermore, parameter recovery is poor. For the finite mixture model, however, the BIC and CAIC criteria perform well in detecting heterogeneity and in identifying the true number of segments. In particular, parameter recovery for both the measurement and structural models is highly satisfactory. The finite mixture method is robust to distributional misspecification; in addition, the method significantly outperforms aggregate and sequential data analysis methods when the form of heterogeneity is misspecified i.e., the true model has random coefficients. Researchers and practitioners should only use the mixture methodology when substantive theory supports the structural equation model, a priori segmentation is infeasible, and theory suggests that the data are heterogeneous and belong to a finite number of unobserved groups. We expect these conditions to hold in many social science applications and, in particular, market segmentation studies. Future research should focus on large-scale simulation studies to test the structural equation mixture model using a wide range of models and statistical distributions. Theoretical research should extend the model by allowing the mixing proportions to depend on prior information and/or subject-specific variables. Finally, in order to provide a fuller treatment of heterogeneity, we need to develop a general random coefficient structural equation model. Such a model is presently unavailable in the statistical and psychometric literatures.

Estimating and interpreting latent variable interactions: A tutorial for applying the latent moderated structural equations method

Abstract: Latent variables are common in psychological research. Research questions involving the interaction of two variables are likewise quite common. Methods for estimating and interpreting interactions between latent variables within a structural equation modeling framework have recently become available. The latent moderated structural equations (LMS) method is one that is built into Mplus software. The potential utility of this method is limited by the fact that the models do not produce traditional model fit indices, standardized coefficients, or effect sizes for the latent interaction, which renders model fitting and interpretation of the latent variable interaction difficult. This article compiles state-of-the-science techniques for assessing LMS model fit, obtaining standardized coefficients, and determining the size of the latent interaction effect in order to create a tutorial for new users of LMS models. The recommended sequence of model estimation and interpretation is demonstrated via a substantive example and a Monte Carlo simulation. Finally, extensions of this method are discussed, such as estimating quadratic effects of latent factors and interactions between latent slope and intercept factors, which hold significant potential for testing and advancing developmental theories.

Random effects models in latent class analysis for evaluating accuracy of diagnostic tests.

Abstract: When the results of a reference (or gold standard) test are missing or not error-free, the accuracy of diagnostic tests is often assessed through latent class models with two latent classes, representing diseased or nondiseased status. Such models, however, require that conditional on the true disease status, the tests are statistically independent, an assumption often violated in practice. Consequently, the model generally fits the data poorly. In this paper, we develop a general latent class model with random effects to model the conditional dependence among multiple diagnostic tests (or readers). We also develop a graphical method for checking whether or not the conditional dependence is of concern and for identifying the pattern of the correlation. Using the random-effects model and the graphical method, a simple adequate model that is easy to interpret can be obtained. The methods are illustrated with three examples from the biometric literature. The proposed methodology is also applicable when the true disease status is indeed known and conditional dependence could well be present.