Construction Principles for Latent Trait Models

The monitoring and diagnosis of multivariate categorical processes (MCPs) have drawn increasing attention lately, as categorical variables have been frequently involved in modern quality control applications. In these applications, there may exist causal relationships among multiple categorical variables, where the attribute level of a cause variable influences that of its effect variable. In such a case, shifts occurring in a cause variable will propagate to its effect variable based on the causal structure. Furthermore, there usually exists natural order among the attribute levels of some categorical variables such as good, neutral, and bad for measuring the product quality. By assuming a latent continuous variable, the attribute levels of an ordinal categorical variable can be determined by classifying the value of the latent variable based on thresholds. In this paper, we leverage Bayesian networks (BNs) to characterize MCPs with a causal structure, where the categorical variables can be either nominal, ordinal or a combination of both. We develop one general control chart and one directional control chart, both of which fully exploit the causal relationships and the ordinal information for better process monitoring and diagnosis. Numerical simulations have demonstrated the superiority and robustness of our method in detecting and diagnosing the conditional probability shifts of nominal factors as well as the conditional latent location shifts of ordinal factors. Note to Practitioners-This paper aims at addressing the challenges in monitoring and diagnosing MCPs when there are causal relationships among the categorical variables. The developed method is greatly beneficial, especially when there are nominal and ordinal variables involved in the MCP. Specifically, a BN is employed to characterize the dependence structure of the variables involved in the process, and a latent continuous variable is utilized to model the orders of attribute levels of the ordinal variables. Then, a novel method is proposed to detect the probability shift in the nominal factors and the location shift on the latent variables of the ordinal variables based on the likelihood ratio test. A general monitoring control chart as well as a directional version which also facilitates diagnosis is proposed. In this paper, although our method is based on the assumption that the latent continuous variables of the ordinal variables follow logistic distributions, the proposed charts are demonstrated to perform efficiently and robustly in various cases as shown in the simulations and case studies.

In recent years a number of measures have been suggested for the assessment of fit of overidentified models with latent variables (i.e., covariance structure models). This article discusses the logic of the fit problem, reviews the analytical intentions of six of these measures, with emphasis on their dependence on sample size, and compares the operational behavior of these measures in three-model situations: in a confirmatory factor model based on small N, and in two covariance structure models, one based on a slightly larger N and the other based on a large N. Given that these models and data are “typical,” results suggest that certain measures are both more stable across sample sizes and more sensitive to important variation in fit across substantively plausible models. The article concludes by suggesting a three-component approach to fitting: use of multiple measures, strategical overfitting, and comparison of parameter estimates in borderline versus more clearly sufficient models in terms of fit.

A novel Bayesian modeling framework for response accuracy (RA), response times (RTs) and other process data is proposed. In a Bayesian covariance structure modeling approach, nested and crossed dependences within test-taker data (e.g., within a testlet, between RAs and RTs for an item) are explicitly modeled. The local dependences are modeled directly through covariance parameters in an additive covariance matrix. The inclusion of random effects (on person or group level) is not necessary, which allows constructing parsimonious models for responses and multiple types of process data. Bayesian Covariance Structure Models (BCSMs) are presented for various well-known dependence structures. Through truncated shifted inverse-gamma priors, closed-form expressions for the conditional posteriors of the covariance parameters are derived. The priors avoid boundary effects at zero, and ensure the positive definiteness of the additive covariance structure at any layer. Dependences of categorical outcome data are modeled through latent continuous variables. In a simulation study, a BCSM for RAs and RTs is compared to van der Linden's hierarchical model (LHM; van der Linden, 2007). Under the BCSM, the dependence structure is extended to allow variations in test-takers' working speed and ability and is estimated with a satisfying performance. Under the LHM, the assumption of local independence is violated, which results in a biased estimate of the variance of the ability distribution. Moreover, the BCSM provides insight in changes in the speed-accuracy trade-off. With an empirical example, the flexibility and relevance of the BCSM for complex dependence structures in a real-world setting are discussed.

Latent variable (LV) models are increasingly being used in environmental epidemiology as a way to summarize multiple environmental exposures and thus minimize statistical concerns that arise in multiple regression. LV models may be especially useful when multivariate exposures are collected repeatedly over time. LV models can accommodate a variety of assumptions but, at the same time, present the user with many choices for model specification particularly in the case of exposure data collected repeatedly over time. For instance, the user could assume conditional independence of observed exposure biomarkers given the latent exposure and, in the case of longitudinal latent exposure variables, time invariance of the measurement model. Choosing which assumptions to relax is not always straightforward. We were motivated by a study of prenatal lead exposure and mental development, where assumptions of the measurement model for the time-changing longitudinal exposure have appreciable impact on (maximum-likelihood) inferences about the health effects of lead exposure. Although we were not particularly interested in characterizing the change of the LV itself, imposing a longitudinal LV structure on the repeated multivariate exposure measures could result in high efficiency gains for the exposure-disease association. We examine the biases of maximum likelihood estimators when assumptions about the measurement model for the longitudinal latent exposure variable are violated. We adapt existing instrumental variable estimators to the case of longitudinal exposures and propose them as an alternative to estimate the health effects of a time-changing latent predictor. We show that instrumental variable estimators remain unbiased for a wide range of data generating models and have advantages in terms of mean squared error. Copyright © 2017 John Wiley & Sons, Ltd.

Flexible methods that relax restrictive conditional independence assumptions of latent classanalysis (LCA) are described. Dichotomous and ordered category manifest variables are viewed asdiscretized latent continuous variables. The latent continuous variables are assumed to have a mixtureofmultivariate-normals distribution. Within a latent class, conditional dependence is modeled as the mutual association of all or some latent continuous variables with a continuous latent trait (or in special cases, multiple latent traits). The relaxation of conditional independence assumptions allows LCA to better model natural taxa. Comparisons of specific restricted and unrestricted models permit statistical tests of specific aspects of latent taxonic structure. Latent class, latent trait, and latent distribution analysis can be viewed as special cases of the mixed latent trait model. The relationship between the multivariate probit mixture model proposed here and Rost’s mixed Rasch (1990, 1991) model is discussed. Two studies illustrate different uses of the proposed model.

A latent variable representation of count data models to accommodate spatial and temporal dependence: Application to predicting crash frequency at intersections

Many scientific research programs aim to learn the causal structure of real world phenomena. This learning problem is made more difficult when the target of study cannot be directly observed. One strategy commonly used by social scientists is to create measurable "indicator" variables that covary with the latent variables of interest. Before leveraging the indicator variables to learn about the latent variables, however, one needs a measurement model of the causal relations between the indicators and their corresponding latents. These measurement models are a special class of Bayesian networks. This paper addresses the problem of reliably inferring measurement models from measured indicators, without prior knowledge of the causal relations or the number of latent variables. We present a provably correct novel algorithm, FindOneFactorClusters (FOFC), for solving this inference problem. Compared to other state of the art algorithms, FOFC is faster, scales to larger sets of indicators, and is more reliable at small sample sizes. We also present the first correctness proofs for this problem that do not assume linearity or acyclicity among the latent variables.

Structural Equation Model (SEM) is a statistical technique with simultaneous processing involves measurement errors, indicator variables, and latent variables. SEM is used to test hypotheses that state the relationships between latent variables when latent variables have been assessed through each of the indicator variables. Multiple Group SEM is a basic model analysis that uses more than one sample. This analysis aims to determine whether the components or models of measurement and structural models are invariant for the two sample groups. In this study, the data generated by some requirements. First, the data generated with sample size n = 250. The first generated data is homogeneous data where the measurement model is the same as the structural model in group 1 and group 2, while the second data is non-homogeneous data where the measurement model and the structural model in group 1 and group 2 is not the same. The data was analyzed using the help of the lavaan package available in R to obtain SEM estimation results and Goodness of Fit Model from some data that was formed. From the results of the merger of the two groups, it shows that the invariant of the two models with the largest df (63) which is Fit Mean model states the simplest model. However, the smallest df (48) with Fit.configural model states the most complex model.
 Keywords: SEM, Multiple Group, R Program

In this article, we illustrate ways in which generalizability theory (G-theory) can be used with continuous latent response variables (CLRVs) to address problems of scale coarseness resulting from categorization errors caused by representing ranges of continuous variables by discrete data points and transformation errors caused by unequal interval widths between those data points. The mechanism to address these problems is applying structural equation modeling (SEM) as a tool in deriving variance components needed to estimate indices of score consistency and validity. Illustrations include quantification of multiple sources of measurement error, use of non-nested and nested designs, derivation of indices of consistency for norm- and criterion-referenced interpretation of scores, estimation of effects when changing measurement procedures and designs, and disattenuation of correlation coefficients for measurement error. These illustrations underscore the effectiveness of G-theory with continuous latent response variables in providing stable indices of reliability and validity that are reasonably independent of the number of original scale points used, unevenness of scale intervals, and average degree of item skewness. We discuss general distinctions in reliability estimation within G-theory, SEM, and classical test theory; make specific recommendations for using G-theory on raw score and CLRV metrics; and provide computer code in an online supplement for doing all key analyses demonstrated in the article using R and Mplus. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

As part of an alcohol misuse prevention evaluation, questionnaires were administered to 4,157 junior high school students to determine levels of alcohol misuse, exposure to peer use and misuse of alcohol, susceptibility to peer pressure, internal health locus of control, and self-esteem. A conceptual model of the antecedents of adolescent alcohol misuse and the effectiveness of a prevention effort was tested using covariance structure modeling techniques. The factor loadings for the model were all moderate to high, indicating that the observed variables served well as measurement instruments for the latent variables. The hypothesized structural relationships among the latent variables of alcohol misuse, exposure to peer use and misuse of alcohol, susceptibility to peer pressure, internal health locus of control, and self-esteem were supported by the data. The full model explained 45 percent of the variance in alcohol misuse in the analysis based on the total sample. The direct effect of the intervention on alcohol misuse was small but significant in the hypothesized direction. The direct effects of the intervention on susceptibility to peer pressure and internal health locus of control were not significant. The model was tested separately for groups of students who had high versus low scores on susceptibility to peer pressure in order to test the interaction between susceptibility to peer pressure and exposure to peer use and misuse of alcohol. The percentage of variance accounted for in alcohol misuse did not increase upon testing the model separately for students who had high versus low scores on susceptibility to peer pressure. Observed differences in the significance of the parameter estimates between the high and low susceptibility to peer pressure groups suggest that different approaches to the design and evaluation of substance abuse prevention programs may be necessary for different subgroups of students.

Environmental spaces are important for residents to enjoy in daily life and to take refuge in case of earthquake disaster. Therefore spatial planning must be considered with both situation and their consciousness. This paper makes clear the location of space for mitigation and the relation between user's mental factors and these characteristics.Fieldwork and consciousness research concerning natural spaces at Hokusetsu region in Osaka prefecture were done. These characteristics that give influence to users are structured with ISM, and these are classified to hierarchy by area. The districts where new space needed were made clear by the analysis using earthquake hazard map. Above relation is modeled with latent variables that are given factors by exploratory factor analysis model. These relations are analyzed with covariance structure model, and made clear by every hierarchy.

The goal of network analysis is to focus on relationships between social entities. It is used widely in the social and behavioral sciences, as well as in political science, economics, psychology andorganizational science. The social network approach has a long history and it has been developed over the last 60 years by researchers in psychology, sociology and anthropology. Nowadays, using high-speed computers, network analysis is mostly used for graphical presentation of relationships and dependencies; moreover, networks comprise graphical representations of the relationships (edges) between variables (nodes). Network analysis provides the capacity to estimate complex patterns of relationships and the network structure can be analyzed to reveal core features of the network. Recent developments however, stress the usefulness of network-based approaches for measurement models in social sciences, where CFA and IRT are are complemented by network approaches. In this paper we provide an overview of networks of European economic universities, and present and compare the results of classical Item Response Theory (Birnbaum model) and Latent Network Models (Ising and Residual Network Model) for measurement of networking ability among Polish economic universities. All calculations are conducted using R software. The results of IRT model shows that the highest significant difficulty parameters (that can be regarded as network “attractiveness”) are characteristic for CEEMAN, CESEENET and MAGNACARTA networks, whereas the lowest but insignificant parameters are related to ATLAS, PRME and NICE. Because of lack of evidence of unidimenstionality of common factor IRT model and lot of insignificant parameters, the Latent Network Model and Residual Network Model were used. The application of LNM and RNM revealed three-dimensional structure of latent networks. First cluster consists with relatively attractive networks (EUA, CESEENET, MAGNACARTA, NICE, CEEMAN), second cluster represents the average attractiveness (CEMS, EDAMBA, PIM) and the third is based on networks with lowest difficulty parameters (EFMD, PRME, ATLAS).

Chi-square tests based on maximum likelihood (ML) estimation of covariance structures often incorrectly over-reject the null hypothesis: Σ = Σ θ when the sample size is small. Reweighted least squares (RLS) avoids this problem. In some models, the vector of parameter must contain means, variances, and covariances, yet whether RLS also works in mean and covariance structures remains unexamined. This research extends RLS to mean and covariance structures, evaluating a generalized least squares function with ML parameter estimates. A Monte Carlo simulation study was carried out to examine the statistical performance of ML vs RLS with multivariate normal data. Based on empirical rejection frequencies and empirical averages of test statistics, this study shows that RLS performs much better than ML in mean and covariance structure models when sample sizes are small, whereas it does not perform better than ML to reject misspecified models.

Linear structural equation models with latent variables are common in psychology, econometrics, sociology, and political science. Such models have two parts, a measurement model that specifies how the latent variables are measured, and a structural model which specifies the causal relations among the latent variables. In this paper I discuss search procedures for finding a ‘pure’ measurement model and for using this pure model to determine features of the structural model. The procedures are implemented as the Purify and MIMbuild modules of the TETRAD II program.KeywordsLatent VariableMeasurement ModelCausal StructureLatent Variable ModelMeasured IndicatorThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

The Role of Providers in Mental Health Services Offered to American-Indian Youths