结构方程模型和IRT等级反应模型在人格量表项目筛选中的对比研究

为比较结构方程模型和 IRT等级反应模型在人格量表项目筛选上的作用,以《中国大学生人格量表》的7229个实际测量数据为基础,针对因素二“爽直”分别以Lisrel8.70和Multilog7.03进行结构方程模型和等级反应模型的参数估计与拟合,比较两种方法的项目筛选结果.二者统计结果均认为项目5、6、7、8拟合度不佳,在结构方程模型上表现为因子负荷较低,整体拟合指数不理想;在等级反应模型上表现为区分度参数和位置参数不理想,相关项目的特征曲线和信息曲线形态较差.但结构方程模型倾向于项目6、8更差,而等级反应模型则倾向于项目5、6更差.结构方程模型和 IRT等级反应模型对人格量表项目的统计推断结果从总体上讲是一致的,但在个别项目上略有差异.二者各有优势,可以结合使用.     

Models and Strategies for Factor Mixture Analysis: An Example Concerning the Structure Underlying Psychological Disorders

The factor mixture model (FMM) uses a hybrid of both categorical and continuous latent variables. The FMM is a good model for the underlying structure of psychopathology because the use of both categorical and continuous latent variables allows the structure to be simultaneously categorical and dimensional. This is useful because both diagnostic class membership and the range of severity within and across diagnostic classes can be modeled concurrently. Although the conceptualization of the FMM has been explained in the literature, the use of the FMM is still not prevalent. One reason is that there is little research about how such models should be applied in practice and, once a well-fitting model is obtained, how it should be interpreted. In this article, the FMM is explored by studying a real data example on conduct disorder. By exploring this example, this article aims to explain the different formulations of the FMM, the various steps in building a FMM, and how to decide between an FMM and alternative models.     

A Mixture IRTree Model for Extreme Response Style: Accounting for Response Process Uncertainty

This paper presents a mixture item response tree (IRTree) model for extreme response style. Unlike traditional applications of single IRTree models, a mixture approach provides a way of representing the mixture of respondents following different underlying response processes (between individuals), as well as the uncertainty present at the individual level (within an individual). Simulation analyses reveal the potential of the mixture approach in identifying subgroups of respondents exhibiting response behavior reflective of different underlying response processes. Application to real data from the Students Like Learning Mathematics (SLM) scale of Trends in International Mathematics and Science Study (TIMSS) 2015 demonstrates the superior comparative fit of the mixture representation, as well as the consequences of applying the mixture on the estimation of content and response style traits. We argue that methodology applied to investigate response styles should attend to the inherent uncertainty of response style influence due to the likely influence of both response styles and the content trait on the selection of extreme response categories.     

Fitting Unstructured Finite Mixture Models in Longitudinal Design: A Recommendation for Model Selection and Estimation of the Number of Classes

In longitudinal design, investigating interindividual differences of intraindividual changes enables researchers to better understand the potential variety of development and growth. Although latent growth curve mixture models have been widely used, unstructured finite mixture models (uFMMs) are also useful as a preliminary tool and are expected to be more robust in identifying classes under the influence of possible model misspecifications, which are very common in actual practice. In this study, large-scale simulations were performed in which various normal uFMMs and nonnormal uFMMs were fit to evaluate their utility and the performance of each model selection procedure for estimating the number of classes in longitudinal designs. Results show that normal uFMMs assuming invariance of variance–covariance structures among classes perform better on average. Among model selection procedures, the Calinski–Harabasz statistic, which has a nonparametric nature, performed better on average than information criteria, including the Bayesian information criterion.     

Covariates and Mixture Modeling: Results of a Simulation Study Exploring the Impact of Misspecified Effects on Class Enumeration

For some time, there have been differing recommendations about how and when to include covariates in the mixture model building process. Some have advocated the inclusion of covariates after enumeration, whereas others recommend including them early on in the modeling process. These conflicting recommendations have led to inconsistent practices and unease in trusting modeling results. In an attempt to resolve this discord, we conducted a Monte Carlo simulation to examine the impact of covariate exclusion and misspecification of covariate effects on the enumeration process. We considered population and analysis models with both direct and indirect paths from the covariates to the latent class indicators. As expected, misspecified covariate effects most commonly led to the overextraction of classes. Findings suggest that the number of classes could be reliably determined using the unconditional latent class model, thus our recommendation is that class enumeration be done prior to the inclusion of covariates.     

An NCME Instructional Module on Latent DIF Analysis Using Mixture Item Response Models

The purpose of this ITEMS module is to provide an introduction to differential item functioning (DIF) analysis using mixture item response models. The mixture item response models for DIF analysis involve comparing item profiles across latent groups, instead of manifest groups. First, an overview of DIF analysis based on latent groups, called latent DIF analysis, is provided and its applications in the literature are surveyed. Then, the methodological issues pertaining to latent DIF analysis are described, including mixture item response models, parameter estimation, and latent DIF detection methods. Finally, recommended steps for latent DIF analysis are illustrated using empirical data.     

General Growth Mixture Analysis of Adolescents' Developmental Trajectories of Anxiety: The Impact of Untested Invariance Assumptions on Substantive Interpretations

Substantively, this study investigates potential heterogeneity in the developmental trajectories of anxiety in adolescence. Methodologically, this study demonstrates the usefulness of general growth mixture analysis (GGMA) in addressing these issues and illustrates the impact of untested invariance assumptions on substantive interpretations. This study relied on data from the Montreal Adolescent Depression Development Project (MADDP), a 4-year follow-up of more than 1,000 adolescents who completed the Beck Anxiety Inventory each year. GGMA models relying on different invariance assumptions were empirically compared. Each of these models converged on a 5-class solution, but yielded different substantive results. The model with class-varying variance–covariance matrices was retained as providing a better fit to the data. These results showed that although elevated levels of anxiety might fluctuate over time, they clearly do not represent a transient phenomenon. This model was then validated in relation to multiple predictors (mostly related to school violence) and outcomes (grade-point average, school dropout, depression, loneliness, and drug-related problems).     

A Multidimensional Finite Mixture Structural Equation Model for Nonignorable Missing Responses to Test Items

We propose a structural equation model, which reduces to a multidimensional latent class item response theory model, for the analysis of binary item responses with nonignorable missingness. The missingness mechanism is driven by 2 sets of latent variables: one describing the propensity to respond and the other referred to the abilities measured by the test items. These latent variables are assumed to have a discrete distribution, so as to reduce the number of parametric assumptions regarding the latent structure of the model. Individual covariates can also be included through a multinomial logistic parameterization for the distribution of the latent variables. Given the discrete nature of this distribution, the proposed model is efficiently estimated by the expectation–maximization algorithm. A simulation study is performed to evaluate the finite-sample properties of the parameter estimates. Moreover, an application is illustrated with data coming from a student entry test for the admission to some university courses.     

Modeling Predictors of Latent Classes in Regression Mixture Models

The purpose of this study is to provide guidance on a process for including latent class predictors in regression mixture models. We first examine the performance of current practice for using the 1-step and 3-step approaches where the direct covariate effect on the outcome is omitted. None of the approaches show adequate estimates of model parameters. Given that Step 1 of the 3-step approach shows adequate results in class enumeration, we suggest using an alternative approach: (a) decide the number of latent classes without predictors of latent classes, and (b) bring the latent class predictors into the model with the inclusion of hypothesized direct covariate effects. Our simulations show that this approach leads to good estimates for all model parameters. The proposed approach is demonstrated by using empirical data to examine the differential effects of family resources on students’ academic achievement outcome. Implications of the study are discussed.     

Evaluating the Performance of the K-fold Cross-Validation Approach for Model Selection in Growth Mixture Modeling

Deciding on the number of “classes” has been the most prominent and most debated challenge in finite mixture modeling. Recently, a novel strategy has been proposed to select the best model in finite mixture modeling: a k-fold cross-validation approach. However, this approach has not been systematically evaluated, which makes the performance of the k-fold cross-validation approach for model selection in finite mixture modeling largely unknown. Thus, the main motivation for conducting the current work is to systematically evaluate the performance of the k-fold cross-validation approach for model selection in the context of Growth Mixture Modeling. Results revealed that the performance of the k-fold cross-validation approach for model selection in GMM is generally unsatisfactory, and it only performs reasonably well under the condition of very large class separation.     

The Impact of Vertical Scaling Decisions on Growth Interpretations

Most growth models implicitly assume that test scores have been vertically scaled. What may not be widely appreciated are the different choices that must be made when creating a vertical score scale. In this paper empirical patterns of growth in student achievement are compared as a function of different approaches to creating a vertical scale. Longitudinal item‐level data from a standardized reading test are analyzed for two cohorts of students between Grades 3 and 6 and Grades 4 and 7 for the entire state of Colorado from 2003 to 2006. Eight different vertical scales were established on the basis of choices made for three key variables: Item Response Theory modeling approach, linking approach, and ability estimation approach. It is shown that interpretations of empirical growth patterns appear to depend upon the extent to which a vertical scale has been effectively “stretched” or “compressed” by the psychometric decisions made to establish it. While all of the vertical scales considered show patterns of decelerating growth across grade levels, there is little evidence of scale shrinkage.     

Detecting Mixtures From Structural Model Differences Using Latent Variable Mixture Modeling: A Comparison of Relative Model Fit Statistics

The accuracy of structural model parameter estimates in latent variable mixture modeling was explored with a 3 (sample size) × 3 (exogenous latent mean difference) × 3 (endogenous latent mean difference) × 3 (correlation between factors) × 3 (mixture proportions) factorial design. In addition, the efficacy of several likelihood-based statistics (Akaike's Information Criterion [AIC], Bayesian Information Ctriterion [BIC], the sample-size adjusted BIC [ssBIC], the consistent AIC [CAIC], the Vuong-Lo-Mendell-Rubin adjusted likelihood ratio test [aVLMR]), classification-based statistics (CLC [classification likelihood information criterion], ICL-BIC [integrated classification likelihood], normalized entropy criterion [NEC], entropy), and distributional statistics (multivariate skew and kurtosis test) were examined to determine which statistics best recover the correct number of components. Results indicate that the structural parameters were recovered, but the model fit statistics were not exceedingly accurate. The ssBIC statistic was the most accurate statistic, and the CLC, ICL-BIC, and aVLMR showed limited utility. However, none of these statistics were accurate for small samples (n = 500).     

Determining the Number of Latent Classes in Single- and Multiphase Growth Mixture Models

Stage-sequential (or multiphase) growth mixture models are useful for delineating potentially different growth processes across multiple phases over time and for determining whether latent subgroups exist within a population. These models are increasingly important as social behavioral scientists are interested in better understanding change processes across distinctively different phases, such as before and after an intervention. One of the less understood issues related to the use of growth mixture models is how to decide on the optimal number of latent classes. The performance of several traditionally used information criteria for determining the number of classes is examined through a Monte Carlo simulation study in single- and multiphase growth mixture models. For thorough examination, the simulation was carried out in 2 perspectives: the models and the factors. The simulation in terms of the models was carried out to see the overall performance of the information criteria within and across the models, whereas the simulation in terms of the factors was carried out to see the effect of each simulation factor on the performance of the information criteria holding the other factors constant. The findings not only support that sample size adjusted Bayesian Information Criterion would be a good choice under more realistic conditions, such as low class separation, smaller sample size, or missing data, but also increase understanding of the performance of information criteria in single- and multiphase growth mixture models.     

Fitting Structural Equation Model Trees and Latent Growth Curve Mixture Models in Longitudinal Designs: The Influence of Model Misspecification

When conducting longitudinal research, the investigation of between-individual differences in patterns of within-individual change can provide important insights. In this article, we use simulation methods to investigate the performance of a model-based exploratory data mining technique—structural equation model trees (SEM trees; Brandmaier, Oertzen, McArdle, & Lindenberger, 2013)—as a tool for detecting population heterogeneity. We use a latent-change score model as a data generation model and manipulate the precision of the information provided by a covariate about the true latent profile as well as other factors, including sample size, under the possible influences of model misspecifications. Simulation results show that, compared with latent growth curve mixture models, SEM trees might be very sensitive to model misspecification in estimating the number of classes. This can be attributed to the lower statistical power in identifying classes, resulting from smaller differences of parameters prescribed by the template model between classes.     

A Multilevel Mixture IRT Framework for Modeling Response Times as Predictors or Indicators of Response Engagement in IRT Models

Disengaged item responses pose a threat to the validity of the results provided by large-scale assessments. Several procedures for identifying disengaged responses on the basis of observed response times have been suggested, and item response theory (IRT) models for response engagement have been proposed. We outline that response time-based procedures for classifying response engagement and IRT models for response engagement are based on common ideas, and we propose the distinction between independent and dependent latent class IRT models. In all IRT models considered, response engagement is represented by an item-level latent class variable, but the models assume that response times either reflect or predict engagement. We summarize existing IRT models that belong to each group and extend them to increase their flexibility. Furthermore, we propose a flexible multilevel mixture IRT framework in which all IRT models can be estimated by means of marginal maximum likelihood. The framework is based on the widespread Mplus software, thereby making the procedure accessible to a broad audience. The procedures are illustrated on the basis of publicly available large-scale data. Our results show that the different IRT models for response engagement provided slightly different adjustments of item parameters of individuals’ proficiency estimates relative to a conventional IRT model.     

Minimizing the Influence of Item Parameter Estimation Errors in Test Development: A Comparison of Three Selection Procedures

In test development, item response theory (IRT) is a method to determine the amount of information that each item (i.e., item information function) and combination of items (i.e., test information function) provide in the estimation of an examinee's ability. Studies investigating the effects of item parameter estimation errors over a range of ability have demonstrated an overestimation of information when the most discriminating items are selected (i.e., item selection based on maximum information). In the present study, the authors examined the influence of item parameter estimation errors across 3 item selection methods—maximum no target, maximum target, and theta maximum—using the 2- and 3-parameter logistic IRT models. Tests created with the maximum no target and maximum target item selection procedures consistently overestimated the test information function. Conversely, tests created using the theta maximum item selection procedure yielded more consistent estimates of the test information function and, at times, underestimated the test information function. Implications for test development are discussed.     

Combined Approach to Multi-Informant Data Using Latent Factors and Latent Classes: Trifactor Mixture Model

Although collecting data from multiple informants is highly recommended, methods to model the congruence and incongruence between informants are limited. Bauer and colleagues suggested the trifactor model that decomposes the variances into common factor, informant perspective factors, and item-specific factors. This study extends their work to the trifactor mixture model that combines the trifactor model and the mixture model. This combined approach allows researchers to investigate the common and unique perspectives of multiple informants on targets using latent factors and simultaneously take into account potential heterogeneity of targets using latent classes. We demonstrate this model using student self-rated and teacher-rated academic behaviors (N = 24,094). Model specification and testing procedures are explicated in detail. Methodological and practical issues in conducting the trifactor mixture analysis are discussed.     

Examining Population Heterogeneity in Finite Mixture Settings Using Latent Variable Modeling

A latent variable modeling procedure for examining whether a studied population could be a mixture of 2 or more latent classes is discussed. The approach can be used to evaluate a single-class model vis-à-vis competing models of increasing complexity for a given set of observed variables without making any assumptions about their within-class interrelationships. The method is helpful in the initial stages of finite mixture analyses to assess whether models with 2 or more classes should be subsequently considered as opposed to a single-class model. The discussed procedure is illustrated with a numerical example.     

A Unified Latent Growth Curve Model

Applying item response theory models to repeated observations has demonstrated great promise in developmental research. By allowing the researcher to take account of the characteristics of both item response and measurement error in longitudinal trajectory analysis, it improves the reliability and validity of latent growth curve analysis. This has enabled the study, to differentially weigh individual items and examine developmental stability and change over time, to propose a comprehensive modeling framework, combining a measurement model with a structural model. Despite a large number of components requiring attention, this study focuses on model formulation, evaluates the performance of the estimators of model parameters, incorporates prior knowledge from Bayesian analysis, and applies the model using an illustrative example. It is hoped that this fundamental study can demonstrate the breadth of this unified latent growth curve model.     

A Note on the Use of Mixture Models for Individual Prediction

Mixture models capture heterogeneity in data by decomposing the population into latent subgroups, each of which is governed by its own subgroup-specific set of parameters. Despite the flexibility and widespread use of these models, most applications have focused solely on making inferences for whole or subpopulations, rather than individual cases. This article presents a general framework for computing marginal and conditional predicted values for individuals using mixture model results. These predicted values can be used to characterize covariate effects, examine the fit of the model for specific individuals, or forecast future observations from previous ones. Two empirical examples are provided to demonstrate the usefulness of individual predicted values in applications of mixture models. The first example examines the relative timing of initiation of substance use using a multiple event process survival mixture model, whereas the second example evaluates changes in depressive symptoms over adolescence using a growth mixture model.