Multilevel Mixture Models Research Articles

Investigation of Specific Learning Disability and Testing Accommodations Based Differential Item Functioning Using a Multilevel Multidimensional Mixture Item Response Theory Model

The assessment of test data for the presence of differential item functioning (DIF) is a key component of instrument development and validation. Among the many methods that have been used successfully in such analyses is the mixture modeling approach. Using this approach to identify the presence of DIF has been touted as potentially superior for gaining insights into the etiology of DIF, as compared to using intact groups. Recently, researchers have expanded on this work to incorporate multilevel mixture modeling, for cases in which examinees are nested within schools. The current study further expands on this multilevel mixture modeling for DIF detection by using a multidimensional multilevel mixture model that incorporates multiple measured dimensions, as well as the presence of multiple subgroups in the population. This model was applied to a national sample of third-grade students who completed math and language tests. Results of the analysis demonstrate that the multidimensional model provides more complete information regarding the nature of DIF than do separate unidimensional models.

Perceptions of poverty attributions in Europe: a multilevel mixture model approach

The perception of the causes of poverty has long been recognized as a very important factor in the broader study of this social phenomenon. This study covers 15 European Union countries and considers three types of poverty attributions: individualistic, societal, and fatalistic. The individualistic view perception believes the poor are responsible for their situation, the societal perspective blames society for poverty and the fatalistic view considers poverty to be the result of bad luck or fate. A multilevel mixture model with three clusters of countries and six clusters of individuals was identified. Despite the generalization of the social explanations of poverty at the individual or micro level, there are also groups that emphasize more individualistic explanations, blaming the poor for their condition. At the country or macro level, the most developed cluster believes in the individualistic and fatalistic causes of poverty, whereas the least developed clusters explain poverty based on the injustices of society. There is diversity in the way these countries perceive poverty.

Does prison strain lead to prison misbehavior? An application of general strain theory to inmate misconduct

PurposeThis paper applies macro-micro General Strain Theory (GST) to predict prisoner misconduct. It is hypothesized that prison-based strain will adversely affect inmates and increase their misconduct. MethodsData from a large southern state are used to examine how environmental strain measured at the prison level influence inmates’ violent misconduct. Analyses will include a group-based trajectory model on monthly counts of violent misconduct for the first three years of incarceration and assess whether the strain of the environment (using a latent measure of prison deprivation as a proxy for environmental strain) distinguishes between trajectories. The analysis will employ finite multilevel mixture modeling with environmental strain as both a within- and between-class predictor, but at the prison level. ResultsFindings suggest that prison strain is positively associated with prison misconduct; however, the magnitude of the effect varies across distinct inmate trajectories. ConclusionsTheoretical and practical implications are highlighted as are directions for future research.

The Impact of Ignoring a Level of Nesting Structure in Multilevel Mixture Model

Mixture modeling has gained more attention among practitioners and statisticians in recent years. However, when researchers analyze their data using finite mixture model (FMM), some may assume that the units are independent of each other even though it may not always be the case. This article used simulation studies to examine the impact of ignoring a higher nesting structure in multilevel mixture models. Results indicate that the misspecification results in lower classification accuracy of individuals, less accurate fixed effect estimates, inflation of lower level variance estimates, and less accurate standard error estimates in each subpopulation, the latter result of which in turn affects the accuracy of tests of significance for the fixed effects. The magnitude of the intraclass correlation (ICC) coefficient has a substantial impact. The implication for applied researchers is that it is important to model the multilevel data structure in mixture modeling.

Contextual and individual-level predictors of abused children's reentry into out-of-home care: A multilevel mixture survival analysis

Objectives This study examined the effects of individual and contextual factors on reentry into out-of-home care among children who were discharged from child protective services in fiscal year 2004–2005. The objectives were to: (1) examine individual and contextual factors associated with reentry, (2) explore whether there are meaningful groups of youth who differ in terms of risk for reentry, and (3) determine whether relatively homogeneous clusters of child welfare agencies, based on contextual characteristics, differ significantly in terms of the reentry rates of the children whom they serve. Method The study design involved a multilevel longitudinal analysis of administrative data based on an exit cohort. Two Cox proportional hazards multilevel mixture models were tested. The first model included multiple individual level predictors and no agency level predictors. The second model included both levels of predictors. Results The results of multilevel Cox regression mixture modeling indicated that at the individual level, younger age, being placed in out-of-home care because of neglect and having physical, health problems corresponded to a decreased likelihood for reentry. At the agency level, lower average expenditures per child and contracting out case management services were associated with faster reentry into out-of-home care. Conclusions This study demonstrates that children who reenter out-of-home care appear to be a homogeneous population and that reentry is associated with both contextual factors and individual characteristics. Practice implications The most important implication that can be drawn from the study findings is that reentry may be most effectively prevented by focusing on such factors at the organizational level as contracting out case management services and funding allocation. Child welfare agencies that are responsible for an array of services and decide to contract out case management should consider the use of performance-based contracts and emphasize and strengthen quality assurance approaches for contracted services. In addition, to compensate for lower funding allocated for children served in out-of-home care, child welfare workers should become more familiar with community resources and help connect families to these supports.

Are the sources of interest the same for everyone? Using multilevel mixture models to explore individual differences in appraisal structures

How does personality influence the relationship between appraisals and emotions? Recent research suggests individual differences in appraisal structures: people may differ in an emotion's appraisal pattern. We explored individual differences in interest's appraisal structure, assessed as the within-person covariance of appraisals with interest. People viewed images of abstract visual art and provided ratings of interest and of interest's appraisals (novelty–complexity and coping potential) for each picture. A multilevel mixture model found two between-person classes that reflected distinct within-person appraisal styles. For people in the larger class (68%), the novelty–complexity appraisal had a stronger effect on interest; for people in the smaller class (32%), the coping potential appraisal had a stronger effect. People in the larger class were significantly higher in appetitive traits related to novelty seeking (e.g., sensation seeking, openness to experience, and trait curiosity), suggesting that the appraisal classes have substantive meaning. We conclude by discussing the value of within-person mixture models for the study of personality and appraisal.

Examining How Context Changes Intervention Impact: The Use of Effect Sizes in Multilevel Mixture Meta-Analysis.

In describing the impact of an intervention, a single effect size, odds ratio, or other summary measure is often employed. This single measure is useful in calibrating the effect of one intervention against others, but it is less meaningful when the intervention displays variation in impact. A single intervention trial can show differential effects when subgroups respond differentially, when impact varies by environmental context, or when there is varying impact with different outcome measures or across follow-up time. This article presents a multilevel mixture modeling approach for meta-analyses that summarizes these sources of impact variation across trials and measured outcomes.

Using Multilevel Mixtures to Evaluate Intervention Effects in Group Randomized Trials

There is evidence to suggest that the effects of behavioral interventions may be limited to specific types of individuals, but methods for evaluating such outcomes have not been fully developed. This study proposes the use of finite mixture models to evaluate whether interventions, and, specifically, group randomized trials, impact participants with certain characteristics or levels of problem behaviors. This study uses latent classes defined by clustering of individuals based on the targeted behaviors and illustrates the model by testing whether a preventive intervention aimed at reducing problem behaviors affects experimental users of illicit substances differently than problematic substance users or those individuals engaged in more serious problem behaviors. An illustrative example is used to demonstrate the identification of latent classes, specification of random effects in a multilevel mixture model, independent validation of latent classes, and the estimation of power for the proposed models to detect intervention effects. This study proposes specific steps for the estimation of multilevel mixture models and their power and suggests that this model can be applied more broadly to understand the effectiveness of interventions.

Mixture models with multiple levels, with application to the analysis of multifactor gene expression data

Model-based clustering is a popular tool for summarizing high-dimensional data. With the number of high-throughput large-scale gene expression studies still on the rise, the need for effective data- summarizing tools has never been greater. By grouping genes according to a common experimental expression profile, we may gain new insight into the biological pathways that steer biological processes of interest. Clustering of gene profiles can also assist in assigning functions to genes that have not yet been functionally annotated. In this paper, we propose 2 model selection procedures for model-based clustering. Model selection in model-based clustering has to date focused on the identification of data dimensions that are relevant for clustering. However, in more complex data structures, with multiple experimental factors, such an approach does not provide easily interpreted clustering outcomes. We propose a mixture model with multiple levels, , that provides sparse representations both "within" and "between" cluster profiles. We explore various flexible "within-cluster" parameterizations and discuss how efficient parameterizations can greatly enhance the objective interpretability of the generated clusters. Moreover, we allow for a sparse "between-cluster" representation with a different number of clusters at different levels of an experimental factor of interest. This enhances interpretability of clusters generated in multiple-factor contexts. Interpretable cluster profiles can assist in detecting biologically relevant groups of genes that may be missed with less efficient parameterizations. We use our multilevel mixture model to mine a proliferating cell line expression data set for annotational context and regulatory motifs. We also investigate the performance of the multilevel clustering approach on several simulated data sets.

Psychiatric Consultation Record Retrieval Using Scenario-Based Representation and Multilevel Mixture Model

Psychiatric consultation record retrieval attempts to help people to efficiently and effectively locate the consultation records relevant to their depressive problems. Consultation records can also make people aware that they are not alone, because many individuals have suffered from the same or similar problems. Additionally, people can understand how to alleviate their depressive symptoms according to recommendations from health professionals. To achieve this goal, this paper proposes the use of a scenario-based representation, i.e., a symptom-based structural representation, to capture the depressive symptoms and their semantic relations, such as cause-effect and temporal relations, for understanding users' queries clearly. The symptoms and relations are identified from semantic mining and analysis of consultation records. The multilevel mixture model is adopted to estimate the relevance of queries and consultation records based on the structural information. Experimental results show that the proposed approach achieves higher precision than does a term-based flat representation. An experiment is also conducted to examine the effect of error propagation resulting from incorrect identification of symptoms and relations. Experimental results demonstrate that combining different approaches can improve the retrieval robustness.

A discrete-time multilevel mixture model for event history data with long-term survivors, with an application to an analysis of contraceptive sterilization in Bangladesh.

Event history models typically assume that the entire population is at risk of experiencing the event of interest throughout the observation period. However, there will often be individuals, referred to as long-term survivors, who may be considered a priori to have a zero hazard throughout the study period. In this paper, a discrete-time mixture model is proposed in which the probability of long-term survivorship and the timing of event occurrence are modelled jointly. Another feature of event history data that often needs to be considered is that they may come from a population with a hierarchical structure. For example, individuals may be nested within geographical regions and individuals in the same region may have similar risks of experiencing the event of interest due to unobserved regional characteristics. Thus, the discrete-time mixture model is extended to allow for clustering in the likelihood and timing of an event within regions. The model is further extended to allow for unobserved individual heterogeneity in the hazard of event occurrence. The proposed model is applied in an analysis of contraceptive sterilization in Bangladesh. The results show that a woman's religion and education level affect her probability of choosing sterilization, but not when she gets sterilized. There is also evidence of community-level variation in sterilization timing, but not in the probability of sterilization.