PROC LCA: A SAS Procedure for Latent Class Analysis

Latent class analysis (LCA) is a statistical method used to identify a set of discrete, mutually exclusive latent classes of individuals based on their responses to a set of observed categorical variables. In multiple-group LCA, both the measurement part and structural part of the model can vary across groups, and measurement invariance across groups can be empirically tested. LCA with covariates extends the model to include predictors of class membership. In this article, we introduce PROC LCA, a new SAS procedure for conducting LCA, multiple-group LCA, and LCA with covariates. The procedure is demonstrated using data on alcohol use behavior in a national sample of high school seniors.     

A Tutorial in Bayesian Potential Outcomes Mediation Analysis

Statistical mediation analysis is used to investigate intermediate variables in the relation between independent and dependent variables. Causal interpretation of mediation analyses is challenging because randomization of subjects to levels of the independent variable does not rule out the possibility of unmeasured confounders of the mediator to outcome relation. Furthermore, commonly used frequentist methods for mediation analysis compute the probability of the data given the null hypothesis, which is not the probability of a hypothesis given the data as in Bayesian analysis. Under certain assumptions, applying the potential outcomes framework to mediation analysis allows for the computation of causal effects, and statistical mediation in the Bayesian framework gives indirect effects probabilistic interpretations. This tutorial combines causal inference and Bayesian methods for mediation analysis so the indirect and direct effects have both causal and probabilistic interpretations. Steps in Bayesian causal mediation analysis are shown in the application to an empirical example.     

Performance of the Grade of Membership Model Under a Variety of Sample Sizes,Group Size Ratios,and Differential Group Response Probabilities for Dichotomous Indicators

Social scientists are frequently interested in identifying latent subgroups within the population, based on a set of observed variables. One of the more common tools for this purpose is latent class analysis (LCA), which models a scenario involving k finite and mutually exclusive classes within the population. An alternative approach to this problem is presented by the grade of membership (GoM) model, in which individuals are assumed to have partial membership in multiple population subgroups. In this respect, it differs from the hard groupings associated with LCA. The current Monte Carlo simulation study extended on prior work on the GoM by investigating its ability to recover underlying subgroups in the population for a variety of sample sizes, latent group size ratios, and differing group response profiles. In addition, this study compared the performance of GoM with that of LCA. Results demonstrated that when the underlying process conforms to the GoM model form, the GoM approach yielded more accurate classification results than did LCA. In addition, it was found that the GoM modeling paradigm yielded accurate results for samples as small as 200, even when latent subgroups were very unequal in size. Implications for practice were discussed.     

A Comparison of Three-Step Approaches for Auxiliary Variables in Latent Class and Latent Profile Analysis

In this article, 3-step methods to include predictors and distal outcomes in commonly used mixture models are evaluated. Two Monte Carlo simulation studies were conducted to compare the pseudo class (PC), Vermunt’s (2010), and the Lanza, Tan, and Bray (LTB) 3-step approaches with respect to bias of parameter estimates in latent class analysis (LCA) and latent profile analysis (LPA) models with auxiliary variables. For coefficients of predictors of class membership, results indicated that Vermunt’s method yielded more accurate estimates for LCA and LPA compared to the PC method. With distal outcomes of latent classes and latent profiles, the LTB method produced the lowest relative bias of coefficient estimates and Type I error rates close to nominal levels.     

An Evaluation of Latent Growth Models for Propensity Score Matched Groups

Because random assignment is not possible in observational studies, estimates of treatment effects might be biased due to selection on observable and unobservable variables. To strengthen causal inference in longitudinal observational studies of multiple treatments, we present 4 latent growth models for propensity score matched groups, and evaluate their performance with a Monte Carlo simulation study. We found that the 4 models performed similarly with respect to model fit, bias of parameter estimates, Type I error, and power to test the treatment effect. To demonstrate a multigroup latent growth model with dummy treatment indicators, we estimated the effect of students changing schools during elementary school years on their reading and mathematics achievement, using data from the Early Childhood Longitudinal Study Kindergarten Cohort.     

Causal Inferences in the Campbellian Validity System

The purpose of the present paper is to critically examine causal inferences and internal validity as defined by Campbell and co‐workers. Several arguments are given against their counterfactual effect definition, and this effect definition should be considered inadequate for causal research in general. Moreover, their defined independence between internal and construct validity is not meaningful. An alternative causal inference and its validity are proposed, where the causal effect is defined in factual terms, and where the causal inference includes constructs.     

The impact of patterns of trauma exposure among low income children with and without histories of child maltreatment

Previous research has revealed a large prevalence of trauma experienced by children, creating high risk for the development of psychopathology. Research investigating the negative impacts of child maltreatment and other traumas has typically examined these experiences individually, controlling for co-occurring traumas, or has combined these experiences into a general variable of risk, thereby obscuring the complex relationships among environmental traumas and maltreatment. The current study expands on previous research by elucidating relationships between multiple contexts of overlapping traumas and maltreatment experienced by children, and by categorizing how these experiences join together to impact internalizing and externalizing symptomatology. Participants included 316 maltreated children and 269 nonmaltreated children (M age = 9.4, SD = 0.88) who attended a summer day camp research program for low-income children. Latent Class Analysis (LCA) identified three differential patterns of trauma exposure across children: 1) community violence and loss; 2) pervasive trauma; and 3) low trauma. Covariate analyses demonstrated that child maltreatment was significantly associated with class membership, suggesting that maltreated children were more likely to experience diverse traumas extending beyond their maltreatment experiences (pervasive trauma class). A two-way analysis of variance also demonstrated that trauma latent class membership and child maltreatment each represented unique predictors of internalizing and externalizing symptoms, with each having an independent effect on symptomatology. This investigation provides unique insight into the differential impact of patterns of trauma exposure and child maltreatment, providing support for further research and clinical practice addressing multiple levels of a child’s ecology.     

Conducting Confirmatory Latent Class Analysis Using Mplus

Latent class analysis (LCA) is an increasingly popular tool that researchers can use to identify latent groups in the population underlying a sample of responses to categorical observed variables. LCA is most commonly used in an exploratory fashion whereby no parameters are specified a priori. Although this exploratory approach is reasonable when very little prior research has been conducted in the area under study, it can be very limiting when much is already known about the variables and population. Confirmatory latent class analysis (CLCA) provides researchers with a tool for modeling and testing specific hypotheses about response patterns in the observed variables. CLCA is based on placing specific constraints on the parameters to reflect these hypotheses. The popular and easy-to-use latent variable modeling software package Mplus can be used to conduct a variety of CLCA types using these parameter constraints. This article focuses on the basic principles underlying the use of CLCA, and the Mplus programming code necessary for carrying it out.     

Prediction from Latent Classes: A Demonstration of Different Approaches to Include Distal Outcomes in Mixture Models

Including auxiliary variables such as antecedent and consequent variables in mixture models provides valuable insight in understanding the population heterogeneity embodied by a latent class variable. The model building process regarding how to include predictors/correlates and outcomes of the latent class variables into mixture models is an area of active research. As such, new methods of including these variables continue to emerge and best practices for the application of these methods in real data settings (including simple guidelines for choosing amongst them) are still not well established. This paper focuses on one type of auxiliary variable—distal outcomes—providing an overview of the methods currently available for estimating the effects of latent class membership on subsequent distal outcomes. We illustrate the recommended methods in the software packages Mplus and Latent Gold using a latent class model to capture population heterogeneity in students’ mathematics attitudes, linking latent class membership to two distal outcomes.     

儿童在平衡秤任务上的认知规则及评估方法

平衡秤任务是儿童高级认知策略研究非常著名的一种形式,Siegler提出的规则评估技术极大地推动了解题规则的相关研究,但在应用过程中显现了规则评估技术的不稳定性等诸多局限。目前,平衡秤任务的解题规则的研究方法发展迅速,基于潜变量的分析方法已克服了这些不足,在统计方面具有明显优势。因此,我国教育与心理研究者应关注使用潜在类别分析等方法解决高级认知策略研究中的各种问题。     

A Comparison of Approaches for Estimating Covariate Effects in Nonparametric Multilevel Latent Class Models

The inclusion of covariates improves the prediction of class memberships in latent class analysis (LCA). Several methods for examining covariate effects have been developed over the past decade; however, researchers have limited to the comparisons of the performance among these methods in cases of the single-level LCA. The present study investigated the performance of three different methods for examining covariate effects in a multilevel setting. We conducted a simulation to compare the performance of the three methods when level-1 and level-2 covariates were simultaneously incorporated into the nonparametric multilevel latent class model to predict latent class membership at each level. The simulation results revealed that the bias-adjusted three-step maximum likelihood method performed equally well as the one-step method when the sample sizes were sufficiently large and the latent classes were distinct from each other. However, the unadjusted three-step method significantly underestimated the level-1 covariate effect in most conditions.

     

Using causal models to bridge the divide between big data and educational theory

An extraordinary amount of data is becoming available in educational settings, collected from a wide range of Educational Technology tools and services. This creates opportunities for using methods from Artificial Intelligence and Learning Analytics (LA) to improve learning and the environments in which it occurs. And yet, analytics results produced using these methods often fail to link to theoretical concepts from the learning sciences, making them difficult for educators to trust, interpret and act upon. At the same time, many of our educational theories are difficult to formalise into testable models that link to educational data. New methodologies are required to formalise the bridge between big data and educational theory. This paper demonstrates how causal modelling can help to close this gap. It introduces the apparatus of causal modelling, and shows how it can be applied to well-known problems in LA to yield new insights. We conclude with a consideration of what causal modelling adds to the theory-versus-data debate in education, and extend an invitation to other investigators to join this exciting programme of research.

Practitioner notes

What is already known about this topic

• ‘Correlation does not equal causation’ is a familiar claim in many fields of research but increasingly we see the need for a causal understanding of our educational systems.
• Big data bring many opportunities for analysis in education, but also a risk that results will fail to replicate in new contexts.
• Causal inference is a well-developed approach for extracting causal relationships from data, but is yet to become widely used in the learning sciences.

What this paper adds

• An overview of causal modelling to support educational data scientists interested in adopting this promising approach.
• A demonstration of how constructing causal models forces us to more explicitly specify the claims of educational theories.
• An understanding of how we can link educational datasets to theoretical constructs represented as causal models so formulating empirical tests of the educational theories that they represent.

Implications for practice and/or policy

• Causal models can help us to explicitly specify educational theories in a testable format.
• It is sometimes possible to make causal inferences from educational data if we understand our system well enough to construct a sufficiently explicit theoretical model.
• Learning Analysts should work to specify more causal models and test their predictions, as this would advance our theoretical understanding of many educational systems.

     

Latent Class Analysis in Higher Education: An Illustrative Example of Pluralistic Orientation

Although used frequently in related fields such as K-12 education research, educational psychology, sociology, and social survey research, latent class analysis (LCA) has been infrequently used in higher education. This article provides higher education researchers with a pedagogical application of LCA to classify entering freshmen based on their pluralistic orientation. This study utilized data on entering freshmen at a racially diverse institution on the West coast. LCA was used to estimate latent profile probabilities, classify freshmen into latent classes, and relate latent class probabilities to covariates. The findings indicated that a four-class model was the best fitting model: high pluralistic orientation; high-disposition, low-skill; low-disposition, high-skill; and low pluralistic orientation. Similar to previous research, the findings indicated that the probability of being classified into one group versus the other was dependent upon a student’s race/ethnicity and intended major. This approach can aid college administrators in their program planning and targeted interventions around issues of diversity.     

Is there a Complex Trauma Experience typology for Australians experiencing extreme social disadvantage and low housing stability?

Traumatic childhood experiences predict many adverse outcomes in adulthood including Complex-PTSD. Understanding complex trauma within socially disadvantaged populations has important implications for policy development and intervention implementation. This paper examined the nature of complex trauma experienced by disadvantaged individuals using a latent class analysis (LCA) approach. Data were collected through the large-scale Journeys Home Study (N = 1682), utilising a representative sample of individuals experiencing low housing stability. Data on adverse childhood experiences, adulthood interpersonal trauma and relevant covariates were collected through interviews at baseline (Wave 1). Latent class analysis (LCA) was conducted to identify distinct classes of childhood trauma history, which included physical assault, neglect, and sexual abuse. Multinomial logistic regression investigated childhood relevant factors associated with class membership such as biological relationship of primary carer at age 14 years and number of times in foster care. Of the total sample (N = 1682), 99% reported traumatic adverse childhood experiences. The most common included witnessing of violence, threat/experience of physical abuse, and sexual assault. LCA identified six distinct childhood trauma history classes including high violence and multiple traumas. Significant covariate differences between classes included: gender, biological relationship of primary carer at age 14 years, and time in foster care. Identification of six distinct childhood trauma history profiles suggests there might be unique treatment implications for individuals living in extreme social disadvantage. Further research is required to examine the relationship between these classes of experience, consequent impact on adulthood engagement, and future transitions though homelessness.     

Using Propensity Score Analysis for Making Causal Claims in Research Articles

The central role of the propensity score analysis (PSA) in observational studies is for causal inference; as such, PSA is often used for making causal claims in research articles. However, there are still some issues for researchers to consider when making claims of causality using PSA results. This summary first briefly reviews PSA, followed by discussions of its effectiveness and limitations. Finally, a guideline of how to address these concerns is also provided for researchers to make appropriate causal claims using PSA results in their research articles.     

MIMIC Latent Class Analysis Model for Alcoholic Diagnosis

The multiple indicators multiple causes (MIMIC) latent class analysis (LCA) model is an excellent classification method when researchers cannot find a "gold standard" to classify participants. The MIMIC-LCA model includes features of a typical LCA model and also introduces a new relation between the latent class and covariates. In other words, a logistic regression type of analysis between participants' categorical latent status and their background information is added. Detailed statistical setups of the MIMIC-LCA model and algorithmic procedures are derived. The model features, parameter estimations, and model selections for MIMIC-LCA models are also presented. Specifically, the MIMIC-LCA model is estimated by a generalized expectation-maximization algorithm under the maximum likelihood frameworks. A substantive application of the MIMIC-LCA model in diagnosing alcoholics and, in particular, examining potential risk factors for alcoholism is demonstrated.     

Risk of re-report: A latent class analysis of infants reported for maltreatment

A key challenge facing child protective services (CPS) is identifying children who are at greatest risk of future maltreatment. This analysis examined a cohort of children with a first report to CPS during infancy, a vulnerable population at high risk of future CPS reports. Birth records of all infants born in California in 2006 were linked to CPS records; 23,871 infants remaining in the home following an initial report were followed for 5 years to determine if another maltreatment report occurred. Latent class analysis (LCA) was used to identify subpopulations of infants based on varying risks of re-report. LCA model fit was examined using the Bayesian information criterion, a likelihood ratio test, and entropy. Statistical indicators and interpretability suggested the four-class model best fit the data. A second LCA included infant re-report as a distal outcome to examine the association between class membership and the likelihood of re-report. In Class 1 and Class 2 (lowest risk), the probability of a re-report was 44%; in contrast, the probability in Class 4 (highest risk) was 78%. Two birth characteristics clustered in the medium- and highest-risk classes: lack of established paternity and delayed or absent prenatal care. Two risk factors from the initial report of maltreatment emerged as predictors of re-report in the highest-risk class: an initial allegation of neglect and a family history of CPS involvement involving older siblings. Findings suggest that statistical techniques can be used to identify families with a heightened risk of experiencing later CPS contact.     

Exploring the Utility of Background and Cognitive Variables in Explaining Latent Differential Item Functioning: An Example of the PISA 2009 Reading Assessment

Differential item functioning (DIF) may be caused by an interaction of multiple manifest grouping variables or unexplored manifest variables, which cannot be detected by conventional DIF detection methods that are based on a single manifest grouping variable. Such DIF may be detected by a latent approach using the mixture item response theory model and subsequently explained by multiple manifest variables. This study facilitates the interpretation of latent DIF with the use of background and cognitive variables. The PISA 2009 reading assessment and student survey are analyzed. Results show that members in manifest groups were not homogenously advantaged or disadvantaged and that a single manifest grouping variable did not suffice to be a proxy of latent DIF. This study also demonstrates that DIF items arising from the interaction of multiple variables can be effectively screened by the latent DIF analysis approach. Background and cognitive variables jointly well predicted latent class membership.     

Attitudes towards School,Teacher, and Classmates at Classroom and Individual Levels: An application of two‐level confirmatory factor analysis

Pupils' responses in Grade 6 to a 40‐item questionnaire originally constructed to reveal different school attitudes were re‐analysed using recently developed techniques for latent variable analysis of two‐level data. One aim was to test a model for investigation of classroom environment and another aim was to compare exploratory factor analysis and confirmatory factor analysis when applied at individual and class levels. When using confirmatory factor modelling a separation of the individual and class‐level influences on the between‐group matrix was obtained. At class level three factors could be justified: Teachers and Teaching, Social Relations in Classrooms and Work Atmosphere in Classrooms. We conclude that the present analysis encourages further use of this type of questionnaire when investigating pupils' attitudes in a large number of classes. Two‐level latent variable analysis is useful for comparing pupils' attitudes within and between classes     

Subtypes, severity, and structural stability of peer victimization: what does latent class analysis say?

This study uses latent class analysis (LCA) to empirically identify victimization groups during middle school. Approximately 2,000 urban, public middle school students (mean age in sixth grade = 11.57) reported on their peer victimization during the Fall and Spring semesters of their sixth, seventh, and eighth grades. Independent LCA analyses at each semester yielded 3 victim classes based on victimization degree rather than type (e.g., physical vs. relational). The most victimized class always represented the smallest proportion of the sample, decreasing from 20% in sixth grade to 6% by the end of eighth grade. This victimized class also always reported feeling less safe at school concurrently and more depressed than others 1 semester later, illustrating the validity of the LCA approach.