Modeling predictors of latent classes in regression mixture models

Further exploration of the effects of time-varying covariate in growth mixture models with nonlinear trajectories

Growth mixture modeling (GMM) is an analytical tool for identifying multiple unobserved sub-populations in longitudinal processes. In particular, it describes change patterns within each latent sub-population and investigates between-individual differences in within-individual change for each sub-group. A key research interest in using GMMs is examining how covariates influence the heterogeneity in change patterns. Liu & Perera (2022b) extended mixture-of-experts (MoE) models, which primarily focus on time-invariant covariates, to allow covariates to account for both within-group and between-group differences and investigate the heterogeneity in nonlinear trajectories. The present study further extends Liu & Perera, 2022b by examining the effects of time-varying covariates (TVCs) on trajectory heterogeneity. Specifically, we propose methods to decompose a TVC into an initial trait (the baseline value of the TVC) and a set of temporal states (interval-specific slopes or changes of the TVC). The initial trait is allowed to account for within-group differences in growth factors of trajectories (i.e., baseline effect), while the temporal states are allowed to impact observed values of a longitudinal process (i.e., temporal effects). We evaluate the proposed models using a simulation study and real-world data analysis. The simulation study demonstrates that the proposed models are capable of separating trajectories into several clusters and generally producing unbiased and accurate estimates with target coverage probabilities. The proposed models reveal the heterogeneity in initial trait and temporal states of reading ability across latent classes of students' mathematics performance. Additionally, the baseline and temporal effects on mathematics development of reading ability are also heterogeneous across the clusters of students.

Covariate inclusion in factor mixture modeling: Evaluating one-step and three-step approaches under model misspecification and overfitting

Factor mixture modeling (FMM) has been increasingly used in behavioral and social sciences to examine unobserved population heterogeneity. Covariates (e.g., gender, race) are often included in FMM to help understand the formation and characterization of latent subgroups or classes. This Monte Carlo simulation study evaluated the performance of one-step and three-step approaches to covariate inclusion across three scenarios, i.e., correct specification (study 1), model misspecification (study 2), and model overfitting (study 3), in terms of direct covariate effects on factors. Results showed that the performance of these two approaches was comparable when class separation was large and the specification of covariate effect was correct. However, one-step FMM had better class enumeration than the three-step approach when class separation was poor, and was more robust to the misspecification or overfitting concerning direct covariate effects. Recommendations regarding covariate inclusion approaches are provided herein depending on class separation and sample size. Large sample size (1000 or more) and the use of sample size-adjusted BIC (saBIC) in class enumeration are recommended.

Characterizing heterogeneity among people who use cannabis for medicinal reasons: A latent class analysis of a nationally representative Canadian sample

BACKGROUND

Many individuals who use cannabis report doing so for medicinal reasons. Few studies have explored heterogeneity within this population, which may be important to inform targeted interventions. This study used latent class analysis to identify subgroups of people who use cannabis for medicinal reasons and their sociodemographic and cannabis-risk-related correlates.

METHOD

Data were drawn from the 2019 Canadian Alcohol and Drugs Survey, which is a representative survey of Canadians ages 15 years and older. Data from 814 individuals reporting past-year use of cannabis for medicinal or mixed medicinal and non-medicinal reasons were included. Latent class analysis was conducted with forms of cannabis used, cannabis use frequency, concurrent non-medicinal cannabis use, and the medical conditions and symptoms cannabis was used to manage as indicators.

RESULTS

Four distinct latent classes of medicinal cannabis use were identified: a non-daily cannabis flower for mental health and sleep class (39.56% of the sample), a non-daily cannabis flower for pain class (26.41% of the sample), a non-daily cannabis oil for physical health class (20.15% of the sample), and a daily multi-form cannabis for mental health and non-medical reasons class (13.88% of the sample). Sociodemographic factors and risk level for cannabis-related harms were associated with latent class membership.

CONCLUSIONS

Results of this study reveal considerable heterogeneity among people reporting medicinal cannabis use and suggest that the distinct patterns of cannabis use behaviors and motives observed may be important for understanding risk for cannabis-related harms in this population. Findings underscore a need for harm reduction interventions tailored toward specific patterns of medicinal cannabis use.

Evaluating the Quality of Classification in Mixture Model Simulations

The purpose of this study was to evaluate the degree of classification quality in the basic latent class model when covariates are either included or are not included in the model. To accomplish this task, Monte Carlo simulations were conducted in which the results of models with and without a covariate were compared. Based on these simulations, it was determined that models without a covariate better predicted the number of classes. These findings in general supported the use of the popular three-step approach; with its quality of classification determined to be more than 70% under various conditions of covariate effect, sample size, and quality of indicators. In light of these findings, the practical utility of evaluating classification quality is discussed relative to issues that applied researchers need to carefully consider when applying latent class models.

An Unusual College Experience: 16-Month Trajectories of Depressive Symptoms and Anxiety among Chinese New Undergraduate Students of 2019 during the COVID-19 Pandemic

BACKGROUND

This study examines the trajectories of the mental health conditions of 13,494 new undergraduate students who enrolled in 2019 in China from the beginning of the pandemic to the local recurrence of the pandemic, and found factors which may be associated with diverse trajectories.

METHODS

The trajectories of depression-anxiety outcomes were modeled using the growth mixture model. The multinomial logistic regression model was used to identify variables associated with different trajectory groups.

RESULTS

Both depression and anxiety in the new college students slightly increased during the 16-month period. The slopes of depression and anxiety were lower after the local outbreak. From the trajectories of depression and anxiety, five heterogeneous groups were identified: low-stable (64.3%), moderate-increased (18.2%), high-stable (11.1%), recovery (4.5%), and rapid-increased (1.8%). Environmental, somatic, and social factors were used to differentiate the low-stable group from the other groups. We found that college students with female gender, more conflict with parents, and feelings of loneliness during the pandemic were more likely to enter a high stability trajectory compared to a recovery trajectory.

CONCLUSION

Most participants showed a stable mental health status, while others experienced deteriorating or chronic mental health problems, especially those who had sleep disturbances, less social support before the pandemic, or conflicts with parents during the pandemic. These students may need additional support and monitoring from college mental health providers to improve their wellbeing.

Evaluating Covariate Effects on ESM Measurement Model Changes with Latent Markov Factor Analysis: A Three-Step Approach

Invariance of the measurement model (MM) between subjects and within subjects over time is a prerequisite for drawing valid inferences when studying dynamics of psychological factors in intensive longitudinal data. To conveniently evaluate this invariance, latent Markov factor analysis (LMFA) was proposed. LMFA combines a latent Markov model with mixture factor analysis: The Markov model captures changes in MMs over time by clustering subjects' observations into a few states and state-specific factor analyses reveal what the MMs look like. However, to estimate the model, Vogelsmeier, Vermunt, van Roekel, and De Roover (2019) introduced a one-step (full information maximum likelihood; FIML) approach that is counterintuitive for applied researchers and entails cumbersome model selection procedures in the presence of many covariates. In this paper, we simplify the complex LMFA estimation and facilitate the exploration of covariate effects on state memberships by splitting the estimation in three intuitive steps: (1) obtain states with mixture factor analysis while treating repeated measures as independent, (2) assign observations to the states, and (3) use these states in a discrete- or continuous-time latent Markov model taking into account classification errors. A real data example demonstrates the empirical value.

Tailoring dissemination strategies to increase evidence-informed policymaking for opioid use disorder treatment: study protocol

BACKGROUND

Policy is a powerful tool for systematically altering healthcare access and quality, but the research to policy gap impedes translating evidence-based practices into public policy and limits widespread improvements in service and population health outcomes. The US opioid epidemic disproportionately impacts Medicaid members who rely on publicly funded benefits to access evidence-based treatment including medications for opioid use disorder (MOUD). A myriad of misaligned policies and evidence-use behaviors by policymakers across federal agencies, state Medicaid agencies, and managed care organizations limit coverage of and access to MOUD for Medicaid members. Dissemination strategies that improve policymakers' use of current evidence are critical to improving MOUD benefits and reducing health disparities. However, no research describes key determinants of Medicaid policymakers' evidence use behaviors or preferences, and few studies have examined data-driven approaches to developing dissemination strategies to enhance evidence-informed policymaking. This study aims to identify determinants and intermediaries that influence policymakers' evidence use behaviors, then develop and test data-driven tailored dissemination strategies that promote MOUD coverage in benefit arrays.

METHODS

Guided by the Exploration, Preparation, Implementation, and Sustainment (EPIS) framework, we will conduct a national survey of state Medicaid agency and managed care organization policymakers to identify determinants and intermediaries that influence how they seek, receive, and use research in their decision-making processes. We will use latent class methods to empirically identify subgroups of agencies with distinct evidence use behaviors. A 10-step dissemination strategy development and specification process will be used to tailor strategies to significant predictors identified for each latent class. Tailored dissemination strategies will be deployed to each class of policymakers and assessed for their acceptability, appropriateness, and feasibility for delivering evidence about MOUD benefit design.

DISCUSSION

This study will illuminate key determinants and intermediaries that influence policymakers' evidence use behaviors when designing benefits for MOUD. This study will produce a critically needed set of data-driven, tailored policy dissemination strategies. Study results will inform a subsequent multi-site trial measuring the effectiveness of tailored dissemination strategies on MOUD benefit design and implementation. Lessons from dissemination strategy development will inform future research about policymakers' evidence use preferences and offer a replicable process for tailoring dissemination strategies.

Refuting the myth of a 'tsunami' of mental ill-health in populations affected by COVID-19: evidence that response to the pandemic is heterogeneous, not homogeneous

BACKGROUND

The current study argues that population prevalence estimates for mental health disorders, or changes in mean scores over time, may not adequately reflect the heterogeneity in mental health response to the COVID-19 pandemic within the population.

METHODS

The COVID-19 Psychological Research Consortium (C19PRC) Study is a longitudinal, nationally representative, online survey of UK adults. The current study analysed data from its first three waves of data collection: Wave 1 (March 2020, N = 2025), Wave 2 (April 2020, N = 1406) and Wave 3 (July 2020, N = 1166). Anxiety-depression was measured using the Patient Health Questionnaire Anxiety and Depression Scale (a composite measure of the PHQ-9 and GAD-7) and COVID-19-related posttraumatic stress disorder (PTSD) with the International Trauma Questionnaire. Changes in mental health outcomes were modelled across the three waves. Latent class growth analysis was used to identify subgroups of individuals with different trajectories of change in anxiety-depression and COVID-19 PTSD. Latent class membership was regressed on baseline characteristics.

RESULTS

Overall prevalence of anxiety-depression remained stable, while COVID-19 PTSD reduced between Waves 2 and 3. Heterogeneity in mental health response was found, and hypothesised classes reflecting (i) stability, (ii) improvement and (iii) deterioration in mental health were identified. Psychological factors were most likely to differentiate the improving, deteriorating and high-stable classes from the low-stable mental health trajectories.

CONCLUSIONS

A low-stable profile characterised by little-to-no psychological distress ('resilient' class) was the most common trajectory for both anxiety-depression and COVID-19 PTSD. Monitoring these trajectories is necessary moving forward, in particular for the ~30% of individuals with increasing anxiety-depression levels.

Refuting the myth of a 'tsunami' of mental ill-health in populations affected by COVID-19: evidence that response to the pandemic is heterogeneous, not homogeneous

BACKGROUND

The current study argues that population prevalence estimates for mental health disorders, or changes in mean scores over time, may not adequately reflect the heterogeneity in mental health response to the COVID-19 pandemic within the population.

METHODS

The COVID-19 Psychological Research Consortium (C19PRC) Study is a longitudinal, nationally representative, online survey of UK adults. The current study analysed data from its first three waves of data collection: Wave 1 (March 2020, N = 2025), Wave 2 (April 2020, N = 1406) and Wave 3 (July 2020, N = 1166). Anxiety-depression was measured using the Patient Health Questionnaire Anxiety and Depression Scale (a composite measure of the PHQ-9 and GAD-7) and COVID-19-related posttraumatic stress disorder (PTSD) with the International Trauma Questionnaire. Changes in mental health outcomes were modelled across the three waves. Latent class growth analysis was used to identify subgroups of individuals with different trajectories of change in anxiety-depression and COVID-19 PTSD. Latent class membership was regressed on baseline characteristics.

RESULTS

Overall prevalence of anxiety-depression remained stable, while COVID-19 PTSD reduced between Waves 2 and 3. Heterogeneity in mental health response was found, and hypothesised classes reflecting (i) stability, (ii) improvement and (iii) deterioration in mental health were identified. Psychological factors were most likely to differentiate the improving, deteriorating and high-stable classes from the low-stable mental health trajectories.

CONCLUSIONS

A low-stable profile characterised by little-to-no psychological distress ('resilient' class) was the most common trajectory for both anxiety-depression and COVID-19 PTSD. Monitoring these trajectories is necessary moving forward, in particular for the ~30% of individuals with increasing anxiety-depression levels.

Assessing Differential Effects of Somatic Amplification to Positive Affect in Midlife and Late Adulthood-A Regression Mixture Approach

This study aims to provide an empirical demonstration of a novel method, regression mixture model, by examining differential effects of somatic amplification to positive affect and identifying the predictors that contribute to the differential effects. Data derived from the second wave of Midlife in the United States. The analytic sample consisted of 1,766 adults aged from 33 to 84 years. Regression mixture models were fitted using Mplus 7.4, and a two-step model-building approach was adopted. Three latent groups were identified consisting of a maladaptive (32.1%), a vulnerable (62.5%), and a resilient (5.4%) group. Six covariates (i.e., age, education level, positive relations with others, purpose in life, depressive symptoms, and physical health) significantly predicted the latent class membership in the regression mixture model. The study demonstrated the regression mixture model to be a flexible and efficient statistical tool in assessing individual differences in response to adversity and identifying resilience factors, which contributes to aging research.

Trajectories of change in internalizing symptoms during the COVID-19 pandemic: A longitudinal population-based study

BACKGROUND

Longitudinal data indicates that the mental health of the general population may not have been as badly affected by the COVID-19 pandemic as some had feared. Most studies examining change in mental health during the pandemic have assumed population homogeneity which may conceal evidence of worsening mental health for some. In this study, we applied a heterogeneous perspective to determine if there were distinct groups in the population characterised by different patterns of change in internalizing symptoms during the pandemic.

METHODS

Self-report data were collected from a nationally representative sample of Irish adults (N = 1041) at four time-points between April and December 2020.

RESULTS

In the entire sample, mean levels of internalizing symptoms significantly declined from March to December 2020. However, we identified four distinct groups with different patterns of change. The most common response was 'Resilience' (66.7%), followed by 'Improving' (17.9%), 'Worsening' (11.3%), and 'Sustained' (4.1%). Belonging to the 'Worsening' class was associated with younger age, city dwelling, current and past treatment for a mental health problem, higher levels of empathy, and higher levels of loneliness.

LIMITATIONS

Sample attrition was relatively high and although this was managed using robust statistical methods, bias associated with non-responses cannot be entirely ruled out.

CONCLUSION

The majority of adults experienced no change, or an improvement in internalizing symptoms during the pandemic, and a relatively small proportion of adults experienced a worsening of internalizing symptoms. Limited public mental health resources should be targeted toward helping these at-risk individuals.

Latent class analysis of use frequencies for multiple tobacco products in US adults

A persistent challenge is characterizing patterns of tobacco use in terms of product combinations and frequency. Using Wave 4 (2016-17) Population Assessment of Tobacco and Health Study adult data, we conducted latent class analyses (LCA) of past 30-day frequency of use for 9 tobacco products. One-step LCA with joint multinomial logistic regression models compared sociodemographic factors between users (n = 13,716) and non-users (n = 17,457), and between latent classes of users. We accounted for survey design and weights. Our analyses identified 6 classes: in addition to non-users (C0: 75.7%), we found 5 distinct latent classes of users: daily exclusive cigarette users (C1: 15.5%); occasional cigarette and polytobacco users (C2: 3.8%); frequent e-product and occasional cigarette users (C3: 2.2%); daily smokeless tobacco (SLT) and infrequent cigarette users (C4: 2.0%); and occasional cigar users (C5: 0.8%). Compared to C1: C2 and C3 had higher odds of being male (versus female), younger (especially 18-24 versus 55 years), and having higher education; C2 had higher, while C3 and C4 had lower, odds of being a racial/ethnic minority (versus Non-Hispanic White); C4 and C5 had much higher odds of being male (versus female) and heterosexual (versus sexual minority) and having higher income; and C5 had higher odds of college or more education. We identified three classes of daily or frequent users of a primary product (cigarettes, SLT or e-products) and two classes of occasional users (cigarettes, cigars and polytobacco). Sociodemographic differences in class membership may influence tobacco-related health disparities associated with specific patterns of use.

Bayesian approaches to variable selection in mixture models with application to disease clustering

In biomedical research, cluster analysis is often performed to identify patient subgroups based on patients' characteristics or traits. In the model-based clustering for identifying patient subgroups, mixture models have played a fundamental role in modeling. While there is an increasing interest in using mixture modeling for identifying patient subgroups, little work has been done in selecting the predictors that are associated with the class assignment. In this study, we develop and compare two approaches to perform variable selection in the context of a mixture model to identify important predictors that are associated with the class assignment. These two approaches are the one-step approach and the stepwise approach. The former refers to an approach in which clustering and variable selection are performed simultaneously in one overall model, whereas the latter refers to an approach in which clustering and variable selection are performed in two sequential steps. We considered both shrinkage prior and spike-and-slab prior to select the importance of variables. Markov chain Monte Carlo algorithms are developed to estimate the posterior distribution of the model parameters. Practical applications and simulation studies are carried out to evaluate the clustering and variable selection performance of the proposed models.

Latent classes of aggression and peer victimization: Measurement invariance and differential item functioning across sex, race-ethnicity, cohort, and study site

Peer victimization is common and linked to maladjustment. Prior research has typically identified four peer victimization subgroups: aggressors, victims, aggressive‐victims, and uninvolved. However, findings related to sex and racial‐ethnic differences in subgroup membership have been mixed. Using data collected in September of 2002 and 2003, this study conducted confirmatory latent class analysis of a racially‐ethnically diverse sample of 5415 sixth graders (49% boys; 50.6% Black; 20.9% Hispanic) representing two cohorts from 37 schools in four U.S. communities to replicate the four subgroups and evaluate measurement invariance of latent class indicators across cohort, sex, race‐ethnicity, and study site. Results replicated the four‐class solution and illustrated that sociodemographic differences in subgroup membership were less evident after accounting for differential item functioning.

Latent Class Mediation: A Comparison of Six Approaches

Latent class mediation modeling is designed to estimate the mediation effect when both the mediator and the outcome are latent class variables. We suggest using an adjusted one-step approach in which the latent class models for the mediator and the outcome are estimated first to decide on the number of classes, then the latent class models and the mediation model are jointly estimated. We present both an empirical demonstration and a simulation study to compare the performance of this one-step approach to a standard three-step approach with modal assignment (modal) and four different modern three-step approaches. Results from the study indicate that unadjusted modal, which ignores the classification errors of the latent class models, produced biased mediation effects. On the other hand, the adjusted one-step approach and the modern three-step approaches performed well with respect to bias for estimating mediation effects, regardless of measurement quality (i.e., model entropy) and latent class size. Among the three-step approaches we investigated, the maximum likelihood method with modal assignment and the BCH correction with robust standard error estimators are good alternatives to the adjusted one-step approach, given their unbiased standard error estimations.

Testing Measurement Invariance Across Unobserved Groups: The Role of Covariates in Factor Mixture Modeling

Factor mixture modeling (FMM) has been increasingly used to investigate unobserved population heterogeneity. This study examined the issue of covariate effects with FMM in the context of measurement invariance testing. Specifically, the impact of excluding and misspecifying covariate effects on measurement invariance testing and class enumeration was investigated via Monte Carlo simulations. Data were generated based on FMM models with (1) a zero covariate effect, (2) a covariate effect on the latent class variable, and (3) covariate effects on both the latent class variable and the factor. For each population model, different analysis models that excluded or misspecified covariate effects were fitted. Results highlighted the importance of including proper covariates in measurement invariance testing and evidenced the utility of a model comparison approach in searching for the correct specification of covariate effects and the level of measurement invariance. This approach was demonstrated using an empirical data set. Implications for methodological and applied research are discussed.

Health-related quality of life and opioid use disorder pharmacotherapy: A secondary analysis of a clinical trial

OBJECTIVE

To examine the health-related quality-of-life (HRQoL) of persons with opioid use disorder (OUD) seeking treatment in an inpatient detoxification or short-term residential setting; continuing treatment as outpatients.

METHODS

We conducted a secondary analysis of data from a clinical trial (N = 508) where participants were randomized to extended-release naltrexone or buprenorphine-naloxone for the prevention of opioid relapse. We used a generalized structural equation regression mixture model to identify associations of HRQoL (EQ-5D) trajectories, including latent characteristics, over the 24-week trial and 36-week follow-up period, among participants who reported HRQoL beyond baseline. This novel framework accounted for baseline and time-varying characteristics, while simultaneously identifying latent classes.

RESULTS

We identified two subpopulations: HRQoL "pharmacotherapy responsive" (82.3 %) and HRQoL "characteristic sensitive" (17.7 %). The pharmacotherapy responsive subpopulation was characterized by a shortterm HRQoL improvement and then stable HRQoL over time, and by a positive association between HRQoL and receiving pharmacotherapy in the past 30 days. The characteristic sensitive subpopulation was characterized by an initial improvement in HRQoL with a gradual decline over time, and no significant HRQoL response to pharmacotherapy. HRQoL changes over time in this subpopulation were more influenced by baseline demographic, socioeconomic, and psychosocial characteristics.

CONCLUSION

Our findings suggest that while HRQoL may be improved and sustained through targeted efforts to promote use of pharmacotherapy for many persons with OUD, an identifiable subpopulation may require additional services that address socioeconomic and psychosocial issues to achieve HRQoL benefits. Our analysis provides insight for improving individualized care for persons with opioid use disorder seeking treatment.

Trajectories of childhood anxiety disorders in two generations at high risk

BACKGROUND

The course of anxiety disorders during childhood is heterogeneous. In two generations at high or low risk, we described the course of childhood anxiety disorders and evaluated whether parent or grandparent major depressive disorder (MDD) predicted a persistent anxiety course.

METHODS

We utilized a multigenerational study (1982-2015), following children (second generation, G2) and grandchildren (third generation, G3) of generation 1 (G1) with either moderate/severe MDD or no psychiatric illness. Psychiatric diagnoses were based on diagnostic interviews. Using group-based trajectory models, we identified clusters of children with similar anxiety disorder trajectories (age 0-17).

RESULTS

We identified three primary trajectories in G2 (N = 275) and G3 (N = 118) cohorts: "no/low anxiety disorder" during childhood (G2 = 66%; G3 = 53%), "nonpersistent" with anxiety during part of childhood (G2 = 16%; G3 = 21%), and "persistent" (G2 = 18%; G3 = 25%). Childhood mood disorders and substance use disorders tended to be more prevalent in children in the persistent anxiety trajectory. In G2 children, parent MDD was associated with an increased likelihood of being in the persistent (84%) or nonpersistent trajectory (82%) versus no/low anxiety trajectory (62%). In G3 children, grandparent MDD, but not parent, was associated with an increased likelihood of being in the persistent (83%) versus nonpersistent (48%) and no/low anxiety (51%) trajectories.

CONCLUSION

Anxiety trajectories move beyond what is captured under binary, single time-point measures. Parent or grandparent history of moderate/severe MDD may offer value in predicting child anxiety disorder course, which could help clinicians and caregivers identify children needing increased attention and screening for other psychiatric conditions.

Measurement Invariance and Differential Item Functioning Across Gender Within a Latent Class Analysis Framework: Evidence From a High-Stakes Test for University Admission in Saudi Arabia

The main aim of the present study was to investigate the presence of Differential Item Functioning (DIF) using a latent class (LC) analysis approach. Particularly, we examined potential sources of DIF in relation to gender. Data came from 6,265 Saudi Arabia students, who completed a high-stakes standardized admission test for university entrance. The results from a Latent Class Analysis (LCA) revealed a three-class solution (i.e., high, average, and low scorers). Then, to better understand the nature of the emerging classes and the characteristics of the people who comprise them, we applied a new stepwise approach, using the Multiple Indicator Multiple Causes (MIMIC) model. The model identified both uniform and non-uniform DIF effects for several items across all scales of the test, although, for the majority of them, the DIF effect sizes were negligible. Findings from this study have important implications for both measurement quality and interpretation of the results. Particularly, results showed that gender is a potential source of DIF for latent class indicators; thus, it is important to include those direct effects in the latent class regression model, to obtain unbiased estimates not only for the measurement parameters but also of the structural parameters. Ignoring these effects might lead to misspecification of the latent classes in terms of both the size and the characteristics of each class, which in turn, could lead to misinterpretations of the obtained latent class results. Implications of the results for practice are discussed.

An overview of mixture modelling for latent evolutions in longitudinal data: Modelling approaches, fit statistics and software

The use of finite mixture modelling (FMM) is becoming increasingly popular for the analysis of longitudinal repeated measures data. FMMs assist in identifying latent classes following similar paths of temporal development. This paper aims to address the confusion experienced by practitioners new to these methods by introducing the various available techniques, which includes an overview of their interrelatedness and applicability. Our focus will be on the commonly used model-based approaches which comprise latent class growth analysis (LCGA), group-based trajectory models (GBTM), and growth mixture modelling (GMM). We discuss criteria for model selection, highlight often encountered challenges and unresolved issues in model fitting, showcase model availability in software, and illustrate a model selection strategy using an applied example.

Assessing the Robustness of Mixture Models to Measurement Noninvariance

Recent work reframes direct effects of covariates on items in mixture models as differential item functioning (DIF) and shows that, when present in the data but omitted from the fitted latent class model, DIF can lead to overextraction of classes. However, less is known about the effects of DIF on model performance-including parameter bias, classification accuracy, and distortion of class-specific response profiles-once the correct number of classes is chosen. First, we replicate and extend prior findings relating DIF to class enumeration using a comprehensive simulation study. In a second simulation study using the same parameters, we show that, while the performance of LCA is robust to the misspecification of DIF effects, it is degraded when DIF is omitted entirely. Moreover, the robustness of LCA to omitted DIF differs widely based on the degree of class separation. Finally, simulation results are contextualized by an empirical example.

Repeated measures regression mixture models

Regression mixture models are one increasingly utilized approach for developing theories about and exploring the heterogeneity of effects. In this study we aimed to extend the current use of regression mixtures to a repeated regression mixture method when repeated measures, such as diary-type and experience-sampling method, data are available. We hypothesized that additional information borrowed from the repeated measures would improve the model performance, in terms of class enumeration and accuracy of the parameter estimates. We specifically compared three types of model specifications in regression mixtures: (a) traditional single-outcome model; (b) repeated measures models with three, five, and seven measures; and (c) a single-outcome model with the average of seven repeated measures. The results showed that the repeated measures regression mixture models substantially outperformed the traditional and average single-outcome models in class enumeration, with less bias in the parameter estimates. For sample size, whereas prior recommendations have suggested that regression mixtures require samples of well over 1,000 participants, even for classes at a large distance from each other (classes with regression weights of .20 vs. .70), the present repeated measures regression mixture models allow for samples as low as 200 participants with an increased number (i.e., seven) of repeated measures. We also demonstrate an application of the proposed repeated measures approach using data from the Sleep Research Project. Implications and limitations of the study are discussed.

The Effects of Sample Size on the Estimation of Regression Mixture Models

Regression mixture models are a statistical approach used for estimating heterogeneity in effects. This study investigates the impact of sample size on regression mixture's ability to produce "stable" results. Monte Carlo simulations and analysis of resamples from an application data set were used to illustrate the types of problems that may occur with small samples in real data sets. The results suggest that (a) when class separation is low, very large sample sizes may be needed to obtain stable results; (b) it may often be necessary to consider a preponderance of evidence in latent class enumeration; (c) regression mixtures with ordinal outcomes result in even more instability; and (d) with small samples, it is possible to obtain spurious results without any clear indication of there being a problem.

A Semiparametric Approach for Modeling Not-Reached Items

Tests administered in studies of student achievement often have a certain amount of not-reached items (NRIs). The propensity for NRIs may depend on the proficiency measured by the test and on additional covariates. This article proposes a semiparametric model to study such relationships. Our model extends Glas and Pimentel's item response theory model for NRIs by (1) including a semiparametric representation of the distribution of the onset of NRIs, (2) modeling the relationships of NRIs with proficiency via a flexible multinomial logit regression, and (3) including additional covariates to predict NRIs. We show that Glas and Pimentel's and our model have close connections to event history analysis, thereby making it possible to apply tools developed in this context to the analysis of NRIs. Our model was applied to a timed low-stakes test of mathematics achievement. Our model fitted the data better than Glas and Pimentel's model, and allowed for a more fine-grained assessment of the onset of NRIs. The results of a simulation study showed that our model accurately recovered the relationships of proficiency and covariates with the onset of NRIs, and reduced bias in the estimates of item parameters, proficiency distributions, and covariate effects on proficiency.

Skew t Mixture Latent State-Trait Analysis: A Monte Carlo Simulation Study on Statistical Performance

This simulation study assessed the statistical performance of a skew t mixture latent state-trait (LST) model for the analysis of longitudinal data. The model aims to identify interpretable latent classes with class-specific LST model parameters. A skew t-distribution within classes is allowed to account for non-normal outcomes. This flexible function covers heavy tails and may reduce the risk of identifying spurious classes, e.g., in case of outliers. Sample size, number of occasions and skewness of the trait variable were varied. Generally, parameter estimation accuracy increases with increasing numbers of observations and occasions. Larger bias compared to other parameters occurs for parameters referring to the skew t-distribution and variances of the latent trait variables. Standard error estimation accuracy shows diffuse patterns across conditions and parameters. Overall model performance is acceptable for large conditions, even though none of the models is free from bias. The application of the skew t mixture model in case of large numbers of occasions and observations may be possible, but results should be treated with caution. Moreover, the skew t approach may be useful for other mixture models.

Evaluating the genetic susceptibility to peer reported bullying behaviors

Bullying is a significant public health concern with lasting impacts on youth. Although environmental risk factors for bullying have been well-characterized, genetic influences on bullying are not well understood. This study explored the role of genetics on early childhood bullying behavior. Participants were 561 children who participated in a longitudinal randomized control trial of a preventive intervention beginning in first grade who were present for the first grade peer nominations used to measure early childhood bullying and who provided genetic data during the age 19-21 year follow-up in the form of blood or saliva. Measures included a polygenic risk score (PRS) derived from a conduct disorder genome wide association study. Latent profile analysis identified three profiles of bullying behaviors during early childhood. Results suggest that the PRS was significantly associated with class membership, with individuals in the moderate bully-victim profile having the highest levels of the PRS and those in the high bully-victim profile having the lowest levels. This line of research has important implications for understanding genetic vulnerability to bullying in early childhood.

Multilevel Latent Profile Analysis With Covariates

Latent profile analysis (LPA) is a person-centered method commonly used in organizational research to identify homogeneous subpopulations of employees within a heterogeneous population. However, in the case of nested data structures, such as employees nested in work departments, multilevel techniques are needed. Multilevel LPA (MLPA) enables adequate modeling of subpopulations in hierarchical data sets. MLPA enables investigation of variability in the proportions of Level 1 profiles across Level 2 units, and of Level 2 latent classes based on the proportions of Level 1 latent profiles and Level 1 ratings, and the extent to which covariates drawn from the different hierarchical levels of the data affect the probability of a membership of a particular profile. We demonstrate the use of MLPA by investigating job characteristics profiles based on the job-demand-control-support (JDCS) model using data from 1,958 university employees clustered in 78 work departments. The implications of the results for organizational research are discussed, together with several issues related to the potential of MLPA for wider application.

Evaluation of Analysis Approaches for Latent Class Analysis with Auxiliary Linear Growth Model

This study investigated the performance of three selected approaches to estimating a two-phase mixture model, where the first phase was a two-class latent class analysis model and the second phase was a linear growth model with four time points. The three evaluated methods were (a) one-step approach, (b) three-step approach, and (c) case-weight approach. As a result, some important results were demonstrated. First, the case-weight and three-step approaches demonstrated higher convergence rate than the one-step approach. Second, it was revealed that case-weight and three-step approaches generally did better in correct model selection than the one-step approach. Third, it was revealed that parameters were similarly recovered well by all three approaches for the larger class. However, parameter recovery for the smaller class differed between the three approaches. For example, the case-weight approach produced constantly lower empirical standard errors. However, the estimated standard errors were substantially underestimated by the case-weight and three-step approaches when class separation was low. Also, bias was substantially higher for the case-weight approach than the other two approaches.

Fitting latent variable mixture models

Latent variable mixture models (LVMMs) are models for multivariate observed data from a potentially heterogeneous population. The responses on the observed variables are thought to be driven by one or more latent continuous factors (e.g. severity of a disorder) and/or latent categorical variables (e.g., subtypes of a disorder). Decomposing the observed covariances in the data into the effects of categorical group membership and the effects of continuous trait differences is not trivial, and requires the consideration of a number of different aspects of LVMMs. The first part of this paper provides the theoretical background of LVMMs and emphasizes their exploratory character, outlines the general framework together with assumptions and necessary constraints, highlights the difference between models with and without covariates, and discusses the interrelation between the number of classes and the complexity of the within-class model as well as the relevance of measurement invariance. The second part provides a growth mixture modeling example with simulated data and covers several practical issues when fitting LVMMs.

A Comparison of Methods for Uncovering Sample Heterogeneity: Structural Equation Model Trees and Finite Mixture Models

Although finite mixture models have received considerable attention, particularly in the social and behavioral sciences, an alternative method for creating homogeneous groups, structural equation model trees (Brandmaier, von Oertzen, McArdle, & Lindenberger, 2013), is a recent development that has received much less application and consideration. It is our aim to compare and contrast these methods for uncovering sample heterogeneity. We illustrate the use of these methods with longitudinal reading achievement data collected as part of the Early Childhood Longitudinal Study-Kindergarten Cohort. We present the use of structural equation model trees as an alternative framework that does not assume the classes are latent and uses observed covariates to derive their structure. We consider these methods as complementary and discuss their respective strengths and limitations for creating homogeneous groups.