Covariance pattern mixture models: Eliminating random effects to improve convergence and performance

Early-Onset Trajectories of Emotional Dysregulation in Autistic Children

OBJECTIVES

Emotional dysregulation is a common and debilitating problem for autistic children and their families. However, we know little about early-onset patterns of dysregulation, associated risk factors, and child and family outcomes. We aimed to characterize trajectories of emotional dysregulation in an inception cohort of autistic preschoolers.

METHOD

Caregivers reported on the emotional dysregulation of 396 autistic children using the Aberrant Behavior Checklist (ABC) irritability and hyperactivity scales at 6 timepoints from shortly after ASD diagnosis (ages 2-4 years) to pre-adolescence (10-11 years). Covariance pattern mixture modeling was used to characterize the number and shape of latent dysregulation trajectories that best fit underlying data. Child and family correlates were measured at baseline and ages 10-11 years to characterize early risk factors and pre-adolescent profiles associated with distinct latent trajectories.

RESULTS

Three distinct trajectory classes best fit the data: persistently self-regulated (18% of sample); moderate and declining (54%), and persistently dysregulated (28%). Children classified in the persistently dysregulated trajectory lived with more depressed caregivers and in families reporting greater relationship problems and lower household incomes compared to lower-risk trajectories. Few associations were found with baseline child characteristics. Persistent dysregulation problems were associated with significantly worse child mental health and functional outcomes during pre-adolescent years.

CONCLUSION

Risk of persistent severe emotional dysregulation may be identifiable at time of early autism diagnosis. Diagnostic assessments should include contextual risk factors and links to evidence-based family supports and interventions.

Trajectories of depressive symptoms and subjective well-being before and after the onset of the COVID-19 pandemic: Two six-year longitudinal studies

Previous research investigated the trajectories of mental health and well-being during and after the onset of the COVID-19 pandemic. However, less is known about the trajectories of mental health and well-being before, during, and two years after the onset of the pandemic. The aim of the current study was to investigate the trajectory of depression symptoms and subjective well-being (i.e., life satisfaction and positive and negative affect) trajectories over six time points (2017-2022), three before the pandemic and three after the onset of the pandemic. To increase the robustness of our overall conclusions and avoid reliance on data from only one country, we used data from two nationwide representative longitudinal surveys conducted in Germany (GESIS Panel study; N = 5184) and Switzerland (Swiss Household Panel study; N = 17,074). Using covariance pattern mixture models, the results revealed that a four-class model best fit the data. The Stable/resilient trajectory was the most common across outcomes (74.2%-90.1% of participants). Three additional trajectories of Chronic/Low, Upright U-shaped, and Inverted U-shaped emerged in the analysis of negative affect and depression symptoms, while distinct trajectory classes of Worsening, Improving/Stable, and Upright U-shaped also emerged for analyses of positive affect and life satisfaction shaped. In conclusion, there was no evidence of a long-term impact of the pandemic for the vast majority of participants (about 90%). For the remaining participants, the COVID-19 pandemic (along with its exceptional circumstances) was a turning point or a catalyst that reversed, accelerated, or flattened a pre-pandemic trend. These changes in trends were not only negative (e.g., greater depression symptoms), but also positive (e.g., less depression symptoms).

Chronic, increasing, and decreasing peer victimization trajectories and the development of externalizing and internalizing problems in middle childhood

Children's peer victimization trajectories and their longitudinal associations with externalizing and internalizing problems were investigated from Grades 2 to 5. Secondary data analysis was performed with the Early Childhood Longitudinal Study (ECLS-K-2011; n = 13,860, M age = 8.1 years old in the spring of Grade 2; 51.1% male, 46.7% White, 13.2% African-American, 25.3% Hispanic or Latino, 8.5% Asian, and 6.1% other or biracial). Children who experienced high and persistent levels of peer victimization (high-chronic victims) exhibited co-occurring externalizing and internalizing problems. Moreover, among high-chronic victims, boys had a more pronounced increase in their externalizing trajectories, and girls had greater increases in their social anxiety trajectories. In contrast, those with decreasing peer victimization across time exhibited signs of recovery, particularly with respect to their social anxiety. These findings elucidated how chronic, increasing, and decreasing victims exhibited distinct patterns in the co-occurring development of their externalizing and internalizing problems, and how findings varied depending on the form of problem behavior and by child sex.

Exploration of model misspecification in latent class methods for longitudinal data: Correlation structure matters

Modeling longitudinal trajectories and identifying latent classes of trajectories is of great interest in biomedical research, and software to identify latent classes of such is readily available for latent class trajectory analysis (LCTA), growth mixture modeling (GMM) and covariance pattern mixture models (CPMM). In biomedical applications, the level of within-person correlation is often non-negligible, which can impact the model choice and interpretation. LCTA does not incorporate this correlation. GMM does so through random effects, while CPMM specifies a model for within-class marginal covariance matrix. Previous work has investigated the impact of constraining covariance structures, both within and across classes, in GMMs-an approach often used to solve convergence problems. Using simulation, we focused specifically on how misspecification of the temporal correlation structure and strength, but correct variances, impacts class enumeration and parameter estimation under LCTA and CPMM. We found (1) even in the presence of weak correlation, LCTA often does not reproduce original classes, (2) CPMM performs well in class enumeration when the correct correlation structure is selected, and (3) regardless of misspecification of the correlation structure, both LCTA and CPMM give unbiased estimates of the class trajectory parameters when the within-individual correlation is weak and the number of classes is correctly specified. However, the bias increases markedly when the correlation is moderate for LCTA and when the incorrect correlation structure is used for CPMM. This work highlights the importance of correlation alone in obtaining appropriate model interpretations and provides insight into model choice.

Facilitating Growth Mixture Model Convergence in Preventive Interventions

Growth mixture models (GMMs) are applied to intervention studies with repeated measures to explore heterogeneity in the intervention effect. However, traditional GMMs are known to be difficult to estimate, especially at sample sizes common in single-center interventions. Common strategies to coerce GMMs to converge involve post hoc adjustments to the model, particularly constraining covariance parameters to equality across classes. Methodological studies have shown that although convergence is improved with post hoc adjustments, they embed additional tenuous assumptions into the model that can adversely impact key aspects of the model such as number of classes extracted and the estimated growth trajectories in each class. To facilitate convergence without post hoc adjustments, this paper reviews the recent literature on covariance pattern mixture models, which approach GMMs from a marginal modeling tradition rather than the random effect modeling tradition used by traditional GMMs. We discuss how the marginal modeling tradition can avoid complexities in estimation encountered by GMMs that feature random effects, and we use data from a lifestyle intervention for increasing insulin sensitivity (a risk factor for type 2 diabetes) among 90 Latino adolescents with obesity to demonstrate our point. Specifically, GMMs featuring random effects-even with post hoc adjustments-fail to converge due to estimation errors, whereas covariance pattern mixture models following the marginal model tradition encounter no issues with estimation while maintaining the ability to answer all the research questions.

Association of BMI trajectories with cardiometabolic risk among low-income Mexican American children

BACKGROUND

The aim of this study was to identify distinct trajectories of BMI growth from 2 to 7.5 years and examine their associations with markers of cardiometabolic risk at age 7.5 years among a sample of low-income Mexican American children.

METHODS

This longitudinal cohort study recruited 322 mother-child dyads to participate prenatally and at child age 2, 3, 4.5, 6, and 7.5 years. Child height/weight, waist circumference, and blood pressure were assessed at each time point. Blood was collected from child at 7.5 years.

RESULTS

Covarying for birthweight, three BMI trajectories were identified: Low-Stable BMI (73% of the sample), High-Stable BMI (5.6% of the sample), and Increasing BMI over time (21.4% of the sample). The High-Stable and Increasing BMI classes had higher waist circumference and systolic blood pressure and lower HDL-c than the Low-Stable BMI class (ps < 0.05). Among children with BMIs below the 85th percentile, 16% had three or more cardiometabolic risk indicators.

CONCLUSIONS

BMI classes were consistent with existing literature. For youth, standard medical practice is to examine cardiometabolic risk indicators when BMI is high; however, this practice would miss 16% of youth in our sample who exhibit cardiometabolic risk but do not screen in based on BMI.

IMPACT

Research indicates Mexican American youth are at risk for cardiometabolic dysregulation relative to other ethnic groups, yet there is a paucity of longitudinal research. An Increasing BMI and a High-Stable BMI class were associated with larger waist circumference, higher systolic blood pressure, and lower HDL cholesterol than the Low-Stable BMI class. BMI trajectories in childhood predict cardiometabolic risk indicators. As the sole screener for deciding when to test cardiometabolic indicators, BMI alone will miss some children exhibiting cardiometabolic dysregulation.

Linear Mixed Model Analysis of Polygenic Hazard Score on Verbal Memory Decline in Alzheimer's Disease

BACKGROUND

Alzheimer's disease (AD) is a chronic, progressive, degenerative disease characterized by cognitive dysfunction, including verbal memory loss. Studies were lacking in examining the longitudinal effect of polygenic hazard score on the Rey Auditory Verbal Learning Test-Delayed Total (AVDELTOT) score (a common measure of verbal memory). A key step in analyzing longitudinal changes in cognitive measures using a linear mixed model (LMM) is choosing a suitable covariance structure.

OBJECTIVES

The study aims to determine the association between the polygenic hazard score and the AVDELTOT score accounting for repeated measures (the covariance structure).

METHODS

The AVDELTOT scores were collected at baseline, 12 months, 24 months, 36 months, and 48 months from 283 participants with AD, 347 with cognitive normal, and 846 with mild cognitive impairment in the Alzheimer's Disease Neuroimaging Initiative. The Bayesian information criterion statistic was used to select the best covariance structure from 10 covariance structures in longitudinal analysis of AVDELTOT scores. The multivariable LMM was used to investigate the effect of polygenic hazard score status (low vs. medium vs. high) on changes in AVDELTOT scores while adjusted for age, gender, education, APOE-ε4 genotype, and baseline Mini-Mental State Examination score.

RESULTS

One-way analysis of variance revealed significant differences in AVDELTOT scores, Mini-Mental State Examination scores, and polygenic hazard scores among AD diagnoses at baseline. Bayesian information criterion favored the compound symmetry covariance structure in the LMM analysis. Using the multivariate LMM, the APOE-ε4 allele and high polygenic hazard score value was significantly associated with AVDELTOT declines. Significant polygenic hazard score status by follow-up visit interactions was discovered.

CONCLUSION

Our findings provide the first evidence of the effect of polygenic hazard score status and APOE-ε4 allele on declines in verbal memory in people with AD.

Does group-based trajectory modeling estimate spurious trajectories?

BACKGROUND

Group-based trajectory modelling (GBTM) is increasingly used to identify subgroups of individuals with similar patterns. In this paper, we use simulated and real-life data to illustrate that GBTM is susceptible to generating spurious findings in some circumstances.

METHODS

Six plausible scenarios, two of which mimicked published analyses, were simulated. Models with 1 to 10 trajectory subgroups were estimated and the model that minimized the Bayes criterion was selected. For each scenario, we assessed whether the method identified the correct number of trajectories, the correct shapes of the trajectories, and the mean number of participants of each trajectory subgroup. The performance of the average posterior probabilities, relative entropy and mismatch criteria to assess classification adequacy were compared.

RESULTS

Among the six scenarios, the correct number of trajectories was identified in two, the correct shapes in four and the mean number of participants of each trajectory subgroup in only one. Relative entropy and mismatch outperformed the average posterior probability in detecting spurious trajectories.

CONCLUSION

Researchers should be aware that GBTM can generate spurious findings, especially when the average posterior probability is used as the sole criterion to evaluate model fit. Several model adequacy criteria should be used to assess classification adequacy.

Children's Daily Negative Affect Patterns and Food Consumption on Weekends: An Ecological Momentary Assessment Study

OBJECTIVE

This study evaluated the association between children's daily negative affect (NA) trajectories and unhealthy food consumption during weekends using ecological momentary assessment (EMA).

DESIGN

Children answered mobile phone-based EMA surveys 7 times a day for 2 weekend days per wave, with each survey assessing current NA and past 2-hour consumption of fried foods (chips or fries), sweets (pastries or sweets), and sugary beverages (drank soda or energy drinks).

SETTING

Los Angeles, California.

PARTICIPANTS

The sample consisted of 195 children (51% female; mean age, 9.65 years; SD, 0.93) from the Mothers and Their Children's Health cohort study.

MAIN OUTCOMES MEASURES

Negative affect trajectory (independent variable), unhealthy food consumption (dependent variable).

ANALYSIS

Latent growth mixture modeling classified NA trajectories across days and examined their association with unhealthy food consumption.

RESULTS

The latent growth mixture modeling identified 3 classes of daily NA trajectories: (1) stable low, (2) early increasing and late decreasing and (3) early decreasing and late increasing. Fried food consumption was higher on early increasing and late decreasing and early decreasing and late increasing NA trajectories than days with stable low NA.

CONCLUSIONS AND IMPLICATIONS

By better understanding day-to-day variability in children's affect and eating, we can individually tailor obesity interventions to account for the emotional contexts in which unhealthy eating occurs.

Underreporting of Energy Intake Increases over Pregnancy: An Intensive Longitudinal Study of Women with Overweight and Obesity

(1) Background: Energy intake (EI) underreporting is a widespread problem of great relevance to public health, yet is poorly described among pregnant women. This study aimed to describe and predict error in self-reported EI across pregnancy among women with overweight or obesity. (2) Methods: Participants were from the Healthy Mom Zone study, an adaptive intervention to regulate gestational weight gain (GWG) tested in a feasibility RCT and followed women (n = 21) with body mass index (BMI) ≥25 from 8−12 weeks to ~36 weeks gestation. Mobile health technology was used to measure daily weight (Wi-Fi Smart Scale), physical activity (activity monitor), and self-reported EI (MyFitnessPal App). Estimated EI was back-calculated daily from measured weight and physical activity data. Associations between underreporting and gestational age, demographics, pre-pregnancy BMI, GWG, perceived stress, and eating behaviors were tested. (3) Results: On average, women were 30.7 years old and primiparous (62%); reporting error was −38% ± 26 (range: −134% (underreporting) to 97% (overreporting)), representing an ~1134 kcal daily underestimation of EI (1404 observations). Estimated (back-calculated), but not self-reported, EI increased across gestation (p < 0.0001). Higher pre-pregnancy BMI (p = 0.01) and weekly GWG (p = 0.0007) was associated with greater underreporting. Underreporting was lower when participants reported higher stress (p = 0.02) and emotional eating (p < 0.0001) compared with their own average. (4) Conclusions: These findings suggest systemic underreporting in pregnant women with elevated BMI using a popular mobile app to monitor diet. Advances in technology that allow estimation of EI from weight and physical activity data may provide more accurate dietary self-monitoring during pregnancy.

[Growth trajectories of intrinsic value beliefs in mathematics and French: Relations with career orientations]

This longitudinal study investigated different trajectories in the development of intrinsic value beliefs in the subjects Mathematics and French in Grades 9 to 11 and their correlations with career aspirations. Using data from 850 students from German-Swiss high schools (54% female, age T1: 15.6 years), five distinct growth classes were identified in a bivariate growth model. Two of these classes showed clear differentiation between intrinsic value beliefs regarding the two subjects and stable growth in the preferred subject. The other three classes were characterized by mean differences (high, medium, low intrinsic value beliefs) and moderate decline in both subjects. The five growth classes were associated with different career orientations at the end of the 11th grade, with students exhibiting particularly high career orientations in one subject when intrinsic value regarding the other subject was low. Gender differences in career orientations could be fully explained by gender membership in the five growth classes.

Reducing Incidence of Nonpositive Definite Covariance Matrices in Mixed Effect Models

Deciding which random effects to retain is a central decision in mixed effect models. Recent recommendations advise a maximal structure whereby all theoretically relevant random effects are retained. Nonetheless, including many random effects often leads to nonpositive definiteness. A typical remedy is to simplify the random effect structure by removing random effects or associated covariances. However, this practice is known to bias estimates of remaining covariance parameters and compromise fixed effect inferences. Cholesky decompositions frequently are suggested as an alternative and are automatically implemented in some software. Instead of Cholesky decompositions, we describe factor analytic structures as an approach to avoid nonpositive definiteness. This approach is occasionally employed in biosciences like plant breeding, but, ironically, has not been established in behavioral sciences despite the close historical connection with factor analysis in these fields. We discuss how a factor analytic structure facilitates estimation and conduct simulations to compare convergence and performance to simplifying the random effects structure or Cholesky decomposition approaches. Results show a lower rate of nonpositive definiteness with the factor analytic structure than Cholesky decomposition and suggest that factor analytic covariance structure may be useful to combating nonpositive definiteness, especially in models with many random effects.

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.

Response heterogeneity to lifestyle intervention among Latino adolescents

OBJECTIVE

To characterize the heterogeneity in response to lifestyle intervention among Latino adolescents with obesity.

METHODS

We conducted secondary data analysis of 90 Latino adolescents (age 15.4 ± 0.9 y, female 56.7%) with obesity (BMI% 98.1 ± 1.5%) that were enrolled in a 3 month lifestyle intervention and were followed for a year. Covariance pattern mixture models identified response phenotypes defined by changes in insulin sensitivity as measured using a 2 hour oral glucose tolerance test. Baseline characteristics were compared across response phenotypes using one-way ANOVA and chi-square test.

RESULTS

Three distinct response phenotypes (PH1, PH2, PH3) were identified. PH1 exhibited the most robust response defined by the greatest increase in insulin sensitivity over time (β ± SE, linear 0.52 ± 0.17, P < .001; quadratic -0.03 ± 0.01, P = .001). PH2 showed non-significant changes, while PH3 demonstrated modest short-term increases in insulin sensitivity which were not sustained over time (linear 0.08 ± 0.03, P = .002; quadratic -0.01 ± 0.002, P = .003). At baseline, PH3 (1.1 ± 0.4) was the most insulin resistant phenotype and exhibited the highest BMI% (98.5 ± 1.1%), 2 hours glucose concentrations (144.0 ± 27.5 mg/dL), and lowest beta-cell function as estimated by the oral disposition index (4.5 ± 2.8).

CONCLUSION

Response to lifestyle intervention varies among Latino youth with obesity and suggests that precision approaches are warranted to meet the prevention needs of high risk youth.

Class enumeration false positive in skew-t family of continuous growth mixture models

Growth Mixture Modeling (GMM) has gained great popularity in the last decades as a methodology for longitudinal data analysis. The usual assumption of normally distributed repeated measures has been shown as problematic in real-life data applications. Namely, performing normal GMM on data that is even slightly skewed can lead to an over selection of the number of latent classes. In order to ameliorate this unwanted result, GMM based on the skew t family of continuous distributions has been proposed. This family of distributions includes the normal, skew normal, t, and skew t. This simulation study aims to determine the efficiency of selecting the “true” number of latent groups in GMM based on the skew t family of continuous distributions, using fit indices and likelihood ratio tests. Results show that the skew t GMM was the only model considered that showed fit indices and LRT false positive rates under the 0.05 cutoff value across sample sizes and for normal, and skewed and kurtic data. Simulation results are corroborated by a real educational data application example. These findings favor the development of practical guides of the benefits and risks of using the GMM based on this family of distributions.