Chapter Four · failure evidence
What Longitudinal Growth & Latent Curve Modeling got wrong, from 53 dissertations
The records describe methodological and computational challenges encountered when estimating longitudinal growth and latent trajectory models across diverse empirical datasets. Researchers frequently faced optimization failures, distributional and functional form misspecifications, and breakdowns in latent measurement structures across repeated observations. These records come from PhD theses at 20 institutions, 2021 to 2026. Each links to its thesis. They were extracted by language models reading the full text, so treat each as a lead to read, not a verdict.
Latent class and growth mixture models suffer from optimization failures and degenerate solutions as class counts increase
Extracting multiple latent classes or estimating class-specific variances frequently triggered numerical non-convergence, boundary estimation problems, and local maxima. Higher-order class solutions often produced near-empty or poorly separated trajectory profiles that failed to replicate hypothesized developmental patterns.
Tried and failed
latent class analysis with fixed effects applied to multivariate survey exposure data. Outcome: did not converge. Reason: Model fitting failures and boundary estimation issues during optimization across multiple phases.
Tried and failed
latent profile analysis with freely estimated variances applied to multi-indicator observational data. Outcome: did not converge. Reason: overparameterization from estimating class-specific variances across many continuous indicators
Tried and failed
latent class discrete choice modeling applied to longitudinal discrete choice panels. Outcome: did not converge. Reason: simultaneous estimation of latent classes and random effects failed to achieve convergence and valid parameter estimates
Tried and failed
growth mixture modeling applied to longitudinal substance use survey trajectories. Outcome: did not converge. Reason: unresolvable estimation errors when fitting multi-class trajectory models
Alcohol use among Latina/o adolescents : the role of immigration, family, and peer stressors · UT Austin
Tried and failed
joint estimation of measurement and latent class models applied to multivariate discrete outcome modeling. Outcome: did not converge. Reason: numerical non-convergence and intractable conditional independence violations across multiple latent constructs
Considered and rejected
Considered and rejected: Rejected using 5-class latent class model because the estimation failed to converge.
Consumer Preference for Dairy Products in China · Research Repository UCD
Considered and rejected
Considered and rejected: Rejected a latent profile analysis model with freely estimated variances across profiles for all 10 indicators due to model convergence failures.
Tried and failed
Factor mixture modeling with multiple latent classes applied to cognitive ability test battery data. Outcome: did not generalise. Reason: Higher-order class solutions failed to show the hypothesized monotonic decrease in factor variance across class means
Are the effects of g on achievement smaller at higher ability levels? · UT Austin
Tried and failed
growth mixture modeling for trajectory clustering applied to longitudinal student attendance rates. Outcome: no signal. Reason: Lack of class separation and small subpopulation sizes caused single-class models to fit best.
Tried and failed
high-order latent factor mixture modeling applied to cognitive ability test score data. Outcome: unstable. Reason: over-extraction led to degenerate class solutions, near-empty classes, or collapse into a single class
Are the effects of g on achievement smaller at higher ability levels? · UT Austin
Tried and failed
latent class choice modeling with many classes applied to discrete choice experiment survey data. Outcome: did not converge. Reason: model complexity with higher numbers of classes exceeded what the data could support
To plant or not to plant? Drivers of native woodland creation in the United Kingdom · Imperial
Tried and failed
latent class analysis with expectation maximisation applied to synthetic clustering benchmarks. Outcome: worse than baseline. Reason: lack of true latent variable structure in the data
Predictive and Prescriptive Analytics in Operations Management · MIT
Tried and failed
increasing latent class count in mixture modeling applied to dichotomous behavioral survey indicators. Outcome: worse than baseline. Reason: four-class model showed non-significant likelihood ratio tests and worse information criteria than three-class model
Understanding patterns of electronic nicotine delivery systems use among young adults · UT Austin
Tried and failed
latent profile analysis with many classes applied to longitudinal survey data. Outcome: unstable. Reason: non-positive definite first-order derivative product matrix caused untrustworthy parameter standard errors
Tried and failed
latent profile analysis on standardized sum scores applied to psychological subscale scores. Outcome: no signal. Reason: hypothesized theoretical subgroup profile failed to emerge from the latent mixture model
Substance use disorder, shame, and self-forgiveness: A latent profile analysis · Iowa State
Considered and rejected
Considered and rejected: Rejected one-step simultaneous mixture modeling for substantive analyses because estimating growth and LCA simultaneously fundamentally changes latent class definitions beyond the observed indicator patterns.
Considered and rejected
Considered and rejected: Rejected a 4-class latent class growth curve model for depression because solutions converged on local maxima, had higher BIC (294141.890), lower entropy (0.79), and low class prevalence (3%).
Longitudinal Analyses Of Epigenetic Correlates Of Externalizing And Internalizing Disorders · Penn
Considered and rejected
Considered and rejected: Rejected a 5-class latent class model due to convergence difficulties and lack of theoretical interpretability/distinctness over the 4-class solution
Complex multi-process and constrained latent growth architectures fail to achieve numerical convergence
Specifications involving parallel processes, multigroup comparisons, time-varying covariates, or structured residuals routinely exceeded software iteration limits or generated singular fits. Optimization algorithms repeatedly produced non-positive definite residual covariance matrices and failed to compute reliable higher-level standard errors.
Tried and failed
latent growth curve modeling with structured residuals applied to longitudinal measurement invariance testing. Outcome: did not converge. Reason: Non-positive definite residual covariance matrices under configural, weak, or strict invariance constraints
Longitudinal reciprocal relations among reading, executive function, and social emotional skills · UT Austin
Tried and failed
multigroup parallel process latent growth curve modeling applied to longitudinal behavioral and mindset data. Outcome: did not converge. Reason: model complexity and parameter estimation constraints caused numerical convergence failure
Tried and failed
latent growth curve modeling applied to high-frequency longitudinal self-report data. Outcome: did not converge. Reason: severe multicollinearity across dense measurement waves and insufficient sample size causing singularity errors
Trait and state individual differences’ impact on rapid immersed symptoms of cybersickness (RISC) trajectories · Iowa State
Tried and failed
multilevel modeling with aggregate contextual predictors applied to longitudinal adolescent mental health data. Outcome: did not converge. Reason: insufficient convergence to compute higher-level standard errors
Tried and failed
random intercept outcome model with predictor growth curve applied to longitudinal data with trending outcomes. Outcome: did not converge. Reason: model misspecification by assuming constant outcome mean over time when outcome actually exhibits a linear trend
Tried and failed
multigroup parallel process latent growth modeling applied to longitudinal multi-wave behavioral co-development. Outcome: did not converge. Reason: None
Tried and failed
Latent growth curve modeling with time-varying covariates applied to longitudinal substance use survey data. Outcome: did not converge. Reason: Model complexity with time-varying covariates exceeded estimation limits even after 100,000 iterations
Alcohol use among Latina/o adolescents : the role of immigration, family, and peer stressors · UT Austin
Tried and failed
fully latent product-indicator structural equation modeling applied to moderated mediation analysis. Outcome: did not converge. Reason: numerical convergence issues with complex latent interaction estimation
Career Calling in Older Adults: A Socioemotional Selectivity Perspective · Georgia Tech
Tried and failed
Linear mixed-effects modeling applied to longitudinal plant growth count data. Outcome: did not converge. Reason: Singular fit errors caused by non-linearity in the response variable
Ecology and evolution of the African ant acacia, Vachellia drepanolobium, and its multiple symbionts · Harvard
Considered and rejected
Considered and rejected: Rejected quadratic latent growth models in Chapter 4 due to model non-convergence under the multi-step ML approach.
Considered and rejected
Considered and rejected: Rejected a latent variable SEM approach for SRM-dependent Response Surface Analysis because the structural equation models failed to converge.
Stereotypes and Social Decisions: The Interpersonal Consequences of Socioeconomic Status · Scholars' Bank
Considered and rejected
Considered and rejected: Rejected quadratic growth models in piecewise latent growth curve models due to insufficient fixed parameters and unresolvable estimation errors in Mplus.
Considered and rejected
Considered and rejected: Rejected treating cognitive impairment as a latent variable across waves due to non-convergence, using an exogenous manifest baseline variable instead.
Unmodeled trends and distributional or residual structure violations distort growth parameter estimates
Omitting underlying temporal trends, autoregressive dynamics, or measurement error heteroskedasticity introduced severe parameter bias and inflated standard errors. Additionally, violating normality assumptions in longitudinal data caused massive positive bias in trajectory parameters and latent covariances.
Tried and failed
linear mixed models with factor analytic covariance applied to longitudinal multi-environment trial data. Reason: models produced systematic bias in trend estimation across multi-decade unbalanced historical series
Strategies to untangle genetic and non-genetic sources of variation in cultivar development programs · Iowa State
Tried and failed
replacing autoregressive term with static seasonal indicator applied to hierarchical longitudinal survey response modeling. Outcome: did not converge. Reason: removing autoregressive dependence failed to adequately capture temporal dynamics necessary for successful model fit
Tried and failed
ordinary least squares linear regression applied to biomarker trajectory modeling. Reason: residuals violated homoscedasticity and normality assumptions
Tried and failed
random intercept model without predictor detrending applied to longitudinal data with trending predictors. Outcome: unstable. Reason: linear time trends in predictors were unmodeled, causing severe parameter bias and standard error inflation
Tried and failed
two-wave latent growth modeling applied to longitudinal trajectory estimation with heteroscedasticity. Outcome: worse than baseline. Reason: heteroscedastic residual errors and large residual variance inflated standard errors and reduced statistical power
How Well Can Two-Wave Models Recover the Three-Wave Second Order Latent Model Parameters? · Virginia Tech
Tried and failed
omitting measurement error heteroskedasticity in moderated models applied to latent growth curve modeling. Reason: unmodeled residual variance moderation severely biases latent variance moderation estimates and coverage rates
Tried and failed
Gaussian assumptions in latent growth models applied to non-normal longitudinal data. Outcome: worse than baseline. Reason: distributional misspecification under moderate-to-severe non-normality caused massive positive bias in trajectory parameters and covariances
Factored regression approach for structural equation models with non-normal continuous data · UT Austin
Misspecification of the trajectory functional form causes poor fit and parameter bias
Forcing linear trajectories onto non-linear or multi-phase processes resulted in unacceptable goodness of fit metrics and severe parameter bias. At the same time, overly complex polynomial models such as quadratic and cubic growth curves frequently failed to converge or fit the observed longitudinal data adequately.
Tried and failed
latent growth curve modeling applied to longitudinal proportional compliance data. Reason: poor linear model fit across time waves with high chi-square and RMSEA and low CFI
Considered and rejected
Considered and rejected: Rejected non-linear latent basis growth models for victimization due to linear nested models providing superior fit (T = .053, df = 1, p = .82)
Polygenic Resilience on the Association between Childhood Maltreatment, Delinquency, and Victimization · DSpace at SHSU
Considered and rejected
Considered and rejected: Linear latent growth curve model was rejected (χ2(7) = 16.33, p = .02, CFI = 0.92, RMSEA = 0.06, SRMR = 0.10) because it failed established cut-offs for excellent fit compared to the quadratic model.
A Longitudinal Study of Gaming Patterns during the First Nine Months of the COVID-19 Pandemic · YorkSpace
Tried and failed
propensity-weighted latent growth modeling applied to longitudinal treatment effect estimation. Outcome: unstable. Reason: growth trajectory functional form misspecification caused severe parameter bias and frequent non-positive definite covariance matrices
Considered and rejected
Considered and rejected: Latent growth curves were considered but decided against because linear change across distinct phases was not expected and maximum likelihood mixed-effects handle missing data better
Effectiveness of the Trauma Practice Approach for Adults in Trauma Treatment · YorkSpace
Considered and rejected
Considered and rejected: Cubic growth curve model rejected because it could not be fit adequately to the longitudinal data despite multiple modifications
Differential Effects of Multisystemic Factors on the Developmental Trajectories of Emotion Regulation · YorkSpace
Failures of longitudinal measurement invariance and latent factor instability prevent valid growth modeling
Longitudinal analyses were abandoned when measures shifted across waves or failed to satisfy longitudinal scalar measurement invariance constraints. Forcing unidimensional structures onto multidimensional constructs or fitting unstable indicator sets generated out of bounds correlation estimates and Heywood cases.
Considered and rejected
Considered and rejected: Rejected proceeding with latent growth modeling for managerial skills and self-esteem because longitudinal scalar invariance was not achieved.
Three Essays On Noncognitive Factors, Friendship Networks And Education Outcomes · Penn
Considered and rejected
Considered and rejected: Rejected Latent Transition Analysis (LTA) because measures changed between Grade 1 and Grade 2 (lacked measurement invariance).
Cognitive Dimensions of Early Numeracy: Exploring Profiles of Early Math Achievement in Canadian Students · Carleton University Institutional Repository
Tried and failed
collapsing distinct latent factors into single construct applied to structural equation modeling of cognitive rates. Reason: forced unidimensionality caused significant model misfit because underlying components represent dissociable processes
Explaining Individual Differences in the Rate of Focusing Attention: Dissociating Attention Control from Drift Rates · Georgia Tech
Tried and failed
Confirmatory factor analysis applied to Crowdsourced psychological survey data. Outcome: unstable. Reason: Produced Heywood cases and out-of-bounds latent correlation estimates exceeding 1.0 due to poor data quality
Concerns and Recommendations for Pain and Masculinity Research using Amazon Mechanical Turk: A Cautionary Tale · Texas Tech
Considered and rejected
Considered and rejected: Discarded the Ebbinghaus latent factor from SEM Model D due to unsolvable Heywood cases (negative error variance / explained variance exceeding 100%).
Individual differences in visual (mis)perception: a multivariate statistical approach · EPFL
Small sample sizes combined with high residual variance or missing data imputation create estimation instability
Fitting latent growth models to small samples with high occasion-specific residual variance produced biased trajectory parameters and underestimated standard errors. In planned missing designs, using principal component auxiliary variables in small samples led to excessive non-admissible solutions and persistent slope estimation bias.
Tried and failed
principal component auxiliary variable imputation applied to planned missing longitudinal latent growth models. Outcome: worse than baseline. Reason: slope parameter estimates exhibited persistent high bias exceeding acceptable thresholds across all conditions
Tried and failed
second-order latent growth modeling applied to small-sample longitudinal data with high residual variance. Outcome: unstable. Reason: small sample size combined with large time-specific residual variance produced biased estimates and underestimated standard errors
How Well Can Two-Wave Models Recover the Three-Wave Second Order Latent Model Parameters? · Virginia Tech
Tried and failed
principal component auxiliary variables for missing data applied to small sample longitudinal growth modeling. Outcome: unstable. Reason: small per-group sample sizes caused excessive non-admissible solutions in planned missing designs
Left open by the authors
Problems the authors named and did not get to.
Left open
Apply growth mixture modeling to longitudinal middle school engagement indicators to identify declining engagement sub-populations for dropout prediction. Blocker: Access to longitudinal student-level administrative education data.
Using Machine Learning to Advance High School Dropout Prediction and Prevention · Penn
Left open
Fit latent growth models to longitudinally evaluate the interplay between adolescent negative affect and functional outcomes using the study's multi-wave cohort data. Blocker: Requires the private longitudinal multi-wave adolescent clinical/behavioral dataset used in the thesis.
Left open
Model longitudinal reciprocal relations between reading and social-emotional learning skills during adolescence or high school transitions using latent growth modeling with structured residuals. Blocker: Requires longitudinal adolescent cohort data measuring reading and social-emotional learning skills across high school transitions.
Longitudinal reciprocal relations among reading, executive function, and social emotional skills · UT Austin
Left open
Extend the mixed-effects LASSO simulation evaluation to early childhood education data from study years beyond the first two years. Blocker: Requires access to longitudinal early childhood education study data beyond the first two years
The Importance of Random Effects in Variable Selection: A Case Study of Early Childhood Education · Harvard
Left open
Investigate long-term effects and diminishing returns of repeated multi-session interactions with AI learning tools through longitudinal user studies. Blocker: Requires designing and conducting multi-session longitudinal human subject studies with students over extended periods
EMPIRICAL EVIDENCE THAT USING AI TOOLS CAN ENHANCE HUMAN COGNITION · Penn
Left open
Fit longitudinal growth models across multiple time points to predict summer reading outcomes using longitudinal student reading scores. Blocker: Requires private multi-time-point longitudinal reading assessment data from the specific student cohort studied
Self-reported summer reading of English learners with reading difficulties · UT Austin
Left open
Compare contextual economic inequality measures to resolve theoretical divergences between cross-sectional and longitudinal empirical patterns. Blocker: Lack of specific theoretical framework or methodological approach for resolving the cross-sectional versus longitudinal divergences.
Left open
Evaluate early childhood absenteeism trajectories and contextual household risk factors during and post-COVID-19 pandemic using longitudinal latent growth modeling. Blocker: Requires restricted longitudinal student attendance and household-level demographic data spanning the COVID-19 pandemic period
Left open
Evaluate long-term retention and downstream problem-solving transfer of learned inquiry conceptual models using post-test or delayed assessment data. Blocker: Requires longitudinal student learning experiments or downstream assessment data not provided in the dataset
Generalised Modeling of Inquiry Behaviour: From Learning to Understanding · EPFL
Left open
Develop theoretical frameworks and longitudinal studies to measure the effects of gamified learning on knowledge retention and critical learning skills. Blocker: Requires human subjects, longitudinal classroom testing, and lacks concrete operational methodology.
Learners, Players, Designers | Un approccio gamificato all'innovazione educativa e all'apprendimento permanente in Design · IRIS - POLITO - prod
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