Modeling Change over Time in the Presence of Non-Randomly Missing Data

Danielle Dean, M.A.Department of PsychologyUniversity of North Carolina, Chapel Hill

Nisha Gottfredson, Ph.D.Transdisciplinary Prevention Research CenterDuke University

Modern Modeling MethodsMay 2012Novel Applications of Mixture Models to Social Science DataIntroduction: Indirect Mixture ApplicationsPresented by Nisha GottfredsonMixture Models Enable Analysts to Relax Parametric Assumptions Marron and Wand (1992) showed that it is possible to replicate nearly any univariate distribution using a finite mixture of normal distributions Variable means, variances, and proportions

Bimodal density2 normal distributionsStrongly skewed 8 normal distributionsMultivariate Mixture ModelsEach class g has a class-specific mean vector , covariance matrix , and mixing proportion

Examples include Growth Mixture Models (mixtures of latent curve models; Verbeke & Lesaffre, 1996; Muthn & Shedden, 1999) and Structural Equation Mixture Models (Jedidi, Jagpal, & Desarbo, 1997; Dolan & van der Maas, 1998)

Direct versus Indirect ApplicationsMcLachlan & Peel (2000) distinguished between direct and indirect applications of finite mixture modelingDirect applications more common in social sciencesUsers believe that there is qualitative heterogeneity in the populationInterpret class-specific estimatesAim is to recover true groupingsIndirect applications more common in statisticsAnalysts uncomfortable with parametric assumptionsAggregate over class-specific estimatesTrue groupings do not exist

Direct versus Indirect Interpretation is in the Eye of the BeholderThere is no empirical way to distinguish between groups as truth and groups as statistical convenienceAIC/BIC almost always suggest that classes improve model fit (Bauer & Curran, 2003; 2004; Bauer, 2007)Non-normality of variablesNon-linearityWhen in doubt, indirect interpretation is more robust than direct interpretation (Sterba et al., 2012)Overview of TalksIndirect applications of mixture modelsSurvival Mixture Models with study on multiple survival processes during transition to adulthoodShared Parameter Mixture Models to handle non-randomly missing data in longitudinal studies

Survival Mixture Models for Simultaneously Capturing Multiple Survival ProcessesAn Application with Data on Transitioning to Adulthood

Presented by Danielle DeanMultiple Survival ProcessesHow may we analyze multiple non-repeatable events which may occur at the same point in time for an individual?E.g. age of onset of different drugsE.g. age of transition to multiple rolesPersonEventAge 18Age 19Age 20Age 211Parent001.1Marriage001.1College00002Parent00..2Marriage1...2College00..Survival AnalysisSurvival or event history models

Multivariate survival analysisMultiple Survival ProcessesNon-repeatable events which may occur at the same point in time

Many researchers currently run a separate survival analysis for each event process but dont analyze how the events are relatedUnivariate Survival AnalysisOne non-repeatable eventThree main functions: survival, lifetime distribution, and hazard

IndividualWeek01234Event time10000142001..23000..??401...150000.?? Univariate Survival Analysis E.g. therapy completion:

Model the hazard:

Compute the lifetime distribution and survival function

Multiple non-repeatable eventsHow are the events related? Distribution of risk for multiple events is of unknown formModel assumes the population is composed of a finite number of latent classes in order to parsimoniously describe the underlying distribution of risk (multiple event version of model presented by Muthn & Masyn, 2005)

Purpose of modelParsimoniously describe the underlying distribution of risk for multiple events, without assuming a specific mathematical form for the distributionPurpose is to draw attention to differences in the causes and consequences of different pathways (rather than to suggest the population is composed of literally distinct groups)In spirit of indirect application, can compute model-implied functions weighting over latent classes to evaluate the effects of covariatesE.g. model implied risk for multiple events for males versus females, controlling for other covariatesTransitions to AdulthoodLife course theoryOrder and timing of social rolesMeaning of a social roleE.g., working parentIdentify general structures of the life course

MethodsNational Longitudinal Study of Adolescent HealthN = 15,7014 events: Parenthood, Full-time work, Marriage, CollegeAges 18-30ModelFit using Mplus 6.12Identify pathways through the life course (Model 1)Influence of covariates on pathways (Model 2)Gender, Race, Parental Educationy1,18 y1,30y4,18 y4,30CX. . . Model SelectionLatent Classes-2LLBICAICSmallest Class SizeEntropyLMR Test1-102521.76205541.99205147.531.001.00N/A2-98444.65197895.81197099.290.330.790.003-97481.09196476.75195278.190.260.740.634-96784.46195591.54193990.930.110.760.495-96425.50195381.66193379.000.100.710.606-96087.98195214.68192809.970.090.720.637-95879.40195305.55192498.790.090.700.71Model SelectionSubstantively redundant latent class in 6 class solutionLifetime Distributions:

5 class solution (hazards)5 class solution (lifetime dist.)Order / Timing of EventsMedian event time

Classes aggregate back to sample observed functions, average squared residual