Effect Estimation with Latent Variables Bengt Muth´ en Professor Emeritus, UCLA Mplus [email protected]& Tihomir Asparouhov Mplus Presentation at the Data Science in the Social and Behavioral Sciences Virtual Opening Workshop on SEMs, DAGs, and Causal Inference, January 11, 2021 We thank Noah Hastings for expert assistance. Bengt Muth´ en & Tihomir Asparouhov Latent Variable Effect Estimation 1/ 18
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Quick overview - a roadmap for further readings (slides posted at the Mpluswebsite www.statmodel.com):
Mediation analysis in the Mplus software using counterfactually-definedeffectsFocus on effect estimation with latent variables:
Latent continuous constructs (factors) as mediatorsLatent categorical variables (finite mixture modeling) used forcomplier-average causal effects (CACE)Latent centering and latent variable interactions in multilevelmediation modelingRandom effects used for propensity scores, moderators, andmediators in multilevel time series analysis of intensivelongitudinal data
Thoughts on dissemination of new techniques and further steps
Mediation Analysis: Counterfactual Effects in Mplus
Options for counterfactually-defined effects in mediation analysis:
Effects: CDE, TNDE, PNDE, TNIE, PNIEVanderWeele & Vansteelandt (2009). Statistics and Its InterfaceValeri & VanderWeele (2013). Psychological Methods
Mediators: Continuous, binary, ordinal, nominal, and latentOutcomes: Continuous, binary, count, two-part, and latentParametric models: Linear, probit, logit, Poisson, negative binomialEstimators: ML, Weighted Least Squares, BayesSensitivity analysis for mediator-outcome confounding (Imai, 2010)
The counterfactually-defined effects are causal only when a set of assumptionsare fulfilled - a strength of the approach is that it tells us how to define effects
Muthen & Asparouhov (2015). Causal effects in mediation modeling: Anintroduction with applications to latent variables. Structural EquationModeling: A Multidisciplinary Journal
Latent Mediator: Factor Measured by Multiple Indicators
harms
juv
breaks takes fights
fm
x
xz
z
SEM model diagram convention:Boxes: Observed variablesCircles: Latent variablesArrows: Regressions, residuals,
covariances.
Muthen, Muthen & Asparouhov (2016).
Randomized intervention trial in Baltimore public schools: X is Grade 1intervention aimed at reducing aggressive-disruptive behavior in the classroom
Mediator FM: Avoiding measurement error by a factor measured in Grade 5 byteacher-rated items: Harms others, Breaks things, Takes property, Fights
Outcome Y: Juvenile court record (binary variable; not a rare event)
Sensitivity to model specifications? Continuous or ordinal factor indicators,normality assumption, probit or logit, conditional independence, XMinteraction, M-Y confounder?
Hong & Raudenbush (2006). Evaluating Kindergarten retention policy:A case study of causal inference for multilevel observational data. JASA
Propensity score approachVanderWeele (2010). Direct and indirect effects for neighborhood-basedclustered and longitudinal data. Sociological Methods & Research
Counterfactually-defined effects
SEM oriented papers:
Preacher, Zyphur & Zhang (2010-2016) papers on SEM multilevelmediation in Psychological Methods and Structural Equation ModelingAsparouhov & Muthen (2019). Latent variable centering of predictorsand mediators in multilevel and time-series models. Structural EquationModelingAsparouhov & Muthen (2020). Bayesian estimation of single andmultilevel models with latent variable interactions. Structural EquationModeling
Within level = time, between level = individual. Variation in within levelparameters across individuals can be characterized by many random effects(continuous latent variables): Mean (level), variance, auto-correlation, slopes,amplitude
Asparouhov, Hamaker & Muthen (2018). Dynamic structural equationmodels. Structural Equation Modeling: A Multidisciplinary Journal(introduced in Mplus 2017)Hamaker et al. (2018). At the frontiers of modeling intensivelongitudinal data... Multivariate Behavioral ResearchSchultzberg & Muthen (2018). Number of subjects and time pointsneeded for multilevel time series analysis: A simulation study ofdynamic structural equation modeling. Structural Equation ModelingMcNeish & Hamaker (2020). A primer on two-level dynamic structuralequation models for intensive longitudinal data in Mplus. Psych MethodsMore references and short course videos at:http://www.statmodel.com/TimeSeries
A Multilevel Time Series Application: VAR Modeling
Within
Between
Decomposition
ZtYt
Yb
Ytw Zt
w
Yt-1w
t-1ZwZt
w
Ytw
Zb Yb ZbZZφ YZφ ZYφ YYφ
ZZφ
YZφZYφ
YYφ
Vector auto regressive modeling (lag 1)
Dynamic structural equation modeling (DSEM, Asparouhov et al., 2018)in Mplus uses a latent variable decomposition (avoids dynamic panelbias referred to as Nickell’s bias, Nickell, 1981)
“Decomposing into within and between ensures that
at the within level we no longer have to worry about time invariantbetween person confoundingat the between level we do not have to worry about confounding due totemporal within person fluctuations” (Hamaker et al., 2018, 2021)
Time series version of RI-CLPM (Hamaker et al., 2015 in Psych Methods) butwith more random effects; see also Usami et al. (2019) in Psych Methods
Applications: dyadic interactions among couples (Bolger & Laurenceau, 2013;book on ILD), stress and alcohol consumption (Lieu & West, 2015 in JP),religion and mental health (VanderWeele et al., 2016 in Soc Psychiatry Epi),positive and negative affect (Hamaker et al., 2018 in MBR; N≈200, T≈ 100)
Causal interpretation tempting with patterns seen in long time series with closemeasurements - but threats to causal inference (VanderWeele et al., 2016):marginal structural models (Robins, 1999), inverse-probability weighting
Effect Estimation in Multilevel Time Series Analysis:Randomized Studies
Experience sampling method (ESM): T= 60 pre-intervention, 60 post (eachperiod has 10 beeps/day via digital wristwatch for 6 days), N=119
Geschwind et al. (2011). Mindfulness training increases momentary positiveemotions and reward experience in adults vulnerable to depression: Arandomized controlled trial. Journal of Consulting and Clinical Psychology
Muthen et al. (2020). In preparation: DSEM with daily cycles in positive affectmodeled by sine-cosine curve with random effects
The talk has focused on modeling and estimation, not effect identification,DAGs, or evaluation of causal assumptions
Opportunities for more flexible modeling such as using splines
Opportunities for more causal inference research
Bringing it all together - will the resulting technology be easy enough tounderstand and apply by substantive researchers with limited methodologicaltraining or will there be a need to rely on statistical experts/consultants?
How do researchers respond to and master new methods and software? Mplussupport questions has provided 22 years of experience