Intensive Longitudinal Data,Multilevel Modeling, and SEM:
New Features in Mplus Version 8.1Part 1
Bengt [email protected]
Tihomir Asparouhov
PSMG presentation, May 8, 2018
We thank Ellen Hamaker for helpful comments and NoahHastings for excellent assistance
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The Forthcoming Mplus Version 8.1:Time Series Specific Developments
Further developments for time series analysis of intensive longitudinaldata using dynamic structural equation modeling (DSEM):
RDSEM: Residual dynamic structural equation modeling.Auto-regression between residuals instead of between outcomesCategorical dynamic structural equation modeling: Laggedcategorical variable, random slope for categorical predictor withlatent centering (DSEM, not yet RDSEM, regular 2-level)Key reference: Asparouhov, Hamaker & Muthen (2018)A source of inspiration: Bolger & Laurenceau (2013)New examples: Asparouhov & Muthen (2018a)New theory: Asparouhov & Muthen (2018b)
DSEM references and training material:http://www.statmodel.com/TimeSeries.shtml
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The Forthcoming Mplus Version 8.1:General Developments
Multilevel modeling (Asparouhov & Muthen, 2018b)
Random slopes with latent variable centered predictors (DSEM,RDSEM, general)
Structural equation modeling (Asparouhov & Muthen, 2018c, d)
Automatic checking of whether two models are nested (Bentler &Satorra, 2010); generalized to multiple groups and categoricaland censored outcomes (WLSMV)SRMR for new cases: WLSMV; changes for multilevel andmodels with covariatesWLSMV additions: bivariate residual tests, SEs for factor scoresTwolevel, cluster-specific plotsExtended odds ratio output
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DSEM - RDSEM Distinction: Typical Examples
DSEM:
Hamaker et al. (2018): Daily measurements of negative andpositive affect over 100 daysAutoregressive parameter indicating “how quickly a personrestores equilibrium after being perturbed”: inertia
Focus on yt regressed on yt−1
RDSEM:
Liu & West (2015): Daily diary study over 60 daysStress during the day influencing alcohol consumption thatevening
Focus on yt regressed on xt
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DSEM vs RDSEM: Autocorrelation in Two-Level Regression
yt-1 yt
xt-1 xt
logv
s
phi
yt-1 yt
xt-1 xt
r logv
s
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RDSEM: Autocorrelated Residuals in Two-Level Regression
yt-1 yt
xt-1 xt
Within
Between
y s logv r
r logv
s
w
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RDSEM: Autocorrelated Residuals in Two-Level Regression.The Full Story
yt-1 yt
xt-1 xt
Within
Between
ry logv
s
w w
ww
rx
w
yb xb s rylogv rx
Latent variabledecomposition
xt
xtw
xb
ytw
yb
yt
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New Language for RDSEM
DSEM AR(1):s | y ON x;phi | y ON y&1;x ON x&1;
RDSEM AR(1) in V8.1:s | y ON x;
r | yˆ ON yˆ1;xˆ ON xˆ1;
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RDSEM: Two-Level Time Series Mediation Analysis
yt-1 yt
xt-1 xt
Within
Between
w
mt-1 mt
y m sym syx smx logvy logvm ry rm
See, however, Laughlin et al. (2018) in MBR: Cross-SectionalAnalysis of Longitudinal Mediation Processes
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RDSEM: Two-Level Time Series Factor Analysis
xt-1 xt
ft-1 ft
y1 y1y2 y2y3 y3t-1 t-1t-1 t t t
Within
Between
s logv ry1 y2 y3
fb w
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Growth Modeling with Time-Varying Covariates inSingle-Level Wide Format with Auto-Correlated Residuals
y1 y2 y3 y4 y5
i
s
w
x1 x2 x3 x4 x5
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RDSEM: Two-Level Time Series Trend Analysis
yt-1 yt
xt-1 xt
Within
Between
w
y s sx logv r
r logv
timet-1 timet
sx s
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New DSEM Features with Categorical Variables
Lagged categorical variable: ut regressed on ut−1
Random slope for categorical predictor with latent centering(DSEM, not yet RDSEM, but also regular 2-level)
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Categorical DSEM: A Way to Handle Strong Floor Effects
Overall: 42% at the floor value (smoking urge in cessation study)
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Early: 27% at the floor value
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Late: 47% at the floor value
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Two-Part Modeling of Floor Effects
Transform the variable into 2 variables:- A binary u and a continuous y (DATA TWOPART)
u = 0 if at the floor: y is missing
u = 1 if not at the floor: y is observed
Probit model for u
Log normal model for y
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Two-Part DSEM Regression ModelingContinuous and Binary Outcome
yt-1 yt
ut-1 ut
xt-1 xt
Two-part trend/growth modeling can be done in line with the MplusUser’s Guide ex 6.16.
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Quick questions/comments on Part 1 before we turn to Part 2?
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References
Asparouhov, T., Hamaker, E.L. & Muthen, B. (2018). Dynamic structural equationmodels. Structural Equation Modeling: A Multidisciplinary Journal, 25:3,359-388.
Asparouhov, T. & Muthen, B. (2018a). Comparison of DSEM and RDSEM.
Asparouhov, T. & Muthen, B. (2018b). Centering predictor and mediator variables inmultilevel and time series models.
Asparouhov, T. & Muthen, B. (2018c). Nesting and equivalence testing in Mplus.
Asparouhov, T. & Muthen, B. (2018d). SRMR in Mplus.
Bentler, P. & Satorra, A. (2010). Testing model nesting and equivalence.Psychological Methods, 15, 111-123.
Bolger, N. & Laurenceau, J-P. (2013). Intensive longitudinal methods: Anintroduction to diary and experience sampling research. New York: Guilford.
Hamaker, E.L., Asparouhov, T., Brose, A., Schmiedek, F. & Muthen, B. (2018). Atthe frontiers of modeling intensive longitudinal data: Dynamic structuralequation models for the affective measurements from the COGITO study.Multivariate Behavioral Research.
Liu, Y. & West, S. (2015). Weekly cycles in daily report data: An overlooked issue.Journal of Personality, 84, 560-579.
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