intensive longitudinal data, multilevel modeling, and sem

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

Bengt Muthen & Tihomir Asparouhov Mplus Version 8.1 1/ 18

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


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


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


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


RDSEM: Autocorrelated Residuals in Two-Level Regression

yt-1 yt

xt-1 xt

Within

Between

y s logv r

r logv

s

w


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


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;


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


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


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


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


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)


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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5

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5

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5

2.7

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5

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5

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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


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.


Quick questions/comments on Part 1 before we turn to Part 2?


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.


intensive longitudinal data, multilevel modeling, and sem

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