Over-time Actor-partner Interdependence Model (correlations)

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Marta Vigier

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Jul 24, 2018, 8:21:12 AM7/24/18

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Dear Lavaan Experts,

First of all, please let me apologize for all my errors, as I am new to Lavaan and SEM.

I tried to estimate the over-time Actor-Partner Independence Model for indistinguishable dyads, in order to analyze physiological synchrony (heart rate) across three-time points.

I wanted to estimate concurrent synchrony (between two individuals at the same time point) and cross-lagged synchrony (one person's heart rate at Time1 predicts other person's heart rate at Time2).

If I understand correctly, Lavaan treats Time1 for both subjects as an exogenous variable and gives their covariance. The Time2 and Time3 are treated as endogenous variables. So two residual variances are correlated and result in residual covariance. And the covariance between exogenous variables seems not to be the same thing as the residual covariance between endogenous variables. Therefore, I am wondering if this is possible to interpret the results of residual covariance (Time2 and Time3) in terms of concurrent synchrony. The results seem to shrink systematically at each time point. I would like to ask if there is any possibility to estimate correlations within Time2 and within Time3 or maybe I choose the wrong method.

Please, see my Lavaan output below.

Many thanks for your help.

Best regards,

Marta Vigier

RECOVERYI_MAIN<- '

+ # actor effects (autoregressive, stability)

+ # Subject2

+ Warte2_HR_m.2 ~ a3*Warte1_HR_m.2 #Time 3- Time 4

+ Warte3_HR_m.2 ~ a4*Warte2_HR_m.2 # Time 4-Time 5

+ # Subject1

+ Warte2_HR_m.1 ~ a3*Warte1_HR_m.1 #Time 3- Time 4

+ Warte3_HR_m.1 ~ a4*Warte2_HR_m.1 # Time 4-Time 5

+ # partner effects (influence)

+ Warte2_HR_m.2 ~ p3*Warte1_HR_m.1

+ Warte3_HR_m.2 ~ p4*Warte2_HR_m.1

+ Warte2_HR_m.1 ~ p3*Warte1_HR_m.2

+ Warte3_HR_m.1 ~ p4*Warte2_HR_m.2

+ # intercepts

+ Warte1_HR_m.2 ~ mz*1

+ Warte1_HR_m.1 ~ mz*1

+ Warte2_HR_m.2 ~ mq*1

+ Warte2_HR_m.1 ~ mq*1

+ Warte3_HR_m.2 ~ mp*1

+ Warte3_HR_m.1~ mp*1

+ # Covariances

+ Warte1_HR_m.2 ~~ cz*Warte1_HR_m.1

+ Warte2_HR_m.2 ~~ cq*Warte2_HR_m.1

+ Warte3_HR_m.2 ~~ cp*Warte3_HR_m.1

+ # Variances

+ Warte1_HR_m.2 ~~ vz*Warte1_HR_m.2

+ Warte1_HR_m.1 ~~ vz*Warte1_HR_m.1

+ Warte2_HR_m.2 ~~ vq*Warte2_HR_m.2

+ Warte2_HR_m.1 ~~ vq*Warte2_HR_m.1

+ Warte3_HR_m.2 ~~ vp*Warte3_HR_m.2

+ Warte3_HR_m.1 ~~ vp*Warte3_HR_m.1'

> RECOVERYI_MAINt <- sem(RECOVERYI_MAIN, data=df_together, meanstructure=TRUE, fixed.x=FALSE)

> summary(RECOVERYI_MAINt, fit.measures = TRUE)

lavaan (0.6-1) converged normally after 114 iterations

Number of observations 24

Estimator ML

Model Fit Test Statistic 9.525

Degrees of freedom 14

P-value (Chi-square) 0.796

Model test baseline model:

Minimum Function Test Statistic 342.369

Degrees of freedom 15

P-value 0.000

User model versus baseline model:

Comparative Fit Index (CFI) 1.000

Tucker-Lewis Index (TLI) 1.015

Loglikelihood and Information Criteria:

Loglikelihood user model (H0) -398.156

Loglikelihood unrestricted model (H1) -393.393

Number of free parameters 13

Akaike (AIC) 822.312

Bayesian (BIC) 837.626

Sample-size adjusted Bayesian (BIC) 797.352

Root Mean Square Error of Approximation:

RMSEA 0.000

90 Percent Confidence Interval 0.000 0.130

P-value RMSEA <= 0.05 0.832

Standardized Root Mean Square Residual:

SRMR 0.104

Parameter Estimates:

Information Expected

Information saturated (h1) model Structured

Standard Errors Standard

Regressions:

Estimate Std.Err z-value P(>|z|)

Warte2_HR_m.2 ~

Wr1_HR_.2 (a3) 0.969 0.025 38.211 0.000

Warte3_HR_m.2 ~

Wr2_HR_.2 (a4) 1.013 0.033 30.869 0.000

Warte2_HR_m.1 ~

Wr1_HR_.1 (a3) 0.969 0.025 38.211 0.000

Warte3_HR_m.1 ~

Wr2_HR_.1 (a4) 1.013 0.033 30.869 0.000

Warte2_HR_m.2 ~

Wr1_HR_.1 (p3) -0.024 0.025 -0.929 0.353

Warte3_HR_m.2 ~

Wr2_HR_.1 (p4) -0.020 0.033 -0.609 0.542

Warte2_HR_m.1 ~

Wr1_HR_.2 (p3) -0.024 0.025 -0.929 0.353

Warte3_HR_m.1 ~

Wr2_HR_.2 (p4) -0.020 0.033 -0.609 0.542

Covariances:

Estimate Std.Err z-value P(>|z|)

Warte1_HR_m.2 ~~

Wr1_HR_.1 (cz) 79.347 35.621 2.228 0.026

.Warte2_HR_m.2 ~~

.Wr2_HR_.1 (cq) 1.118 0.871 1.284 0.199

.Warte3_HR_m.2 ~~

.Wr3_HR_.1 (cp) 0.380 1.245 0.305 0.760

Intercepts:

Estimate Std.Err z-value P(>|z|)

Wr1_HR_.2 (mz) 75.260 2.212 34.030 0.000

Wr1_HR_.1 (mz) 75.260 2.212 34.030 0.000

.Wr2_HR_.2 (mq) 4.487 2.317 1.936 0.053

.Wr2_HR_.1 (mq) 4.487 2.317 1.936 0.053

.Wr3_HR_.2 (mp) 0.767 2.703 0.284 0.777

.Wr3_HR_.1 (mp) 0.767 2.703 0.284 0.777

Variances:

Estimate Std.Err z-value P(>|z|)

Wr1_HR_.2 (vz) 155.424 35.621 4.363 0.000

Wr1_HR_.1 (vz) 155.424 35.621 4.363 0.000

.Wr2_HR_.2 (vq) 4.116 0.871 4.728 0.000

.Wr2_HR_.1 (vq) 4.116 0.871 4.728 0.000

.Wr3_HR_.2 (vp) 6.088 1.245 4.889 0.000

.Wr3_HR_.1 (vp) 6.088 1.245 4.889 0.000

Terrence Jorgensen

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Jul 24, 2018, 9:56:35 AM7/24/18

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If I understand correctly, Lavaan treats Time1 for both subjects as an exogenous variable and gives their covariance.

Yes, if you use the sem() or cfa() functions, exogenous covariances are estimated by default.

I would like to ask if there is any possibility to estimate correlations within Time2 and within Time3 or maybe I choose the wrong method.

The residual covariances controlling for autoregressive effect of a previous occasion, whereas the exogenous covariance does not. You can request them in correlation metric (the std.all column) with summary(..., std = TRUE).

Terrence D. Jorgensen

Postdoctoral Researcher, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam