# Over-time Actor-partner Interdependence Model (correlations)

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### Marta Vigier

Jul 24, 2018, 8:21:12 AM7/24/18
to lavaan
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

Jul 24, 2018, 9:56:35 AM7/24/18
to lavaan
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