Map

Definitions

The dyad is the unit of interpersonal interaction

• Partners
• Friends
• Family
• Co-workers

Types of dyads

Dyad Variability

Mixed

• Risk factor
• Age

Interdependence

Non independence

“If the two scores from the two members of the dyad are non-independent, then those two scores are more similar to (or different from) from one another than are two scores from two people who are not members of the same dyad”.

• More similar within the dyad than the average

Exercise

Jamboard

Data structure

Type of models

• Multilevel model
• Structural Equation Model
• Actor Partner Interdependence Model

Data set

The data

Things we can do

• Estimate the mean for future.
• Using contribution, estimate if more contributions-more positive future
• Using culture, we can estimate differences between groups.
• Finally, the interaction between culture, contribution and future.

Estimate a model using multiple regression

Estimate a model using lmer (random effect)

Is the random effect significant?

Data: data_example
Models:
lmm_wrong: Future ~ Contribution + Culture + Contribution * Culture
lmm: Future ~ Contribution + Culture + Contribution * Culture + (1 | Dyad)
          npar    AIC    BIC  logLik deviance  Chisq Df Pr(>Chisq)   
lmm_wrong    5 168.52 173.50 -79.260   158.52                        
lmm          6 161.89 167.86 -74.943   149.89 8.6345  1   0.003299 **
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Interclass correlation

How many random effects are in this model?

Two random factors:

• The dyadic covariance (the variance of the intercept)
• The error variance

Compute Interclass Correlation Coefficient

Linear mixed model fit by REML ['lmerMod']
Formula: Future ~ (1 | Dyad)
   Data: data_example

REML criterion at convergence: 158.5

Scaled residuals: 
     Min       1Q   Median       3Q      Max 
-1.19559 -0.66688  0.06362  0.56923  1.33335 

Random effects:
 Groups   Name        Variance Std.Dev.
 Dyad     (Intercept) 255.5    15.983  
 Residual              82.3     9.072  
Number of obs: 20, groups:  Dyad, 10

Fixed effects:
            Estimate Std. Error t value
(Intercept)   71.100      5.446   13.05

255.5 / (255.5 + 82.3) = 0.7563647

R square

     R2m       R2c
[1,]   0 0.7563286

Compute ICC

Linear mixed model fit by REML ['lmerMod']
Formula: Future ~ Contribution + Culture + Contribution * Culture + (1 |  
    Dyad)
   Data: data_example

REML criterion at convergence: 142.9

Scaled residuals: 
    Min      1Q  Median      3Q     Max 
-1.5738 -0.5010  0.1035  0.3899  1.4818 

Random effects:
 Groups   Name        Variance Std.Dev.
 Dyad     (Intercept) 176.42   13.282  
 Residual              43.76    6.615  
Number of obs: 20, groups:  Dyad, 10

Fixed effects:
                     Estimate Std. Error t value
(Intercept)           71.8309     4.4696  16.071
Contribution           0.8448     0.2557   3.304
Culture               -9.0328     4.4696  -2.021
Contribution:Culture   0.4873     0.2557   1.906

Correlation of Fixed Effects:
            (Intr) Cntrbt Cultur
Contributin 0.050               
Culture     0.004  0.086        
Cntrbtn:Clt 0.086  0.587  0.050 

Compute ICC

How much variance is explained by the two predictors and the interaction?

1 - ((176.42 + 43.76) / (255.5 + 82.3)) = 34.8%

Actor-Partner Interdependence Model (APIM)

Actor Partner Interdependece Model

Actor-Partner Interdependence Model (APIM)

• Pairwise data set
• Distinguishable and indistinguishable
• The trick for indistinguishable dyads is to constraint the parameters to be equal. It results in one actor effect and one partner effect.
• The null model for dyadic analysis is not the all-free model. The null model should have constrained the means and variances of the actors.

Structural Equation Model Approach

Confirmatory Factor Analysis

Structural Equation Model Approach

SEM approach

Example in Mplus

• Open dyadic.inp

• Data are on dyadic_data.dta

• Run

• What is the correlation between dyads?

Aditional resources

• “How to Use the Actor-Partner Interdependence Model (APIM) To Estimate Different Dyadic Patterns in MPLUS: A Step-by-Step Tutorial”

• “Quantitude”

• “Shiny APIM”