Modeling Longitudinal Dyadic Data in the SEM Framework

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2 DEPARTMENT DATA ANALYSIS Modeling Longitudinal Dyadic Data in the SEM Framework Fien Gistelinck Promoter: Tom Loeys

3 CONTENT Longitudinal dyadic data Modeling framework Fien Gistelinck RSSB /18

4 Longitudinal dyadic data Fien Gistelinck RSSB /18

5 Cross-sectional APIM What is the eect of positive relational feelings on the perceived intimacy in heterosexual couples? PosRel M Intim M 1 ε M (X) PosRel F a F 1 Intim F ε F Fien Gistelinck RSSB /18

6 Cross-sectional APIM What is the eect of positive relational feelings on the perceived intimacy in heterosexual couples? PosRel M Intim M 1 ε M (X) PosRel F a F 1 Intim F ε F Fien Gistelinck RSSB /18

7 Cross-sectional APIM What is the eect of positive relational feelings on the perceived intimacy in heterosexual couples? PosRel M Intim M 1 ε M (X) PosRel F a F 1 Intim F ε F Fien Gistelinck RSSB /18

8 Cross-sectional APIM What is the eect of positive relational feelings on the perceived intimacy in heterosexual couples? PosRel M Intim M 1 ε M (X) PosRel F a F 1 Intim F ε F Fien Gistelinck RSSB /18

9 Research Questions How does an increase in positive relational feelings of one's partner on a particular day (as compared to his/her partner's average positive relational feelings) aect one's own perceived intimacy? To what extent is the perceived intimacy of one dyad member related to the perceived intimacy of the partner? On a particular day? On average? How strong is the association between the perceived intimacy on one day with the amount of perceived intimacy on the next day within a given person? Fien Gistelinck RSSB /18

10 Longitudinal APIM PosRel AM TIME 1 a M pmf a M PosRel SM1 PosRel SF1 p FM a F Intim M1 Intim F1 ε M1 ε F1 σ 2 M i M PosRel AF a F pfm a F TIME 2 p MF PosRel SM2 PosRel SF2 a F Intim M2 Intim F2 ε M2 ε F2 σ 2 F i F Fien Gistelinck RSSB /18

11 Longitudinal APIM PosRel AM TIME 1 a M pmf a M PosRel SM1 PosRel SF1 p FM a F Intim M1 Intim F1 ε M1 ε F1 σ 2 M i M PosRel AF a F pfm a F TIME 2 p MF PosRel SM2 PosRel SF2 a F Intim M2 Intim F2 ε M2 ε F2 σ 2 F i F Fien Gistelinck RSSB /18

12 Longitudinal APIM PosRel AM TIME 1 a M pmf a M PosRel SM1 PosRel SF1 p FM a F Intim M1 Intim F1 ε M1 ε F1 σ 2 M i M PosRel AF a F pfm a F TIME 2 p MF PosRel SM2 PosRel SF2 a F Intim M2 Intim F2 ε M2 ε F2 σ 2 F i F Fien Gistelinck RSSB /18

13 Longitudinal APIM PosRel AM TIME 1 a M pmf a M PosRel SM1 PosRel SF1 p FM a F Intim M1 Intim F1 ε M1 ε F1 σ 2 M i M PosRel AF a F pfm a F TIME 2 p MF PosRel SM2 PosRel SF2 a F Intim M2 Intim F2 ε M2 ε F2 σ 2 F i F Fien Gistelinck RSSB /18

14 Longitudinal APIM PosRel AM TIME 1 a M pmf a M PosRel SM1 PosRel SF1 p FM a F Intim M1 Intim F1 ε M1 ε F1 σ 2 M i M PosRel AF a F pfm a F TIME 2 p MF PosRel SM2 PosRel SF2 a F Intim M2 Intim F2 ε M2 ε F2 σ 2 F i F Fien Gistelinck RSSB /18

15 Longitudinal APIM PosRel AM TIME 1 a M pmf a M PosRel SM1 PosRel SF1 p FM a F Intim M1 Intim F1 ε M1 ε F1 σ 2 M i M PosRel AF a F pfm a F TIME 2 p MF PosRel SM2 PosRel SF2 a F Intim M2 Intim F2 ε M2 ε F2 σ 2 F i F Fien Gistelinck RSSB /18

16 Residual Covariance Structure Cov( ε M1 ε M2 ε MT ε F1 ε F2 ε FT ) = ( σ 2 M 2 ) σ F 1 T 1 1 T 2 T 1 T 2 1 Fien Gistelinck RSSB /18

17 Statistical Challenges 1 The correlation between dyad members 2 The autocorrelation 3 The eect of actor and partner characteristics 4 The partitioning into time-specic and time-averaged eects L-APIM takes up all these challenges Implementation? Fien Gistelinck RSSB /18

18 Modeling framework Fien Gistelinck RSSB /18

19 Multilevel modeling Software: nmle, lme4, SAS, HLM,... Between-dyad variation: Using random eects? Residual covariance structure Standard packages fail SAS: Indistinguishable dyads Fien Gistelinck RSSB /18

20 Structural equation modeling Software: lavaan, Mplus, EQS, LISREL,... Between-dyad variation: Using latent variables? Residual covariance structure MSEM fails Standard SEM: use constraints Computational intensive Fien Gistelinck RSSB /18

21 Moving Average Approach Intim M1 ZM1 Intim M2 ZM2 Intim M3 ZM3 (1 2 ) Intim F1 Intim F2 ZF1 ZF2 (1 2 ) Intim F3 ZF3 Fien Gistelinck RSSB /18

22 Moving Average Approach Intim M1 ZM1 Intim M2 ZM2 Intim M3 ZM3 (1 2 ) Intim F1 Intim F2 Intim F3 ZF1 ZF2 ZF3 (1 2 ) Fien Gistelinck RSSB /18

23 Moving Average Approach Intim M1 ZM1 0, σ 2 M Intim M2 ZM2 0, σ 2 M Intim M3 ZM3 0, σ 2 M (1 2 ) Intim F1 ZF1 0, σ 2 F Intim F2 ZF2 0, σ 2 F (1 2 ) Intim F3 ZF3 0, σ 2 F Fien Gistelinck RSSB /18

24 Moving Average Approach Intim M1 Intim M2 Intim M3 ZM1 ZM2 ZM3 0, σ 2 M 0, ν 2 M2 = σ 2 M(1 2 ) 0, ν 2 M3 = σ 2 M(1 2 ) (1 2 ) Intim F1 ZF1 0, σ 2 F Intim F2 ZF2 0, ν 2 F2 = σ 2 F(1 2 ) (1 2 ) Intim F3 ZF3 0, ν 3 F2 = σ 2 F(1 2 ) Fien Gistelinck RSSB /18

25 Moving Average Approach Intim M1 Intim M2 Intim M3 ZM1 ZM2 ZM3 0, σ 2 M 0, ν 2 M2 = σ 2 M(1 2 ) 0, ν 2 M3 = σ 2 M(1 2 ) (1 2 ) Intim F1 ZF1 0, σ 2 F Intim F2 ZF2 0, ν 2 F2 = σ 2 F(1 2 ) (1 2 ) Intim F3 ZF3 0, ν 3 F2 = σ 2 F(1 2 ) Fien Gistelinck RSSB /18

26 Advantages SEM Allows latent outcome variables Incorporates measurement error Allows latent decomposition No imposed manifest approach Easily implements constraints Easily relaxes the assumptions of the L-APIM Assumes wide data structure Applies FIML to deal with missingness Assumes wide data structure Multi-equation coding Fien Gistelinck RSSB /18

27 R-Shiny application Fien Gistelinck RSSB /18

28 Conclusion The L-APIM extends the cross-sectional APIM allows researchers to model longitudinal dyadic data tackles the statistical challenges within the SEM framework can be tted using the R-Shiny app: Fien Gistelinck RSSB /18

29 Any Questions? A Shiny-what? Fien Gistelinck RSSB /18

30 Fien Gistelinck PhD Student DEPARTMENT OF DATA ANALYSIS P Tom Loeys Ghent University E T Ghent University Fien Gistelinck RSSB /18