USING STRUCTURAL EQUATION MODELING APPROACHES FOR ANALYSING THREE MODE DATA WITH REPEATED MEASURES DESIGN Appendix 3

STRUCTURAL EQUATION MODELING TECHNIQUES (SEM) FOR THE STUDYING TIME CHANGES (Analysis Repeated Measured)  Recurrent (Autoregressive) Modeling  Latent curve Modeling (LCM)  Confirmatory Dynamical Factor Analysis  Multilevel Analysis Dynamics Of Change

 Recurrent (Autoregressive) Modeling  Recurrent measured variables modeling (measured- variable path analysis) Univariate (one measured variable) X 11 X 21 X 31 … X I-11 X I1 E 21 E 31 E I-11 E I1 X 21 = α 121 *X 11 +E 21 X 31 = α 131 *X 11 + α 231 *X 21 +E 31 … X I1 = α 1n1 *X 11 + α 2n1 *X 21 +… + α I-1I1 *X I-1 +E I1

 Recurrent (Autoregressive) Modeling  Recurrent measured variables modeling – Multivariate Associative - examining the within-time correlations and between-time determinations different variables X 11 X 21 X 31 … X I-11 X I1 X 12 X 22 X 32 … X I-12 X I2 X 1J X 2J X 3J … X I-1J X IJ E X22 E X2J E X21 E X32 E X3J E X31 E XI-12 E XI-1J E XI-11 E XI2 E XIJ E XI1 …

 Recurrent (Autoregressive) Modeling  Recurrent latent variables modeling (latent-variable path analysis) X 11 F1F1 X 12 X 1J E X11 E X12 E X1J … X i1 FiFi X i2 X iJ E Xi1 E Xi2 E XiJ … X I1 FIFI X I2 X IJ E XI1 E XI2 E XIJ imposing latent constructs at each of the data waves to reflect within-time interactions of measured variables and at each of the data waves, testing for unique or specific effects involving residual terms as predictors and outcomes (Newcomb 1994) DiDi DIDI

 Recurrent (Autoregressive) Modeling  Recurrent latent variables modeling (latent-variable path analysis) Without ↔ With determinants and covariates (socio and psychological predictors of behaviors) Simple (one latent construct) ↔ Associative (several latent constructs)

 Latent Curve Modeling (LCM)  Studying latent constructs (factors) determining changes during time Simple (univariate - one studied behavior) X1X1 X2X2 X3X3 …X I-1 XIXI E2E2 E3E3 E I-1 EIEI E1E1 ConstantLinearCubic… n12I-1I0 14(n-1) 2 n2n2 0 Level 2 0(I-1) 2 I2I2 0 Shape Quadratic X 1 = 1F 1 + E 1 X 2 = 1F 1 + 1F 2 + 1F 3 + 1F 4 + E 2 X 3 = 1F 1 + 2F 2 + 4F 3 + 8F 4 + E 3 X I-1 =1F 1 +(I-1)F 2 +(I-1) 2 F 3 +(I-1) 3 F 4 + E I- 1 X I = 1F 1 + IF 2 + I 2 F 3 + I 3 F 4 + E I

 Latent Curve Modeling  Studying latent constructs (factors) determining changes during time Multivariate (variables are analyzed separately) X 11 X i1 X I1 … Level X1 Shape X1 … X 12 X i2 X I2 … Level X2 Shape X2 … X 1J X iJ X IJ … Level XJ Shape XJ …

 Latent Curve Modeling  Studying latent constructs (factors) determining changes during time Without ↔ With socio and psychological determinants and covariates X 11 X i1 X I1 … Level X Shape X … ŵ

 Latent Curve Modeling  Higher order Multivariate LCM Factor-Of-Curves Models – Second order factors (Latent constructs) of development constructs of changes X 11 X i1 X I1 … Level X1 Shape X1 … X 12 X i2 X I2 … Level X2 Shape X2 … X 1J X iJ X IJ … Level XJ Shape XJ … Common Level Common Shape

 Latent Curve Modeling  Higher order Multivariate LCM Curve-Of-Factors Models – Development constructs of changes of factors X 11 F1F1 X 12 X 1J … X i1 FiFi X i2 X iJ … X I1 FJFJ X I2 X IJ LevelShape

EXAMPLE Using model latent curve modeling for study determination Internet activity by Internet access Experimental psychosemantics study O.Mitina, A.Vojskunskiy Psychological department Moscow State University

Concepts: I myself Woman – regular Internet user, Man – regular Internet user, Typical Russian woman Typical Russian man, My Ideal woman, My Ideal man.

Factors of Internet activity: 1. Professional and business uses of the Internet 2. Internet-based education of children 3. Entertainments 4. Competent Internet use in order to realize personal goals 5. Compensatory Internet use 6. Cognitive uses of the Internet 7. Highly qualified use of the Internet 8. Internet-mediated communication

Subjects 95 persons: Moscow colleges’ students 47 males and 48 females

Independent variable – «Internet access» Ordinal scale Internet access. Criteria – average time spending in Internet. Concepts were ordered in increasing: –Typical Russian (male/female), –Ideal (male/female), –Regular Internet user (male/female) Concepts were ordered for both sex separately

Structural model of Latent Growth Internet activity Typical Russian woman Ideal woman Regular Internet User (female) Female concepts Typical Russian man Ideal man Regular Internet User (male) Male concepts Intercept F Slope F Intercept M Slope M Advance Competence in IT Cognitive uses of the Internet Internet-self-esteem Compensatory Internet use Internet- mediated communication