Causal models notes sems notes notes notes.pdf
- 1. Causal Modelling: SEMs Arnab Jana 2025
- 2. Causal Models • Causal models are mathematical models representing causal relationships within an individual system or population. • They facilitate inferences about causal relationships from statistical data. • They can teach us a good deal about the epistemology of causation, and about the relationship between causation and probability.
- 3. What Is Structural Equation Modeling? • SEM: very general, very powerful multivariate technique. • Specialized versions of other analysis methods. • Major applications of SEM: • Causal modeling or path analysis. • Confirmatory factor analysis (CFA).
- 4. • Test coefficients across multiple between-subjects groups • Ability to handle difficult data • Longitudinal with auto-correlated error • Multi-level data • Non-normal data • Incomplete data
- 5. Terms, Nomenclature, Symbols, and Vocabulary • Experimental research • independent and dependent variables. • Non-experimental research • predictor and criterion variables • Observed (or manifest) • Latent (or factors)
- 6. Sample Size • Rules of Thumb Ratio of Sample Size to the Number of Free Parameters Tanaka (1987): 20 to 1 (Most analysts now think that is unrealistically high.) Goal: Bentler & Chou (1987): 5 to 1 Several published studies do not meet this goal. Sample Size 200 is seen as a goal for SEM research Lower sample sizes can be used for Models with no latent variables Models where all loadings are fixed (usually to one) Models with strong correlations Simpler models • Models for which there is an upper limit on N (e.g., countries or years as the unit), 200 might be an unrealistic standard.
- 7. SEM details • Measurement model • That part of a SEM model dealing with latent variables and indicators. • Structural model • Contrasted with the above • Set of exogenous and endogenous variables in the model with arrows and disturbance terms
- 8. Measurement Model: Confirmatory Factor Analysis GHQ Hostility Hopelessness Self-rated health Psychosocial health D1 e4 e3 e2 e1 Singh-Manoux, Clark and Marmot. 2002. Multiple measures of socio-economic position and psychosocial health: proximal and distal measures. Latent construct or factor Observed or manifest variables
- 9. Structural Model with Additional Variables GHQ Hostility Hopelessness Income Occupation Education Self-rated health Psychosocial health D1 e4 e3 e2 e1 Latent construct or factor Observed or manifest variables
- 10. Causal Modeling or Path Analysis and Confirmatory Factor Analysis GHQ Hostility Hopelessness Occupation Income Education Self-rated health Psychosocial health D3 e4 e3 e2 e1 D1 D2 a= direct effect c b+c=indirect
- 11. What’s a Good Model? • Fit measures: –Chi-square test –CFI (Comparative Fit Index) –RMSE (Root Mean Square Error) –TLI (Tucker Lewis Index) –GFI (Goodness of Fit Index) –And many, many, many more –IFI, NFI, AIC, CIAC, BIC, BCC
- 12. CFAs & EFAs
- 13. CFAs and EFAs • CFAs include a certain level of systematic measurement error in the form of cross-loadings. Given that items are rarely pure indicators of their corresponding constructs • at least some degree of construct-relevant association can be expected between items and the non-target • recent review of simulation studies (Asparouhov et al., 2015) showed that even small cross-loadings (as small as 0.100) should be explicitly taken into account
- 14. CFAs and EFAs • the Exploratory Structural Equation Modeling (ESEM) framework (Asparouhov and Muthén, 2009; Marsh et al., 2014) has been developed which incorporates the advantages of the less restrictive EFA (i.e., allowing cross-loadings) and the more advanced CFA (i.e., goodness-of-fit or multigroup models) at the same time, providing a synergy that is “the best of both worlds”
- 15. Software • LISREL 9.1 from SSI (Scientific Software International) • IBM’s SPSS Amos • EQS (Multivariate Software) • Mplus (Linda and Bengt Muthen) • CALIS (module from SAS) • Stata’s new sem module • R (lavaan and sem modules)
- 16. AMOS
- 17. STATA
- 18. Books…. • Barbara M. Byrne (2012): Structural Equation Modeling with Mplus, Routledge Press • She also has an earlier work using Amos • Rex Kline (2010): Principles and Practice of Structural Equation Modeling, Guilford Press • Niels Blunch (2012): Introduction to Structural Equation Modeling Using IBM SPSS Statistics and Amos, Sage Publications • James L. Arbuckle (2012): IBM SPSS Amos 21 User’s Guide, IBM Corporation (free from the Web) • Rick H. Hoyle (2012): Handbook of Structural Equation Modeling, Guilford Press • Great fit index site: • http://www.psych-it.com.au/Psychlopedia/article.asp?id=277