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SEM and Path analysis (Multi-step regressions (MS-Path analysis (some…

- - - - Strongly affected by
        
        multivariate non-normality
        
        correlation size
        
        size of the unique variances
        
        sample size
  - - - proportion of the observed variance-covariance matrix explained by the model
      - RMR
        
        average difference between observed and model-estimated covariance matrices
        
        smaller--> good fit, 0 is perfect
        
        depend on range of observed variables
        
        SRMR
        
        standardised version
        
        covarinace matrices--> correlation matrices
        
        range 0 to 1 (0=perfect fit)
        
        .08 regarded as good by Hu and Bentler
    - - relative improvement in fit compared to a baseline
      - CFI
        
        Compares your model to independence (null) model
        
        range 0 to 1 (high values is better)
        
        ideally >.95
      - Tucker-Lewis Index
        
        non-normed fit index
        
        harsher on complex models than CFI
        
        not normed to 0 to 1
        
        highly correlated with CFI
    - - compare model to data but penalise models with too much complexity
        
        rewards models with larger samples and more degrees of freedom
        
        badness of fit statistic
        
        lower is better, 0 is best
    - - Only test the average/overall fit of a model
      - each test reflects only a specific aspect of fit
      - don't relate clearly to the degree/type of model misspecification
      - Well-fitting models do not necessarily have high explanatory power
      - don't indicate whether results are theoretically meaningful
      - say little about person-level-fit
    - - examining modification indices
        
        Indicate the expected change in Chi-square if this relationship were free to vary
      - examining residual covariances
        
        Sample covariances:
        
        our input variancecovariance matrix
        
        Implied covariances
        
        the model-implied
        variance-covariance matrix
        
        Residual covariances
        
        difference between
        sample and implied covariances
        
        Standardized residual covariances
        
        ratios of
        covariance residuals over their standard errors
- - - - simpler
      - paths are uni-directional
      - error terms are independent
      - can be tested with standard multiple regression
    - - can have bi-directional paths
      - can have correlated errors
      - feedback loops
      - require structural equation software to fit them