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					     Conclusions

     Ann Berrington
University of Southampton




                            1
    Review of this morning’s aims
• Aim:
  – To describe, illustrate, compare and contrast the use
    of:
      • graphical chain models
      • structural equation models
      • random effect models
  – for the analysis of panel data
• What are the advantages and disadvantages?
• How different are they? – convergences and
  recent developments


                                                            2
    Advantages and disadvantages of
        graphical chain models
• Advantages
   – Fit relatively simple models for the various types of
     response
   – Can use standard methods to handle the complex
     survey design and non-response
   – Can use Markov properties to draw conclusions about
     conditional independence and dependence structure
     of subsets of variables
• Disadvantages
   – Not using all the information in the repeated
     measures or modelling the reciprocal relationship
     simultaneously
   – Difficult to adjust for measurement error
   – Difficult to assess overall goodness of fit of the model
     or to test for equality of effects across time           3
   Advantages and disadvantages of
    random effects models (MLM)
• Advantages
  – Easy to expand to 3 or more levels
  – Can explicitly incorporate alternative link functions
    e.g. for binary and nominal outcomes
  – Uses data available – e.g. can include individuals until
    they drop out
• Disadvantages
  – Assumption of independence between the random
    effects and the fixed effects
  – Random intercept (but not random coefficient models)
    assume exchangeable correlation structure

                                                           4
   Advantages and disadvantages of
   structural equation models (SEM)
• Advantages
  – Provides an overall measure of model fit
  – Can include multiple indicator latent variables
  – Can decompose total effects into direct and indirect
    effects
• Disadvantages
  – Difficult to incorporate 3+ levels
  – Requires careful interpretation of parameters
  – Many packages do not allow for inclusion of weights,
    complex survey design
  – Some packages do not allow for categorical
    dependent variables esp. those with more than two
    categories
                                                           5
        Convergence in methods
• Latent variables could be incorporated to some extent in
  graphical models (e.g. could have used factor loadings
  for items used for gender role attitude to create a new
  variable)

• 2-level random effects MLM growth model is analytically
  equivalent to a SEM estimation
   – In MLM time is entered as a predictor variable
   – In SEM time is entered as the factor loadings relating
     the repeated measures to the underlying latent
     factors




                                                              6
 Recent developments include:
• All approaches - methods for incorporation of weights
  and complex survey design
• MLM – models for simultaneous processes
• Extension of SEM to 3+ levels
• GLLAMM - generalized linear latent and multilevel
  models
• MPlus – general model framework – e.g. incorporation of
  categorical dependent variables using polychoric
  correlations and weighted least squares estimation




                                                        7
   Result from Random Intercept Model
Random-effects ML regression                   Number of obs      =      5716
Group variable (i): pid                        Number of groups   =      1429

Random effects u_i ~ Gaussian                  Obs per group: min =          4
                                                              avg =        4.0
                                                              max =          4

                                               LR chi2(1)         =     80.17
Log likelihood   = -14015.718                  Prob > chi2        =    0.0000

------------------------------------------------------------------------------
       score |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        time | -.1162701    .0129252    -9.00   0.000    -.1416031   -.0909371
       _cons | 20.37418     .0880119   231.49   0.000     20.20168    20.54668
-------------+----------------------------------------------------------------
    /sigma_u | 2.779735     .0602076    46.17   0.000      2.66173     2.89774
    /sigma_e | 2.185095     .0235981    92.60   0.000     2.138844    2.231347
-------------+----------------------------------------------------------------
         rho | .6180766     .0117726                       .594806    .6409282
------------------------------------------------------------------------------
Likelihood-ratio test of sigma_u=0: chibar2(01)= 2627.65 Prob>=chibar2 = 0.000




                                                                                 8
                       Results from SEM
              Estimates S.E. Est./S.E.
INT  |
  SCORE91      1.000    0.000     0.000
  SCORE93      1.000    0.000     0.000
  SCORE95      1.000    0.000     0.000
  SCORE97      1.000    0.000     0.000

SLOPE |
 SCORE91       0.000    0.000     0.000
 SCORE93       2.000    0.000     0.000
 SCORE95       4.000    0.000     0.000
 SCORE97       6.000    0.000     0.000

Means                                     Residual Variances
 INT         20.374 0.088       231.493     SCORE91            4.775   0.103   46.298
 SLOPE       -0.116 0.013       -8.996      SCORE93            4.775   0.103   46.298
                                            SCORE95            4.775   0.103   46.298
Intercepts                                  SCORE97            4.775   0.103   46.298
  SCORE91      0.000    0.000     0.000
  SCORE93      0.000    0.000     0.000
  SCORE95      0.000    0.000     0.000
  SCORE97      0.000    0.000     0.000

Variances                                      √7.727 = 2.7797
 INT         7.727     0.335    23.085
 SLOPE       0.000     0.000     0.000         √4.775 = 2.1852
                                                                                    9
      Result from SEM: tests of model fit
•   Chi-Square Test of Model Fit
•        Value                   139.127
•        Degrees of Freedom           10
•        P-Value                  0.0000

•   Chi-Square Test of Model Fit for the Baseline Model
•        Value                  2761.481
•        Degrees of Freedom              6
•        P-Value                   0.0000

•   CFI/TLI                                          RMSEA (Root Mean Square Error Of Approximation)
•        CFI                     0.953                   Estimate                0.095
•        TLI                     0.972                   90 Percent C.I.          0.081 0.109
                                                         Probability RMSEA <= .05       0.000
•   Loglikelihood
•         H0 Value              -14015.718           SRMR (Standardized Root Mean Square Residual)
•         H1 Value              -13946.154               Value                 0.038

•   Information Criteria
•         Number of Free Parameters          4
•         Akaike (AIC)                   28039.436
•         Bayesian (BIC)                 28060.495
•         Sample-Size Adjusted BIC       28047.788
•          (n* = (n + 2) / 24)
                                                                                             10

				
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posted:2/15/2013
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