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1 Conclusions Ann Berrington University of Southampton

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2 Review of this mornings 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

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3 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

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4 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

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5 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

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6 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

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7 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

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8 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) = Log likelihood = Prob > chi2 = score | Coef. Std. Err. z P>|z| [95% Conf. Interval] time | _cons | /sigma_u | /sigma_e | rho | Likelihood-ratio test of sigma_u=0: chibar2(01)= Prob>=chibar2 = 0.000

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9 Results from SEM Estimates S.E. Est./S.E. INT | SCORE SCORE SCORE SCORE SLOPE | SCORE SCORE SCORE SCORE Means INT SLOPE Intercepts SCORE SCORE SCORE SCORE Variances INT SLOPE Residual Variances SCORE SCORE SCORE SCORE = =

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10 Result from SEM: tests of model fit Chi-Square Test of Model Fit Value Degrees of Freedom 10 P-Value Chi-Square Test of Model Fit for the Baseline Model Value Degrees of Freedom 6 P-Value CFI/TLI CFI TLI Loglikelihood H0 Value H1 Value Information Criteria Number of Free Parameters 4 Akaike (AIC) Bayesian (BIC) Sample-Size Adjusted BIC (n* = (n + 2) / 24) RMSEA (Root Mean Square Error Of Approximation) Estimate Percent C.I Probability RMSEA <= SRMR (Standardized Root Mean Square Residual) Value 0.038

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