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Longitudinal Relationships & Structural Equation Models in Restrained Eating & Weight Gain

Explore the structural equation models used to estimate longitudinal relationships between restrained eating behavior and weight gain. Understand the paradoxical hypothesis of inducing weight gain through episodes of loss of control eating. Study cross-sectional and longitudinal effects in the Fleurbaix Laventie Ville Santé Study.

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Longitudinal Relationships & Structural Equation Models in Restrained Eating & Weight Gain

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  1. Michel ChavanceINSERM U1018, CESP, Biostatistique Use of Structural Equation Models to estimate longitudinal relationships

  2. Restrained Eating and weight gain • Restrained eating = tendency to consciously restrain food intake to control body weight or promote weight loss • Positive association between Restrained Eating and fat mass • Paradoxical hypothesis : induction of weight gain through frequent episodes of loss of control and dishinibited eating

  3. CRS0 CRS1 U XXX X Adp0 Adp1

  4. X X U U Y Y 1 2 In both cases, we observe In 1) it is not a structural equation, because E[Y|do(X=x)] ≠ a+bx While in 2) it is a structural equation because E[Y|do(X=x)] = a+bx A structural equation is true when the right side variables are observed AND when they are manipulated

  5. X X azx ex U Z bxy Y azy Y ey Is the model identified ???

  6. Cross-sectional and longitudinal effects • Cross-sectional model (time 0) • Model for changes (changes are negatively correlated with baseline values) • Longitudinal extension

  7. CRS0 DC U X Adp0 DA

  8. FLVS II study • Fleurbaix Laventie Ville Santé Study (risk factors for weight and adiposity changes) • 293/394 families recruited on a voluntary basis • 2 measurements (1999 and 2001) • 4 anthropometric measurements • BMI = weight / height2 • WC = Waist Circumference • SSM = Sum of Skinfold Thicknesses (4 measurements) • PBF = % body fat (foot to foot bioimpedance analyzer) • Cognitive restrained scale

  9. Structural Equation and Latent Variable models • Latent variable : several observed variables are imperfect measurements of a single latent concept (e.g. for subject i, 4 indicators Iik of adiposity Ai) • The measurement model postulates relationships between the unobserved value of adiposity A for subject i and its 4 observed measurements Ik, and thus between the observed measurements

  10. Measurement model and factor analysis • Identification problem: the parameters depend on the measurement scale of the latent variable A • Usual solution : constraint l1=1 (i.e. same scale for A and its 1st observed measurement)

  11. Estimation and tests • Aim = modeling the covariance structure • Maximum likelihood estimator (assuming normal distributions) with S(q) the predicted and S the observed covariance matrix • Likelihood ratio test of compared to saturated model (deviance)

  12. Estimation and tests Variance of the estimator Confidence intervals and Wald’s tests

  13. Overal model fit • Normed fit index (Bentler and Bonett, 1980) relative change when comparing deviances of model 1 (D1) and model 0 assuming independence (D0) • RMSEA=Root Mean Squared Error Approximation measures a « distance » between  the true and the model covariance matrices at the population level

  14. Studied population in 1999mean (standard deviation) ** sex difference (p<0.01) *** sex difference (p<0.001) Similar findings in 2001 Beware the sign of the differences ……..

  15. Measurement model Adp 1) 4 separate analyses by sex and time 2) 2 separate analyses (identicalloadingsateach time) 3) all subjectstogether l1=1 l4 l2 l3 %BF log(BMI) Log(SST) Log(WC)

  16. * model with equality constraints The same measurement model holds for both years, but not for both sexes

  17. Measurement model for changes • Measurement model at time j n,4 n,1 1,4 n,4 • Because the loadings are identical at both times, the same measurement model holds for the changes

  18. Estimated Loadings of the Global Measurement Model (Females) Standardized coefficients

  19. Structural Equation Model:Regression Coefficients (Females) Baseline Adiposity

  20. Structural Equation Model:Regression Coefficients (Females) Adiposity Change

  21. Structural Equation Model:Regression Coefficients (Females) CRS Change

  22. Direct and Indirect Effects of Baseline CRS on Adiposity change standard errors obtained by bootstrapping the sample 1,000 times

  23. Often useful to model the changes rather than the successive outcomes. • Structural equation modeling = translation of a DAG, but some models are not identified. • We still need to assume that all confounders of the effect of interest are observed.

  24. CRS0 CRS1 U XXX X Adp0 Adp1

  25. CRS0 CRS1 U XXX X Adp0 Adp1

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