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Michel Chavance INSERM U1018, CESP, Biostatistique

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Michel Chavance INSERM U1018, CESP, Biostatistique. Use of Structural Equation Models to estimate longitudinal relationships. Restrained Eating and weight gain. Restrained eating = tendency to consciously restrain food intake to control body weight or promote weight loss - PowerPoint PPT Presentation

Text of Michel Chavance INSERM U1018, CESP, Biostatistique

  • Michel Chavance

    INSERM U1018, CESP, BiostatistiqueUse of Structural Equation Models to estimate longitudinal relationships

  • Restrained Eating and weight gainRestrained 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

  • CRS1Adp1CRS0Adp0UXXX


  • XYUXYIn 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 becauseE[Y|do(X=x)] = a+bx

    A structural equation is true when the right side variables are observed AND when they are manipulated



    ZazxbxyexeyazyIs the model identified ???

  • Cross-sectional and longitudinal effectsCross-sectional model (time 0)

    Model for changes

    (changes are negatively correlated with baseline values)Longitudinal extension


  • FLVS II studyFleurbaix Laventie Ville Sant Study (risk factors for weight and adiposity changes)293/394 families recruited on a voluntary basis2 measurements (1999 and 2001)4 anthropometric measurementsBMI = weight / height2WC = Waist CircumferenceSSM = Sum of Skinfold Thicknesses (4 measurements)PBF = % body fat (foot to foot bioimpedance analyzer)Cognitive restrained scale

  • Structural Equation and Latent Variable modelsLatent 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

  • Measurement model and factor analysis

    Identification problem: the parameters depend on the measurement scale of the latent variable AUsual solution : constraint l1=1 (i.e. same scale for A and its 1st observed measurement)

  • Estimation and testsAim = modeling the covariance structureMaximum likelihood estimator (assuming normal distributions)

    with S(q) the predicted and S the observed covariance matrixLikelihood ratio test of compared to saturated model (deviance)

  • Estimation and tests Variance of the estimator

    Confidence intervals and Walds tests

  • Overal model fitNormed 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

  • Studied population in 1999mean (standard deviation)

    ** sex difference (p

  • Measurement model

    1) 4 separate analyses by sex and time 2) 2 separate analyses (identical loadings at each time) 3) all subjects togetherAdp%BFlog(BMI)Log(SST)Log(WC)l1=1l4l3l2

  • * model with equality constraints

    The same measurement model holds for both years, but not for both sexes

    MalesFemales19992001Both Years*19992001Both YearsNFI0.9990.9970.960.9880.9960.96

  • Measurement model for changesMeasurement model at time j

    n,4 n,1 1,4 n,4Because the loadings are identical at both times, the same measurement model holds for the changes

  • Estimated Loadings of the Global Measurement Model (Females)

    Standardized coefficients

    EstimateEstimateStandard Dev.Standardized EstimatesBaselineChange%BF1.000-0.9550.603log(BMI)0.0240.00070.9560.996log(SST)0.0550.00210.8790.558log(WC)0.0190.00060.9380.647

  • Structural Equation Model:Regression Coefficients (Females)Baseline Adiposity

    covariatesbsdCI95Age0.2540.096[0.07, 0.44]Baseline CRS0.0510.020[.012, .090]

  • Structural Equation Model:Regression Coefficients (Females)Adiposity Change

    covariatesbsdCI95Adiposity0-0.0240.021[-0.07, 0.02]

    Age00.0380.030[-0.02, 0.10]CRS0-0.0100.007[-.04, 0.02]CRS change-0.0140.010[-0.03, 0.01]

  • Structural Equation Model:Regression Coefficients (Females)CRS Change

    covariatesbsdCI95Adiposity00.4380.134[0.17, 0.70]

    Age00.0230.200[-0.37, 0.42]CRS0-0.2860.042[-0.37, -0.20]

  • Direct and Indirect Effects of Baseline CRS on Adiposity change

    standard errors obtained by bootstrapping the sample 1,000 times

    Estimatesd1: direct-0.00960.00692: indirect through CRS change0.00400.00313: indirect through baseline adiposity-0.00120.00111+2 (partial)-0.00560.00641+2+3 (total)-0.00680.0064

  • 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.

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