Download
skewed random effects in ad model builder n.
Skip this Video
Loading SlideShow in 5 Seconds..
Skewed random effects in AD Model Builder PowerPoint Presentation
Download Presentation
Skewed random effects in AD Model Builder

Skewed random effects in AD Model Builder

106 Views Download Presentation
Download Presentation

Skewed random effects in AD Model Builder

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

  1. Skewed random effects in AD Model Builder

  2. Goal • Analyse model in Section 14.2 of Skrondal and Rabe-Hesketh (2004) Generalized Latent Variable Modeling: Multilevel, Longitudinal and Structural Equation Models. Chapman & Hall • Replace normal distribution with a skewed distribution for the random effects.

  3. 14.2 Diet and heart disease • Covariate measurement error model • 337 middle aged men (bank, transportation) • At requirement: weigh their food • Repeated measurement for 76 men • Heart disease or not? • Covariates: • age (numeric) • bus (0,1)

  4. Model description • Exposure model (true fiber intake) ηj = γ1·agej+γ2·busj + γ3·age*busj+ ζj, ζj ~ N(0, ψ) • Measured fiber intake (i = 1,2) yij = ηj + α0+(i-1)·α1 + ij , ij ~ N(0, θ) • Disease model(D = 0,1) logit(Dj|ηj) = β0 +β1·agej+β2·busj + β3·age*busj + λ·ηj

  5. Setting up and running the model • Prepare data in R: ”diet.s” • Compiling the model • admb -re diet • Running the model (Laplace approx.) • diet -est • Running the model (Gauss-Hermite appr.) • diet -est -gh 20

  6. Skewed distributions for ζ • Skrondal and Rable-Hesket: • Replace N(0,ψ) distribution for ζj by non-parametric distribution (Fig. 14.2) • Skewed distribution for ζj ζj = [a·uj + (1-a)[exp(uj)-exp(0.5)]/c1]/c2, 0 < a < 1 uj ~ N(0, ψ) c1 = sqrt[e(e-1)], c2 = sqrt(a2 + (1-a)2)