Description Usage Arguments Details Value Author(s) References See Also Examples
The covariance matrix of individual teeth measures for each subject follows a Conditional Autoregressive model (CAR) density
1 | CAR_cov_teeth(m, rho, tau)
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m |
Maximum number of units in each cluster, i.e., 28 teeth in each mouth (the 4 third-molars are usually ignored) |
rho |
Association parameter of the CAR model |
tau |
Variation parameter of the CAR model |
CAR_cov_teeth gives the covariance matrix among the teeth within each mouth based on the CAR structure (Besag et al., 1991), given the maximum number of teeth for each subject (m), the variance (τ), and the association (ρ) parameters.
The CAR covariance matrix can be expressed as Σ_{28\times 28} = τ^2 (W - ρ D)^{-1}, where τ^2 > 0, and ρ \in [0, 1] are the parameters that control the magnitude of variation and the degree of spatial association, respectively. For matrix D, the element D_{tt'} is 1 if locations t and t' are adjacent and 0 otherwise. The matrix W is diagonal with diagonal elements W_{tt} = ∑_{t'} D_{tt'}. Note, the argument τ in CAR_cov_teeth is the variance, and not the standard deviation.
The covariance matrix among the teeth in each mouth (assuming full dentition, i.e., 28 teeth) based on a CAR model.
Jing Xu, Dipankar Bandyopadhyay, Douglas Azevedo, Bibhas Chakraborty
Besag, J., York, J. & Mollie, A. (1991), "Bayesian image restoration, with two applications in spatial statistics (With Discussion)", Annals of the Institute of Statistical Mathematics 43, 159.
Reich, B. & Bandyopadhyay, D. (2010), "A latent factor model for spatial data with informative missingness", The Annals of Applied Statistics 4, 439–459.
MC_var_yibar_mis, SampleSize_SMARTp
1 2 3 4 | m <- 28
rho <- 0.975
tau <- 0.85
Sigma <- CAR_cov_teeth(m = m, rho = rho, tau = tau)
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