# R wrapper that accesses C code to fit parametric Leroux CAR spatial regression model that accounts for spatial confounding `par.eCAR.Leroux` is the main function used to fit the parametric Leroux CAR model specified in the spectral domain. ```r par.eCAR.Leroux(y, x, W, E=NULL, C=NULL, model="Gaussian", joint_prior_lamx_lamz = FALSE, lamx.fix.val = NULL, sig2x.fix.val = NULL, mb=0,s2b=10, mg=0,s2g=10.0, alamx=1, blamx=1, alamz=1, blamz=1, asig=1, bsig=1, atau=1, btau=1, asigx=1, bsigx=1, mb0=0,s2b0=100, me=0,s2e=100, mx=0,s2x=100, tau_cand_sd = 1, sig2_cand_sd = 1, draws=10000, burn=5000, thin=5, verbose=TRUE) ``` ## Arguments - `y`: response vector - `x`: covariate vector for which casual effect is desired - `W`: neighborhood matrix comprised of zeros and ones - `E`: This argument is ignored if model is Gaussian. For other models it takes on the following: * Poisson - E is vector that contains expected counts * Binomial - E is vector that contains number of trials * Negative Binomial - E is vector that contains an offset. - `C`: design matrix for the covariates that are included as controls - `model`: Specifies the likelihood or data model. Options are "Gaussian", "Poisson", "Binomial", "Negative Binomial" - `joint_prior_lamx_lamz`: Logical. If TRUE, then a uniform prior on space such that lamz > lamx. If FALSE, independent beta priors are used. - `lamx.fix.val`: If a value is supplied then lambda_x is not updated in the MCMC algorithm, but rather treated as the fixed known supplied value - `sig2x.fix.val`: If a value is supplied then sigma2_x is not updated in the MCMC algorithm, but rather treated as the fixed known supplied value - `mb`: prior mean for beta. default is 0. - `s2b`: prior variance for beta. default is 10 - `mg`: prior mean for gamma, where gamma = rho*(sigz/sigx). default is 0. - `s2g`: prior variance for, gamma), where gamma = rho*(sigz/sigx). default is 10 - `alamx`: prior shape1 parameter for lam.x, default is 1. Only used if joint_prior_lamx_lamz = FALSE - `blamx`: prior shape2 parameter for lam.x, default is 1. Only used if joint_prior_lamx_lamz = FALSE - `alamz`: prior shape1 parameter for lam.z, default is 1. Only used if joint_prior_lamx_lamz = FALSE - `blamz`: prior shape2 parameter for lam.z, default is 1. Only used if joint_prior_lamx_lamz = FALSE - `asig`: prior shape parameter for sigma2, default is 1. Only used if model is Gaussian - `bsig`: prior scale parameter for sigma2, default is 1. Only used if model is Gaussian - `atau`: prior shape parameter for tau, where tau = sigma2.z*(1-rho^2). default is 1 - `btau`: prior scale parameter for tau, where tau = sigma2.z*(1-rho^2). default is 1 - `asigx`: prior shape parameter for sigma2.x, default is 1 - `bsigx`: prior scale parameter for sigma2.x, default is 1 - `mb0`: prior mean parameter for beta0, default is 0. Only used if model is not Gaussian - `s2b0`: prior variance parameter for beta0, default is 100. Only used if model is not Gaussian - `me`: prior mean parameter for eta, default is 0. Only used if C is not NULL - `s2e`: prior variance parameter for eta, default is 100. Only used if C is not NULL - `mx`: prior mean parameter for xi, default is 0. Only used for negative binomial model - `s2x`: prior variance parameter for eta, default is 100. Only used for negative binomial model - `tau_cand_sd`: standard deviation for candidate density in Metropolis step for tau. Default is 1 - `sig2_cand_sd`: standard deviation for candidate density in Metropolis step for sig2. Default is 1. Only used if model is Gaussian - `draws`: number of MCMC iterates to be collected. default is 10000 - `burn`: number of MCMC iterates discared as burn-in. default is 5000 - `thin`: number by which the MCMC chain is thinned. default is 5 - `verbose`: If TRUE, then details associated with data being fit are printed to screen along with MCMC iterate counter ## Returns The function returns an `eCAR` object which is a list that contains the following - **data_model**: Character indicating which model was fit - **beta_omega**: Matrix that contains respectively, the posterior mean lower and upper quantiles of the (spatial scale)-varying beta at each omega value (for the non Gaussian cases it is the exponentiated beta). - **posterior_draws**: List containing posterior draws of the following parameters 1. beta: vector containing draws from the posterior distribution of exposure coefficient 2. gamma: vector containing draws from the posterior distribution of gamma=rho*(sigz/sigx) 3. tau: vector containing draws from tau=sigma2.z*(1-rho^2) 4. sig2x: vector containing draws from sig2x 5. lamx: vector containing draws from the posterior distribution of lamx 6. lamz: vector containing draws from the posterior distribution of lamz 7. sigma2: vector containing draws from the posterior distribution of sigma2. Only available if model is Gaussian 8. rho: vector containing draws from the posterior distribution of rho 9. sig2z: vector containing draws from the posterior distribution of sig2z 10. theta: matrix containing draws from the posterior distribution of theta. Only available if model is not Gaussian 11. beta0: vector containing draws from the posterior distribution of beta0. Only available if model is not Gaussian 12. eta: matrix containing draws from the posterior distribution of eta, regression coefficients of additional confouner variables. Only available if C is not NULL 13. nb_r: matrix containing draws from the posterior distribution of nb_r. 0nly available if model is Negative Binomial - **DIC**: Not available from parametric model yet - **regrcoef**: Not available from parametric model yet ## References Guan, Y; Page, G.L.; Reich, B.J.; Ventrucci, M.; Yang, S; "A spectral adjustment for spatial confounding" ## Examples ```r # Our R-package library(eCAR) data(lipcancer) W <- lipcancer$neighborhood.Matrix M <- diag(apply(W,1,sum)) R <- M-W e.dec <- eigen(R) e.val <- e.dec$values D.eigval = diag(e.val) Y <- lipcancer$data$observed X <- lipcancer$data$pcaff E <- lipcancer$data$expected set.seed(101) fit1 <- par.eCAR.Leroux(y=Y, x=X, W=W, E=E, C=NULL, model="Poisson", draws=10000, burn=5000, thin=1, verbose=FALSE, joint_prior_lamx_lamz=FALSE) plot(fit1) ```

par.eCAR.Leroux function