MCEMfit_gam {refitME}

Function for wrapping the MCEM algorithm on gam objects

Description

Function for wrapping the MCEM algorithm on GAMs where predictors are subject to measurement error/error-in-variables.

Usage

MCEMfit_gam(
  mod,
  family,
  sigma.sq.u,
  B = 50,
  epsilon = 1e-05,
  silent = FALSE,
  ...
)

Arguments

mod

: a gam object (this is the naive fitted model). Make sure the first p input predictor variables entered in the naive model are the specified error-contaminated variables. These p predictors also need the measurement error variance to be specified in sigma.sq.u, see below.

family

: a specified family/distribution.

sigma.sq.u

: measurement error (ME) variance. A scalar if there is only one error-contaminated predictor variable, otherwise this must be stored as a vector (of ME variances) or a matrix if the ME covariance matrix is known.

B

: the number of Monte Carlo replication values (default is set to 50).

epsilon

: convergence threshold (default is set to 0.00001).

silent

: if TRUE, the convergence message (which tells the user if the model has converged and reports the number of iterations required) is suppressed (default is set to FALSE).

...

: further arguments passed to gam.

Value

MCEMfit_gam returns the original naive fitted model object but coefficient estimates and the covariance matrix have been replaced with the final MCEM model fit. Standard errors and the effective sample size (which diagnose how closely the proposal distribution matches the posterior, see equation (2) of Stoklosa, Hwang and Warton) have also been included as outputs.

Author(s)

Jakub Stoklosa, Wen-Han Hwang and David I. Warton.

Source

See https://github.com/JakubStats/refitME for an RMarkdown vignette with examples.

References

Ganguli, B, Staudenmayer, J., and Wand, M. P. (2005). Additive models with predictors subject to measurement error. Australian & New Zealand Journal of Statistics, 47, 193–202.

Wand, M. P. (2018). SemiPar: Semiparametic Regression. R package version 1.0-4.2., URL https://CRAN.R-project.org/package=SemiPar.

Stoklosa, J., Hwang, W-H., and Warton, D.I. refitME: Measurement Error Modelling using Monte Carlo Expectation Maximization in R.

See Also

MCEMfit_glm

Examples

# A GAM example using the air pollution data set from the SemiPar package.

library(refitME)
library(SemiPar)
library(mgcv)
library(dplyr)

data(milan.mort)

dat.air <- sample_n(milan.mort, 100) # Takes a random sample of size 100.

Y <- dat.air[, 6]  # Mortality counts.

n <- length(Y)

z1 <- (dat.air[, 1])
z2 <- (dat.air[, 4])
z3 <- (dat.air[, 5])
w1 <- log(dat.air[, 9])  # The error-contaminated predictor (total suspended particles).

dat <- data.frame(cbind(Y, w1, z1, z2, z3))

gam_naiv <- gam(Y ~ s(w1), family = "poisson", data = dat)

sigma.sq.u <- 0.0915 # Measurement error variance.

B <- 10  # Consider increasing this if you want a more accurate answer.

gam_MCEM <- refitME(gam_naiv, sigma.sq.u, B)

plot(gam_MCEM, select = 1)

detach(package:mgcv)