simex (version 1.0)

simex: Simulation Extrapolation

Description

Implementation of the SIMEX Algorithm for measurement error models according to Cook and Stefanski

Usage

simex(model
	, SIMEXvariable
	, measurement.error
	, lambda = c(0.5,1,1.5,2)
	, B = 100, fitting.method = "quadratic"
	, jackknife.estimation = "quad"
	, asymptotic = TRUE)

Arguments

model

the naive model

SIMEXvariable

character or vector of characters containing the names of the variables with measurement error

measurement.error

vector of standard deviations of the known measurement errors

lambda

vector of lambdas for which the simulation step should be done (without 0)

B

number of iterations for each lambda

fitting.method

fitting method linear,quadratic,nonlinear are implemented. (first 4 letters are enough)

jackknife.estimation

specifying the extrapolation method for jackknife variance estimation. Can be set to FALSE if it should not be performed

asymptotic

logical, indicating if asymptotic variance estimation should be done, in the Naive model the option x = TRUE have to be set.

Value

• Returns an object of class SIMEX which contains:
• coefficients
  the corrected coefficients of the SIMEX model,
• SIMEX.estimates
  the estimates for every lambda,
• model
  the naive model,
• measurement.error
  the known error variances,
• B
  the number of iterations,
• extrapolation
  the model object of the extrapolation step,
• fitting.method
  the fitting method of the extrapolation step,
• residuals
  residuals,
• fitted.values
  fitted values,
• call
  the function call,
• variance.jackknife
  the jackknife variance estimate,
• extrapolation.variance
  the model object of the variance extrapolation,
• variance.jackknife.lambda
  the data set for the extrapolation
• variance.asymptotic
  the asymptotic variance estimates
• theta
  estimates for every B and lambda
• ...

Details

nonlinear is implemented as described in Cook and Stefanski, but is numerically not stable. It is not advisable to use this feature. See fit.nls for details. If a nonlinear extrapolation is desired please use the refit function. Asymptotic is only implemented for naive models of class lm or glm

References

Cook, J.R. and Stefanski, L.A. (1994) Simulation-Extrapolation Estimation in Parametric Measurement error Models. Journal of American Statistical Assosiaction, 89, 1314 -- 1328 Carroll, R.J., K�chenhoff,H., Lombard,F. and Stefanski L.A. (1996) Asymptotics for the SIMEX Estimator in Nonlinear Measurement Error Models. Journal of the American Statistical Association, 91, 242 -- 250 Carrol, R.J., Ruppert, D. and Stefanski L.A. (1995). Measurement Error in Nonlinear Models. London: Chapman and Hall.

See Also

mcsimex for discreete data with misclassification, lm,glm, refit

Examples

# to test nonlinear extrapolation set.seed(3)
x <- rnorm(200,0,100)
u <- rnorm(200,0,25)
w <- x+u
y <- x +rnorm(200,0,9)
true.model <- lm(y~x) # True model
naive.model <- lm(y~w, x=TRUE)
simex.model <- simex(model = naive.model
	, SIMEXvariable = "w"
	, measurement.error= 25)
plot(x,y)
abline(true.model,col="darkblue")
abline(simex.model,col ="red")
abline(naive.model,col = "green")
legend(min(x),max(y),legend=c("True Model","SIMEX model","Naive Model")
	, col = c("darkblue","red","green"),lty=1)

plot(simex.model, mfrow = c(2,2))