Returns the variance-covariance matrix of the parameters estimates (including breakpoints) of a fitted stepmented model object.
# S3 method for stepmented
vcov(object, k=NULL, return.X=FALSE, zero.cor=TRUE, ...)The full matrix of the estimated covariances between the parameter estimates, including the breakpoints.
a fitted model object of class "stepmented", returned by any stepmented method
The power of n for the smooth approximation. Simulation evidence suggests k in [-1, -1/2]; with k=-1/2 providing somewhat 'conservative' standard errors especially at small sample sizes.
If TRUE the (pseudo) design matrix is returned (into a list).
If TRUE the covariances between the jumpoints and the remaining linear coefficients are set to zero.
additional arguments.
Vito Muggeo
The full covariance matrix is based on the smooth approximation
$$I(x>\psi)\approx \Phi((x-\psi)/n^{k})$$
via the sandwich formula using the empirical information matrix and assuming \(x \in [0,1]\). \(\Phi(\cdot)\) is the standard Normal cdf, and \(k\) is the argument k. When k=NULL (default), it is computed via
$$k=-(0.6 + 0.3 \ \log(snr) - (|\hat\psi-0.5|/n)^{1/2})$$
where \(snr\) is the signal-to-noise ratio corresponding to the estimated changepoint \(\hat\psi\) (in the range (0,1)). The above formula comes from extensive simulation studies under different scenarios.
stepmented