By V. M. Starzhinskii
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Additional info for Applied methods in the theory of nonlinear oscillations
By default the results are printed for all nodes. By passing the node argument the results can be returned separately for any node. 2. Fitting a MOB Weibull Model with Adjustment for Measurement Error As already mentioned, a model-based parameter estimation of the Weibull model is integrated in the mob() function. To ﬁt a MOB tree based on a Weibull model with adjustment for measurement error a new object of class StatModel has to be generated. Especially, the fit() function has to be adapted for the new object to conduct a parameter estimation via the corrected log-likelihood, as well as the reweight() function.
If one of these conditions is not fulﬁlled, the algorithm stops. In line 27–63 the extracted data from object is prepared. A new data frame mydata is generated, where the variables are re-ordered. The ﬁrst two columns are the censored survival data, the time variable and status variable. var. If there are further error free covariables, they are attached to the data frame behind the error variables. This ordering is conducted, so that the correction for measurement error can be allocated only to the error variables.
66) 2. Theoretical Background 21 with q is the number of estimated parameters. 68) and where z1−α/2 is the (1 − α/2)-quantile of the standard normal distribution. The τ ∗ ) (this holds because of the invariance of conﬁdence interval for νˆ∗ = exp(ˆ maximum-likelihood estimator) is yielded by taking the exponential function of the lower and upper boundary of the conﬁdence interval for τˆ∗ . 69) ∗ se(βˆX ) J and z= τˆ∗ H0 ∼ N (0, 1). 70) The likelihood ratio test is used to check the signiﬁcance of the entire model.
Applied methods in the theory of nonlinear oscillations by V. M. Starzhinskii