By Hanna Birke
Model-based recursive partitioning (MOB) presents a strong synthesis among machine-learning encouraged recursive partitioning tools and regression types. Hanna Birke extends this strategy via permitting moreover for dimension errors in covariates, as often taking place in biometric (or econometric) reports, for example, while measuring blood strain or caloric consumption in line with day. After an creation into the historical past, the prolonged method is built intimately for the Cox version and the Weibull version, conscientiously applied in R, and investigated in a finished simulation study.
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Extra info for Model-Based Recursive Partitioning with Adjustment for Measurement Error: Applied to the Cox’s Proportional Hazards and Weibull Model
2010). Before the regression model is partitioned, the researcher has to decide, if a certain variable is included in the algorithm as a regressor or as a partitioning variable. This decision usually is based on the researcher’s previous knowledge. , 2008). An advantage of the model-based recursive partitioning is that the tree-structured regression analysis is easy to interpret by visualizing the ﬁtted tree graphically. In 2. Theoretical Background 33 addition, an automated variable selection is included, which is controlled for the Type I error rate in each node (cf.
In addition, the p-values are computed. To determine whether there is some overall instability, it is checked whether at least one of the p-values falls below the pre-speciﬁed signiﬁcance level alpha. To adjust for multiple testing, the p-values are Bonferroni adjusted, if bonferroni = TRUE. 38 3. Implementation If there is signiﬁcant instability, the variable z associated with the minimal p-value is used for splitting the node. Step 3: Split into Nodes In the third step the observations in the current node should be split for the chosen variable z into B children nodes.
C and Ic is the sum of scores in category c. λχ2 (Wj ) is the weighted sum of the squared L2 norm of the increments. The test statistic is asymptotically χ2 -distributed with q · (C − 1) degrees of freedom from which the corresponding p-value pj are computed, where q is number of estimated parameters. In summary the steps for the derivation of the M-ﬂuctuation test in the case of the Cox and Weibull model are as follows: 1. 4 for the proof). 2. 75) including the corrected score function. Under the null hypothesis Wj (t) converges to a Brownian bridge.
Model-Based Recursive Partitioning with Adjustment for Measurement Error: Applied to the Cox’s Proportional Hazards and Weibull Model by Hanna Birke