Assessing trimming methodologies for clustering linear regression data

Abstract

We assess the performance of state-of-the-art robust clustering tools for regression structures under a variety of different data configurations. We focus on two methodologies that use trimming and restrictions on group scatters as their main ingredients. We also give particular care to the data generation process through the development of a flexible simulation tool for mixtures of regressions, where the user can control the degree of overlap between the groups. Level of trimming and restriction factors are input parameters for which appropriate tuning is required. Since we find that incorrect specification of the second-level trimming in the Trimmed CLUSTering REGression model (TCLUST-REG) can deteriorate the performance of the method, we propose an improvement where the second-level trimming is not fixed in advance but is data dependent. We then compare our adaptive version of TCLUST-REG with the Trimmed Cluster Weighted Restricted Model (TCWRM) which provides a powerful extension of the robust clusterwise regression methodology. Our overall conclusion is that the two methods perform comparably, but with notable differences due to the inherent degree of modeling implied by them.

Semiautomatic robust regression clustering of international trade data

“…The original solution in TCLUST-REG was to fix a X in advance, although there is no established indication of the link between this proportion and the breakdown properties of the methodology. Torti et al (2018) have proposed to select a X adaptively from the data using a multivariate outlier detection procedure in the space of the explanatory variables. The observations surviving to the two trimming steps are then used for updating the regression coefficients, weights and scatter matrices.…”

“…This modification of the algorithm is usually referred in the literature as adaptive TCLUST-REG. Torti et al (2018) have also assessed how the performances of TCWM change in presence of possible misspecification of the distribution of the explanatory variables. Their experience is that the superior performance of TCWM can degenerate if the explanatory variable distribution is miss-specified and in this case the TCLUST-REG solution is preferable.…”

“…Once all the other parameters have been estimated it is possible to refine this value using the monitoring approach and the information criteria (MIX-MIX, MIX-CLA, CLA-CLA), given at the beginning of this section. If on the other hand, the data are highly non normal (as in the case of international trade data) we suggest to use TCLUST-REG with flexible second level of trimming as described in Torti et al (2018). In what follows in order to avoid a cumbersome notation with symbol c we denote c y (with c X fixed at 128 in case of TCWM).…”

Robust fitting of mixtures of GLMs by weighted likelihood

“…WEM and WCEM can be initialized by subsampling (Markatou et al 1998 ; Neykov and Müller 2003 ; Neykov et al 2007 ; Torti et al 2019 ). A subsample of size is selected randomly from the data sample; then, the model is fitted to these observations by the classical EM (or CEM) algorithm to get a trial estimate.…”

Weighted likelihood latent class linear regression

“…In particular, TCLUST-REG is characterized by group scatter constraints aimed at making the mixture fitting a well-posed problem and the addition of a second trimming step to mitigate the effect of outliers in the space of explanatory variables acting as leverage points. A very recent adaptive version of TCLUST-REG has been discussed in Torti et al (2019). An alternative approach meant to automatically take into account leverage points has been considered by García-Escudero et al (2017) where trimming and restrictions have been introduced to get a robust version of the cluster weighted model, named Trimmed Clustered Weighted Restricted Model (TCWRM).…”