A Combinatorial Approach to the Variable Selection in Multiple Linear Regression: Analysis of Selwood et al. Data Set – A Case Study

Abstract

A combinatorial protocol (CP) is introduced here to interface it with the multiple linear regression (MLR) for variable selection. The efficiency of CP-MLR is primarily based on the restriction of entry of correlated variables to the model development stage. It has been used for the analysis of Selwood et al data set [16], and the obtained models are compared with those reported from GFA [8] and MUSEUM [9] approaches. For this data set CP-MLR could identify three highly independent models (27, 28 and 31) with Q 2 value in the range of 0.632 ± 0.518. Also, these models are divergent and unique. Even though, the present study does not share any models with GFA [8], and MUSEUM [9] results, there are several descriptors common to all these studies, including the present one. Also a simulation is carried out on the same data set to explain the model formation in CP-MLR. The results demonstrate that the proposed method should be able to offer solutions to data sets with 50 to 60 descriptors in reasonable time frame. By carefully selecting the interparameter correlation cutoff values in CP-MLR one can identify divergent models and handle data sets larger than the present one without involving excessive computer time.

Consensus features of CP-MLR and GA in modeling HIV-1 RT inhibitory activity of 4-benzyl/benzoylpyridin-2-one analogues

“…With this in view, two feature selection approaches namely combinatorial protocol in multiple linear regression (CP-MLR) and GA have been used to identify the descriptors for modeling the activity of 4-benzyl/benzoyl-3-dimethylaminopyridin-2(1H)-ones. In this, CP-MLR is a filter-based feature selection procedure [20][21][22] . It involves a systematic search for the identification of influential features to model the activity.…”

“…With this view, two different feature selection approaches namely CP-MLR (a filter directed approach) 20 and GA (a stochastic approach) 23 have been separately used to identify potential features to model the HIV-1 RT inhibitory activity of benzylpyridinones. The descriptors surfaced from Table 1.…”

QSAR rationales for the 1,2-diarylcyclopentenes as prostaglandin EP1 receptor antagonists: Potentially useful in the treatment of inflammatory pain

“…The combinatorial protocol in multiple linear regression (CP-MLR) [47] and partial least-squares (PLS) [48][49][50] procedures have been used in the present work for developing QSAR models. Before the application of CP-MLR procedure, all those descriptors which are intercorrelated beyond 0.90 and showing a correlation of less than 0.1 with the biological endpoints (descriptor vs. activity, r < 0.1) were excluded.…”

“…The CP-MLR is a 'filter' based variable selection procedure for model development in QSAR studies [47]. Its procedural aspects and implementation are discussed in some of our recent publications [51][52][53][54][55].…”

CP-MLR directed QSAR study of carbonic anhydrase inhibitors: sulfonamide and sulfamate inhibitors

“…The CP-MLR is a 'filter' based variable selection procedure for model development in QSAR studies [30][31][32][33][34]. The procedure employs a combinatorial strategy with MLR to result in selected subset regressions for the extraction of diverse structure-activity models, each having unique combination of descriptors from the generated data set of the compounds under study.…”