Lasso

This is a term introduced by Gokel and co-workers only very recently. The compounds included in this class are those which have single macrorings like crowns but additional pendant donor groups which make them similar in some respects to crytands. The presumption from which the name derives is that a complexed cation will be bound by both the macroring and the sidechain in much the same fashion as a lasso binds an animal. The compounds are named as simple crown derivatives and are illustrated as 16 a 17 below. 

The name lariat ethers has recently been suggested by Gokel and coworkers to describe a class of compounds which are based on crown ethers and have secondary donor groups bound to the macrormg by flexible arms (see Sect. 1.3 5). The name lariat is suggested by the analogy to the lassoes used to rope and tie animals since it is hoped that the more successful molecules of this class will be able to do likewise with sundry cationic species. 

This clearly sets limitations to which any mechanism advanced for the reaction will have to conform, and gives the lie to that prime tenet of lasso chemistry groups are eliminated most readily when closest together ... 

D. Zimmermann, T. Haber, H. Schaal, and M. A. Suhm, Hydrogen bonded rings, chains and lassos The case of tert butyl alcohol clusters. Mol. Phys. 99, 413 426 (2001). 

Simple OLS, robust regression PLS, PCR, multiple OLS, robust regression, Ridge regression, Lasso regression PLS 2, CCA... 

In Section 4.8.2, we will describe a method called Lasso regression. Depending on a tuning parameter, this regression technique forces some of the regression coefficients to be exactly zero. Thus the method can be viewed as a variable selection method where all variables with coefficients different from zero are in the final regression model. 

Solving these minimization problems results in the estimated regression coefficients Bridge and lasso. respectively. The parameters AR and AL are complexity parameters and they control the amount of shrinkage. They have to be chosen to be >0, the larger the complexity parameter the more penalty is on the regression coefficients and the more they are shmnk towards zero. If the complexity parameter is zero,... 

Ridge and Lasso regression can be applied within R as follows ... 

FIGURE 4.39 Lasso regression for the PAC data set. The optimal Lasso parameter is for a fraction 0.3 leading to a SEP value 7.67. 

The denominator in Equation 4.100 is the (absolute) size of all Lasso regression parameters for a particular choice of AL (compare Equation 4.89), and the nominator describes the maximal possible (absolute) size of the Lasso regression parameters (in case there is no singularity problem this would correspond to the OLS solution). The optimal choice is at a fraction of 0.3 which corresponds to a MSEPCy of 63.4 and to a SEPCv of 7.7. 

A further point for the choice of an appropriate method is, whether the final model needs to be interpreted. In this case, and especially in case of many original regressor variables, the interpretation is in general easier if only a few regressor variables are used for the final model. This can be achieved by variable selection (Section 4.5), Lasso regression (Section 4.8.2), or regression trees (Section 4.8.3.3). Also PCR (Section 4.6) or PLS (Section 4.7) can lead to components that can be interpreted if they summarize the information of thematically related x-variables. 

Atrazine (Aatrex 80W), alachlor (Lasso E.C.) 2,4-D ester (Weed-one LV4 E.C.), trifluralin (Treflan E.C.), carbaryl (Sevin 50W) and parathion (Security 15W) were blended, individually and as mixtures, with 60 L of water and 15 kg of sandy loam soil in 110 L... 

C. Corral. A. Lasso, J. Lissavetzky, A. Sanchez Atvarez-Insud u. A. M. Valdeolmillos, Heterocycles 23,... 

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