2. Partial least squares regression (PLS)
✓deals with larger data with many variables
✗ can be hard to interpret model and identify outliers
PLS finds the multidimensional direction in the space of the parameters
(i.e. similar to principal component analysis, PCA, it uses linear combinations
of these parameters) that has the maximum covariance with the observations. PLS
regression is particularly suited when the number of descriptors outnumbers the
observations and when there is collinearity between these descriptors. This is a
common scenario encountered in a catalyst optimization project, due to the
difficulty of synthesizing many different structures, as compared to the ease
with which parameters can be generated!
3. Other types of model construction methods
Machine learning algorithms such as neural networks, k-nearest neighbours,
random forest, etc. can be used to generate QSSR models, typically when larger
datasets are available. The availability of datasets containing at least several
hundred reactions has generally been limited in the development of asymmetric
catalytic reactions. As datasets begin to emerge on this scale, more advanced
statistical algorithms will find use in this area.
5.3.2 Selecting Parameters
There are many selection methods used in QSAR such as genetic algorithms,
stepwise regressions, simulated annealing, etc. [77–79]. In the context of QSSR
applied to asymmetric catalysis, PCA and PLS are most often used in molecular
interaction field-based 3D-QSSR [56]. In MLR, automated parameter selection
algorithms can be applied to retain only those that contribute with statistical significance, including via open access software such as R [80]. One such approach is
forward selection, which starts with an empty initial model. Parameters are included
one at a time to improve the model based on set criteria to determine model quality
such as the adjusted coefficient of determination (R
2
adj ), the Akaike information
criterion (AIC) or significance ( p-value) until the model cannot be improved further.
In contrast, backward elimination starts from a full model with all parameters
included and eliminates one parameter at a time. The objective in both approaches
is to remove extraneous parameters that do not contribute significantly to the
predictive power of a final model.
5.3.3 Evaluation of Fit for MLR
MLR has been most often used in asymmetric catalysis. The following guidelines
and criteria are collected from the literature regarding MLR [54, 57, 81, 82]. Notably,
universal consensus has yet to be agreed. Nevertheless, standard practices and
criteria do emerge from recent literature.
Ligand Design for Asymmetric Catalysis: Combining Mechanistic and. . .
175
✓deals with larger data with many variables
✗ can be hard to interpret model and identify outliers
PLS finds the multidimensional direction in the space of the parameters
(i.e. similar to principal component analysis, PCA, it uses linear combinations
of these parameters) that has the maximum covariance with the observations. PLS
regression is particularly suited when the number of descriptors outnumbers the
observations and when there is collinearity between these descriptors. This is a
common scenario encountered in a catalyst optimization project, due to the
difficulty of synthesizing many different structures, as compared to the ease
with which parameters can be generated!
3. Other types of model construction methods
Machine learning algorithms such as neural networks, k-nearest neighbours,
random forest, etc. can be used to generate QSSR models, typically when larger
datasets are available. The availability of datasets containing at least several
hundred reactions has generally been limited in the development of asymmetric
catalytic reactions. As datasets begin to emerge on this scale, more advanced
statistical algorithms will find use in this area.
5.3.2 Selecting Parameters
There are many selection methods used in QSAR such as genetic algorithms,
stepwise regressions, simulated annealing, etc. [77–79]. In the context of QSSR
applied to asymmetric catalysis, PCA and PLS are most often used in molecular
interaction field-based 3D-QSSR [56]. In MLR, automated parameter selection
algorithms can be applied to retain only those that contribute with statistical significance, including via open access software such as R [80]. One such approach is
forward selection, which starts with an empty initial model. Parameters are included
one at a time to improve the model based on set criteria to determine model quality
such as the adjusted coefficient of determination (R
2
adj ), the Akaike information
criterion (AIC) or significance ( p-value) until the model cannot be improved further.
In contrast, backward elimination starts from a full model with all parameters
included and eliminates one parameter at a time. The objective in both approaches
is to remove extraneous parameters that do not contribute significantly to the
predictive power of a final model.
5.3.3 Evaluation of Fit for MLR
MLR has been most often used in asymmetric catalysis. The following guidelines
and criteria are collected from the literature regarding MLR [54, 57, 81, 82]. Notably,
universal consensus has yet to be agreed. Nevertheless, standard practices and
criteria do emerge from recent literature.
Ligand Design for Asymmetric Catalysis: Combining Mechanistic and. . .
175