Description Usage Arguments Details Value Objects from the Class Slots Methods Author(s) References See Also Examples

Sobol [1] proposed a definition called Sobol Indices for estimating
the importance of single variable or multiple variales' interaction.
We have derived the formulas for Sobol Indices by using sensitivity
analysis under GLM of three link functions in `SobolIndices`

class, and enhanced the computation by automating the whole procedure.

1 2 | ```
SobolIndices(xdata, varinput=1, beta=0, link=c("identity","log","logit"))
summary(object, ...)
``` |

`xdata` |
A data set of class 'matrix' or 'data.frame' which only includes the variables or features. |

`varinput` |
A vector; the indices of the variables which are of interest for computing their interaction (usually high order) sobol indices main effect. |

`beta` |
A vector; the coefficients of the variables estimated by the regression model. |

`link` |
A character; the link function used under the GLM model. |

`object` |
An object of the |

`...` |
Other arguments that could be added. |

The proposed algorithm for computing the Sobol Indices is to use a
simple strategy under the GLM model with independent or multivariate
normal inputs. We derive the conditional expectations of the response
with respect to the input subsets, and then estimate the Sobol'
sensitivity indices directly using closed formulas or approximately
numerically using empirical variance estimates for a large number of
GLMs. The results can enable us to perform ANOVA-type variance
decomposition analysis on data with multicollinearity issue, not only
under Gaussian regression but also under other types of GLMs such
as Poisson and logistic regression. The resulting sobol indices for
the variables interaction (or single variable) of interest are
stored in the `sobol.indices`

slot.

The `SobolIndices`

function computes the sobol indices for variables
of interest, constructs and returns an object of the `SobolIndices`

class.

Objects should be created using the `SobolIndices`

constructor.

`xdata`

:A data set of class 'matrix' or 'data.frame' which only includes the variables or features.

`varinput`

A vector which include the indices of the variables which are of interest for computing their interaction (usually high order) sobol indices main effect.

`beta`

:A vector which are the coefficients of the variables in a regression model.

`link`

:A character which is the link function used under the GLM model.

`sobol.indices`

:A numeric number which is the sobol indices of variable(s) of interest.

- summary
`signature(object = "SobolIndices")`

: ...

Min Wang <wang.1807@mbi.osu.edu>

[1] Sobol, I. M. (1990). On sensitivity estimation for nonlinear mathematical models, Matematicheskoe Modelirovanie, 2, 112-118. [2] Lu, R., Rempala, G. and Wang, M. (2016). Sensitivity Analysis of Generalized Linear models, submitted.

`identitySIfunction`

, `logSIfunction`

and
`logitSIfunction`

to get a complete list of the functions
under different link functions to compute the sobol indices.

1 2 3 4 5 6 7 8 9 10 11 12 | ```
showClass("SobolIndices")
# simulate xdata and beta
xdata <- matrix(rnorm(20*5, 1), ncol=5)
beta <- runif(6, min=-1, max=1)
# variables 1 and 2 interaction is of interest
varinput <- c(1,2)
# link function is identity link (gaussian, possion, etc.)
link <- "identity"
# apply the proposed method
si <- SobolIndices(xdata, varinput=varinput, beta, link="identity")
# Review the results
summary(si)
``` |

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