# SobolIndicesAll-class: Estimating All Sobol Indices of Certain Order Using... In SobolIndices: Computing the Sobol Indices

## Description

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 `SobolIndicesAll` class, and compute the sobol indices of all possible variables interactions of given order by using this algorithm.

## Usage

 ```1 2``` ```SobolIndicesAll(xdata, orderinput=1, beta=0, link=c("identity","log","logit")) summary(object, ...) ```

## Arguments

 `xdata` A data set of class 'matrix' or 'data.frame' which only includes the variables or features. `orderinput` A integer; the order of the interaction of the variables which are of interest for computing all possible interactions' 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 `SobolIndicesAll` class. `...` Other arguments that could be added.

## Details

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 all the variables interaction (of order `orderinput`) of interest are stored in the `sobol.indices.all` slot.

## Value

The `SobolIndicesAll` function computes all the sobol indices for variables interactions of order `orderinput`, constructs and returns an object of the `SobolIndicesAll` class.

## Objects from the Class

Objects should be created using the `SobolIndicesAll` constructor.

## Slots

`xdata`:

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

`orderinput`

A integer which is the order of the interaction of the variables of interest for computing all possible interactions' 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.all`:

A list or a numeric object which stores sobol indices of variables interactions of order `orderinput`.

## Methods

summary

`signature(object = "SobolIndicesAll")`: ...

## Author(s)

Min Wang <[email protected]>

## References

[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.

## See Also

`identitySIfunction`, `logSIfunction` and `logitSIfunction` to get a complete list of the functions under different link functions to compute the sobol indices.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```showClass("SobolIndicesAll") # simulate xdata and beta xdata <- matrix(rnorm(20*5, 1), ncol=5) beta <- runif(6, min=-1, max=1) # all paired variables interactions are of interest orderinput <- 2 # link function is logit link (binomial, etc.) link <- "logit" # apply the proposed method siall <- SobolIndicesAll(xdata, orderinput=orderinput, beta, link="logit") # Review the results summary(siall) ```

SobolIndices documentation built on May 31, 2017, 1:59 a.m.