# logSI: Sobol Indices for the log link model In SobolIndices: Computing the Sobol Indices

## Description

The method is to estimate the sobol indices under the log link model.

## Usage

 ```1 2 3 4 5 6``` ```LogSImainsingle(i, xdata, beta) LogSImain(xdata, beta) LogSIsecpair(pair, xdata, beta) LogSIsec(xdata, beta) LogSIkinter(interaction, xdata, beta) LogSIkorder(k, xdata, beta) ```

## Arguments

 `xdata` A data set of class 'matrix' or 'data.frame' which only includes the variables or features. `beta` A vector; the coefficients of the variables estimated by the regression model. `i` A positive integer; the index of the variable which is of interest for computing the sobol indices main effect. `pair` A vector of length two; the indices of the paired variables which are of interest for computing their interaction sobol indices main effect. `interaction` A vector; the indices of the variables which are of interest for computing their interaction (usually high order) sobol indices main effect. `k` A positive integer; the order which are of interest for computing all variables' possible interactions' (of order `k`) sobol indices main effect.

## Details

This is the proposed method for computing the sobol indices under the log link. The idea is to use the definition of sobol indices to derive formulas for variables' main effect of interest and determine how important the variables are by computational calculations.

## Value

The `LogSImainsingle` function returns a number which is the numerator of sobol indices for deriving single variable's main effect.

The `LogSImain` function returns a vector which are the numerators of sobol indices for deriving all single variables' main effects.

The `LogSIsecpair` function returns a number which is the numerator of sobol indices for deriving paired variables interaction's main effect.

The `LogSIsec` function returns a matrix which are the numerators of sobol indices for deriving all possible paired variables interactions' main effects.

The `LogSIkinter` function returns a number which is the numerator of sobol indices for deriving variables interaction's main effect.

The `LogSIkorder` function returns a list (or numeric object) which are the numerators of sobol indices for deriving the main effects of all possible variables interactions of order `k`.

## Author(s)

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

## References

Sobol, I. M. (1990). On sensitivity estimation for nonlinear mathematical models, Matematicheskoe Modelirovanie, 2, 112-118.

Lu, R., Rempala, G. and Wang, M. (2016). Sensitivity Analysis of Generalized Linear models, submitted.

Methods to address the other link functions can be found at `identitySI2` and `logitSI`.
 ```1 2 3 4 5 6 7 8``` ```xdata <- matrix(rnorm(20*5, 1), ncol=5) beta <- runif(6, min=-1, max=1) LogSImainsingle(1, xdata, beta) LogSImain(xdata, beta) LogSIsecpair(c(1,2), xdata, beta) LogSIsec(xdata, beta) LogSIkinter(c(1,2,3), xdata, beta) LogSIkorder(3, xdata, beta) ```