# Compute trace of (I-rho*W)^-1 matrix

### Description

This function computes (or estimates) the trace of matrix (I-rho*W)^-1, which is often needed when computing impacts in some spatial econometrics models.

### Usage

1 | ```
trIrhoWinv(W, rho, offset = 0, order = 20, direct = TRUE, Df = Matrix::Diagonal(nrow(W)))
``` |

### Arguments

`W` |
Adjacency matrix. Usually, it is row-standardised. |

`rho` |
Value of spatial autocorrelation parameter |

`offset` |
Number of times (I-rho*W)^-1 is multiplied by W (for sdm model). |

`order` |
Order of Taylor expansion used in the approximation of the trace. |

`direct` |
Use direct method, i.e., matrix multiplication, etc. |

`Df` |
Diagonal matrix used to compute the impacts in the Probit model only used if direct=TRUE. |

### Details

This function computes the trace of (I-rho*W)^-1, which is later used to computed the impacts. This is an internal function.

### Value

Numerica value.

### Author(s)

Virgilio G<f3>mez-Rubio <virgilio.gomez@uclm.es>

### References

LeSage and Page (2008) Bivand et al. (2013)

### See Also

`sem.inla`

, `slm.inla`

, `sdm.inla`