Dhat {dbmss} | R Documentation |

## Estimation of the D function

### Description

Estimates the *D* function

### Usage

```
Dhat(X, r = NULL, Cases, Controls = NULL, Intertype = FALSE, CheckArguments = TRUE)
```

### Arguments

`X` |
A weighted, marked, planar point pattern ( |

`r` |
A vector of distances. If |

`Cases` |
One of the point types. |

`Controls` |
One of the point types. If |

`Intertype` |
Logical; if |

`CheckArguments` |
Logical; if |

### Details

The *Di* function allows comparing the structure of the cases to that of the controls around cases, that is to say the comparison is made around the same points. This has been advocated by Arbia et al. (2008) and formalized by Marcon and Puech (2012).

### Value

An object of class `fv`

, see `fv.object`

, which can be plotted directly using `plot.fv`

.

### Note

The computation of `Dhat`

relies on spatstat functions `Kest`

and `Kcross`

.

### References

Arbia, G., Espa, G. and Quah, D. (2008). A class of spatial econometric methods in the empirical analysis of clusters of firms in the space. *Empirical Economics* 34(1): 81-103.

Diggle, P. J. and Chetwynd, A. G. (1991). Second-Order Analysis of Spatial Clustering for Inhomogeneous Populations. *Biometrics* 47(3): 1155-1163.

Marcon, E. and F. Puech (2017). A typology of distance-based measures of spatial concentration. *Regional Science and Urban Economics*. 62:56-67.

### See Also

### Examples

```
data(paracou16)
autoplot(paracou16)
# Calculate D
r <- 0:30
(Paracou <- Dhat(paracou16, r, "V. Americana", "Q. Rosea", Intertype = TRUE))
# Plot (after normalization by pi.r^2)
autoplot(Paracou, ./(pi*r^2) ~ r)
```

*dbmss*version 2.9-0 Index]