Mhat {dbmss} | R Documentation |

## Estimation of the M function

### Description

Estimates the *M* function

### Usage

```
Mhat(X, r = NULL, ReferenceType, NeighborType = ReferenceType,
CaseControl = FALSE, Individual = FALSE, CheckArguments = TRUE)
```

### Arguments

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

`r` |
A vector of distances. If |

`ReferenceType` |
One of the point types. |

`NeighborType` |
One of the point types. By default, the same as reference type. |

`CaseControl` |
Logical; if |

`Individual` |
Logical; if |

`CheckArguments` |
Logical; if |

### Details

*M* is a weighted, cumulative, relative measure of a point pattern structure. Its value at any distance is the ratio of neighbors of the *NeighborType* to all points around *ReferenceType* points, normalized by its value over the windows.

If *CaseControl* is `TRUE`

, then *ReferenceType* points are cases and *NeighborType* points are controls. The univariate concentration of cases is calculated as if *NeighborType* was equal to *ReferenceType*, but only controls are considered when counting all points around cases (Marcon et al., 2012). This makes sense when the sampling design is such that all points of *ReferenceType* (the cases) but only a sample of the other points (the controls) are recorded. Then, the whole distribution of points is better represented by the controls alone.

### Value

An object of class `fv`

, see `fv.object`

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

.

If `Individual`

is set to `TRUE`

, the object also contains the value of the function around each individual *ReferenceType* point taken as the only reference point. The column names of the `fv`

are "M_" followed by the point names, i.e. the row names of the marks of the point pattern.

### References

Marcon, E. and Puech, F. (2010). Measures of the Geographic Concentration of Industries: Improving Distance-Based Methods. *Journal of Economic Geography* 10(5): 745-762.

Marcon, E., F. Puech and S. Traissac (2012). Characterizing the relative spatial structure of point patterns. *International Journal of Ecology* 2012(Article ID 619281): 11.

Marcon, E., and Puech, F. (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 M
autoplot(Mhat(paracou16, , "V. Americana", "Q. Rosea"))
```

*dbmss*version 2.9-0 Index]