mhat(X, r = NULL, ReferenceType, NeighborType = ReferenceType, CaseControl = FALSE, Original = TRUE, Approximate = ifelse(X$n < 10000, 0, 1), Adjust = 1, MaxRange = "ThirdW", CheckArguments = TRUE)wmppp.object) or a Dtable object.
NULL, a default value is set: 64 unequally spaced values are used up to half the maximum distance between points $d_m$. The first value is 0, first steps are small ($d_m/800$) then increase progressively up to $d_m/40$.
TRUE, the case-control version of M is computed. ReferenceType points are cases, NeighborType points are controls.
TRUE, the function arguments are verified. Should be set to FALSE to save time in simulations for example, when the arguments have been checked elsewhere.
wmppp.object) or a Dtable object.
NULL, a default value is set: 512 equally spaced values are used, from the smallest distance to the range defined by MaxRange. the between points to half the diameter of the window.
TRUE, the case-control version of M is computed. ReferenceType points are cases, NeighborType points are controls.
TRUE (by default), the original bandwidth selection by Duranton and Overman (2005) following Silverman (1986: eq 3.31) is used. If FALSE, it is calculated following Sheather and Jones (1991), i.e. the state of the art. See bw.SJ for more details.
Approximate single values equally spaced between 0 and the largest distance. This technique (Scholl and Brenner, 2015) allows saving a lot of memory when addressing large point sets (the default value is 1 over 10000 points). Increasing Approximate allows better precision at the cost of proportional memory use. Ignored if X is a Dtable object.
Original) to be multiplied by Adjust. Setting it to values lower than one (1/2 for example) will sharpen the estimation.
r to consider, ignored if r is not NULL. Default is "ThirdW", one third of the diameter of the window. Other choices are "HalfW", and "QuarterW" and "D02005".
"HalfW", and "QuarterW" are for half or the quarter of the diameter of the window.
"D02005" is for the median distance observed between points, following Duranton and Overman (2005). "ThirdW" should be close to "DO2005" but has the advantage to be independent of the point types chosen as ReferenceType and NeighborType, to simplify comparisons between different types. "D02005" is approximated by "ThirdW" if Approximate is not 0.
if X is a Dtable object, the diameter of the window is taken as the max distance between points.
TRUE, the function arguments are verified. Should be set to FALSE to save time in simulations for example, when the arguments have been checked elsewhere.
Adjust. The bandwidth of Sheather and Jones (1991) would be better but it is very slow to calculate for large point patterns and it sometimes fails. It is often sharper than that of Silverman.
If X is not a Dtable object, the maximum value of r is obtained from the geometry of the window rather than caculating the median distance between points as suggested by Duranton and Overman (2005) to save (a lot of) calculation time.
Lang G., Marcon E. and Puech F. (2014) Distance-Based Measures of Spatial Concentration: Introducing a Relative Density Function. HAL 01082178, 1-18. Scholl, T. and Brenner, T. (2015) Optimizing distance-based methods for large data sets, Journal of Geographical Systems 17(4): 333-351.
Sheather, S. J. and Jones, M. C. (1991) A reliable data-based bandwidth selection method for kernel density estimation. Journal of the Royal Statistical Society series B, 53, 683-690.
Silverman, B. W. (1986). Density estimation for statistics and data analysis. Chapman and Hall, London.
mEnvelope, Kdhat
data(paracou16)
plot(paracou16)
# Calculate M
plot(mhat(paracou16, , "V. Americana", "Q. Rosea"))
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