This function performs local diagnostics of a model fitted for the first-order intensity of a spatio-temporal point pattern, returning the points identified as outlying following the diagnostics procedure on individual points of an observed point pattern, as introduced in Adelfio et al. (2020), and applied in D'Angelo et al. (2022) for the linear network case.
The points resulting from the local diagnostic procedure provided by this function can be inspected via the plot, print, summary, and infl functions.
localdiag(x, intensity, p = 0.95)A list object of class localdiag, containing
xThe stp object provided as input
listasThe LISTA functions, in a list object
idsThe ids of the points identified as outlying
x2A vector with the individual contributions to the Chi-squared statistics, normalized
pThe percentile considered
Either a stp or a stlp object
A vector of intensity values, of the same length as the number
of point in x
The percentile to consider as threshold for the outlying points. Default to 0.95.
Nicoletta D'Angelo and Giada Adelfio
This function performs local diagnostics of a model fitted for the
first-order intensity of a spatio-temporal point pattern, by means of the
local spatio-temporal inhomogeneous K-function (Adelfio et al, 2020)
documented by the function
KLISTAhat of the stpp package (Gabriel et al, 2013).
The function can also perform local diagnostics of a model fitted for the first-order intensity of an spatio-temporal point pattern on a linear network, by means of the local spatio-temporal inhomogeneous K-function on linear networks (D'Angelo et al, 2021) documented by the function localSTLKinhom.
In both cases, it returns the points identified as outlying following the diagnostics procedure on individual points of an observed point pattern, as introduced in Adelfio et al. (2020), and applied in D'Angelo et al. (2022) for the linear network case.
This function computes discrepancies by means of the \(\chi_i^2\) values, obtained following the expression $$ \chi_i^2=\int_L \int_T \Bigg( \frac{\big(\hat{K}^i_{I}(r,h)- \mathbb{E}[\hat{K}^i(r,h) ] \big)^2}{\mathbb{E}[\hat{K}^i(r,h) ]} \Bigg) \text{d}h \text{d}r , $$ one for each point in the point pattern.
Note that the Euclidean procedure is implemented by the
local K-functions of
Adelfio et al. (2020), documented in
KLISTAhat of the stpp package (Gabriel et al, 2013).
The network case uses the local K-functions on networks (D'Angelo et al., 2021),
documented
in localSTLKinhom.
Adelfio, G., Siino, M., Mateu, J., and Rodríguez-Cortés, F. J. (2020). Some properties of local weighted second-order statistics for spatio-temporal point processes. Stochastic Environmental Research and Risk Assessment, 34(1), 149-168.
D’Angelo, N., Adelfio, G. and Mateu, J. (2022) Local inhomogeneous second-order characteristics for spatio-temporal point processes on linear networks. Stat Papers. https://doi.org/10.1007/s00362-022-01338-4
Gabriel, E., Rowlingson, B. S., and Diggle, P. J. (2013). stpp: An R Package for Plotting, Simulating and Analyzing Spatio-Temporal Point Patterns. Journal of Statistical Software, 53(2), 1–29. https://doi.org/10.18637/jss.v053.i02
infl, plot.localdiag, print.localdiag, summary.localdiag, globaldiag
set.seed(2)
inh <- rstpp(lambda = function(x, y, t, a) {exp(a[1] + a[2]*x)},
par = c(.3, 6))
mod1 <- stppm(inh, formula = ~ 1)
resmod1 <- localdiag(inh, mod1$l, p = .9)
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