1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
|
# Gmulti.S
#
# Compute estimates of nearest neighbour distance distribution functions
# for multitype point patterns
#
# S functions:
# Gcross G_{ij}
# Gdot G_{i\bullet}
# Gmulti (generic)
#
# $Revision: 4.45 $ $Date: 2020/10/30 03:59:45 $
#
################################################################################
"Gcross" <-
function(X, i, j, r=NULL, breaks=NULL, ..., correction=c("rs", "km", "han"))
{
# computes G_{ij} estimates
#
# X marked point pattern (of class 'ppp')
# i,j the two mark values to be compared
#
# r: (optional) values of argument r
# breaks: (optional) breakpoints for argument r
#
X <- as.ppp(X)
if(!is.marked(X, dfok=FALSE))
stop(paste("point pattern has no", sQuote("marks")))
stopifnot(is.multitype(X))
#
marx <- marks(X, dfok=FALSE)
if(missing(i)) i <- levels(marx)[1]
if(missing(j)) j <- levels(marx)[2]
#
I <- (marx == i)
if(sum(I) == 0) stop("No points are of type i")
if(i == j){
result <- Gest(X[I], r=r, breaks=breaks, ...)
} else {
J <- (marx == j)
if(sum(J) == 0) stop("No points are of type j")
result <- Gmulti(X, I, J, r=r, breaks=breaks, disjoint=FALSE, ...,
correction=correction)
}
result <- rebadge.as.crossfun(result, "G", NULL, i, j)
return(result)
}
"Gdot" <-
function(X, i, r=NULL, breaks=NULL, ..., correction=c("km","rs","han")) {
# Computes estimate of
# G_{i\bullet}(t) =
# P( a further point of pattern in B(0,t)| a type i point at 0 )
#
# X marked point pattern (of class ppp)
#
# r: (optional) values of argument r
# breaks: (optional) breakpoints for argument r
#
X <- as.ppp(X)
if(!is.marked(X))
stop(paste("point pattern has no", sQuote("marks")))
stopifnot(is.multitype(X))
#
marx <- marks(X, dfok=FALSE)
if(missing(i)) i <- levels(marx)[1]
I <- (marx == i)
if(sum(I) == 0) stop("No points are of type i")
J <- rep.int(TRUE, X$n) # i.e. all points
#
result <- Gmulti(X, I, J, r, breaks, disjoint=FALSE, ...,
correction=correction)
result <- rebadge.as.dotfun(result, "G", NULL, i)
return(result)
}
##########
"Gmulti" <-
function(X, I, J, r=NULL, breaks=NULL, ..., disjoint=NULL,
correction=c("rs", "km", "han")) {
#
# engine for computing the estimate of G_{ij} or G_{i\bullet}
# depending on selection of I, J
#
# X marked point pattern (of class ppp)
#
# I,J logical vectors of length equal to the number of points
# and identifying the two subsets of points to be
# compared.
#
# r: (optional) values of argument r
# breaks: (optional) breakpoints for argument r
#
verifyclass(X, "ppp")
W <- X$window
npts <- npoints(X)
areaW <- area(W)
# check I and J
I <- ppsubset(X, I)
J <- ppsubset(X, J)
if(is.null(I) || is.null(J))
stop("I and J must be valid subset indices")
nI <- sum(I)
nJ <- sum(J)
if(nI == 0) stop("No points satisfy condition I")
if(nJ == 0) stop("No points satisfy condition J")
if(is.null(disjoint))
disjoint <- !any(I & J)
# choose correction(s)
# correction.given <- !missing(correction) && !is.null(correction)
if(is.null(correction))
correction <- c("rs", "km", "han")
correction <- pickoption("correction", correction,
c(none="none",
border="rs",
rs="rs",
KM="km",
km="km",
Kaplan="km",
han="han",
Hanisch="han",
best="km"),
multi=TRUE)
# determine breakpoints for r values
lamJ <- nJ/areaW
rmaxdefault <- rmax.rule("G", W, lamJ)
breaks <- handle.r.b.args(r, breaks, W, rmaxdefault=rmaxdefault)
# brks <- breaks$val
rmax <- breaks$max
rvals <- breaks$r
zeroes <- numeric(length(rvals))
# initialise fv object
df <- data.frame(r=rvals, theo=1-exp(-lamJ * pi * rvals^2))
fname <- c("G", "list(I,J)")
Z <- fv(df, "r", quote(G[I,J](r)), "theo", . ~ r,
c(0,rmax),
c("r", makefvlabel(NULL, NULL, fname, "pois")),
c("distance argument r", "theoretical Poisson %s"),
fname=fname,
yexp=quote(G[list(I,J)](r)))
# "type I to type J" nearest neighbour distances
XI <- X[I]
XJ <- X[J]
if(disjoint)
nnd <- nncross(XI, XJ, what="dist")
else {
seqnp <- seq_len(npts)
iX <- seqnp[I]
iY <- seqnp[J]
nnd <- nncross(XI, XJ, iX, iY, what="dist")
}
# distance to boundary from each type i point
bdry <- bdist.points(XI)
# observations
o <- pmin.int(nnd,bdry)
# censoring indicators
d <- (nnd <= bdry)
#
# calculate estimates
if("none" %in% correction) {
# UNCORRECTED e.d.f. of nearest neighbour distances: use with care
if(npts == 0)
edf <- zeroes
else {
hh <- hist(nnd[nnd <= rmax],breaks=breaks$val,plot=FALSE)$counts
edf <- cumsum(hh)/length(nnd)
}
Z <- bind.fv(Z, data.frame(raw=edf),
makefvlabel(NULL, "hat", fname, "raw"),
"uncorrected estimate of %s", "raw")
}
if("han" %in% correction) {
# Hanisch style estimator
if(npts == 0)
G <- zeroes
else {
# uncensored distances
x <- nnd[d]
# weights
a <- eroded.areas(W, rvals)
# calculate Hanisch estimator
h <- hist(x[x <= rmax], breaks=breaks$val, plot=FALSE)$counts
G <- cumsum(h/a)
G <- G/max(G[is.finite(G)])
}
# add to fv object
Z <- bind.fv(Z, data.frame(han=G),
makefvlabel(NULL, "hat", fname, "han"),
"Hanisch estimate of %s",
"han")
# modify recommended plot range
attr(Z, "alim") <- range(rvals[G <= 0.9])
}
if(any(correction %in% c("rs", "km"))) {
# calculate Kaplan-Meier and border correction (Reduced Sample) estimators
if(npts == 0)
result <- data.frame(rs=zeroes, km=zeroes, hazard=zeroes)
else {
result <- km.rs(o, bdry, d, breaks)
result <- as.data.frame(result[c("rs", "km", "hazard")])
}
# add to fv object
Z <- bind.fv(Z, result,
c(makefvlabel(NULL, "hat", fname, "bord"),
makefvlabel(NULL, "hat", fname, "km"),
"hazard(r)"),
c("border corrected estimate of %s",
"Kaplan-Meier estimate of %s",
"Kaplan-Meier estimate of hazard function lambda(r)"),
"km")
# modify recommended plot range
attr(Z, "alim") <- range(rvals[result$km <= 0.9])
}
nama <- names(Z)
fvnames(Z, ".") <- rev(nama[!(nama %in% c("r", "hazard"))])
unitname(Z) <- unitname(X)
return(Z)
}
|
