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
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
|
plotGOF.LR <- function(
x,
beta.subset = "all",
main = "Graphical Model Check",
xlab,
ylab,
tlab = "item",
xlim,
ylim,
type = "p",
pos = 4,
conf = NULL,
ctrline = NULL,
smooline = NULL,
asp = 1,
x_axis = TRUE,
y_axis = TRUE,
set_par = TRUE,
reset_par = TRUE,
...
){
# graphical model check
# beta.subset...plot only a subset of beta-parameters; either "all" or an index vector
# x...object of class LR (from LRtest)
# tlab ... labelling: "item" abbreviated beta parameter name, "number" number from beta par list,
# "identify" interactive, "none"
# pos ... (where the textlabel appears)
# conf ... confidence ellipses: NULL or
# list(gamma=0.95, col="red", ia=TRUE, lty="dashed", which=all items in beta.subset)
# ctrline ... control lines (confidence bands): NULL or list(gamma=0.95,lty="solid", col="blue")
# smooline ... smoothed control lines (confidence bands): NULL or list(gamma=0.95,lty="solid", col="blue", spar=0.5)
# ... additional graphic parameters
# save current options() and par() values and restore them on exit
old_options <- options(locatorBell = FALSE)
if(set_par){ old_par <- par(mar=c(4,4,3,0)+.5, no.readonly = TRUE) }
on.exit({
if(set_par && reset_par){ par(old_par) }
options(old_options)
})
if(length(x$likgroup) > 2L) warning("Only the parameters for the first two subgroups are plotted!")
if(missing(xlab)) xlab <- paste0("Beta for Group: ", x$spl.gr[1L])
if(missing(ylab)) ylab <- paste0("Beta for Group: ", x$spl.gr[2L])
nparg1 <- length(x$betalist[[1L]])
nparg2 <- length(x$betalist[[2L]])
if(nparg1 != nparg2) stop("Unequal number of parameters in the subgroups! Plot cannot be produced, choose another split in LRtest!")
beta1 <- -x$betalist[[1L]] # -1 to obtain difficulty parameters
beta2 <- -x$betalist[[2L]]
if(is.character(beta.subset)) {
if(beta.subset == "all"){
beta.subset <- seq_along(beta1)
#textlab <- names(beta1)
switch(EXPR = tlab,
item = textlab <- gsub("^beta\\ I", "", names(beta1)), # remove "beta I" from names
number = textlab <- seq_along(beta1),
identify = labs <- gsub("^beta\\ I", "", names(beta1))
)
} else {
textlab <- beta.subset
}
} else {
switch(EXPR = tlab,
item = textlab <- gsub("^beta\\ I", "", names(beta1)[beta.subset]), # remove "beta I" from names
number = textlab <- beta.subset,
identify = labs <- gsub("^beta\\ I", "", names(beta1)[beta.subset])
)
}
# se's needed for ellipses and control lines
if(is.list(conf) || is.list(ctrline) || is.list(smooline)){
if(any(is.na(unlist(x$selist)))) {
warning('Confidence ellipses or control lines cannot be plotted.\n LR object without standard errors.\n Use option "se = TRUE" in LRtest()')
conf <- ctrline <- NULL
} else {
s1 <- x$selist[[1L]]
s2 <- x$selist[[2L]]
v1 <- s1^2
v2 <- s2^2
suspicious.se <- any(cbind(s1, s2)[beta.subset] > 10)
if(suspicious.se) warning("Suspicious size of standard error(s).\n Check model specification, split criterion, data.")
}
#if(any(abs(cbind(beta1,beta2)[beta.subset])>8)){
# warning("Suspicious size of parameter estimate(s).\n Check model specification, split criterion, data.")
# if(is.null(conf)) conf$ia <- FALSE
}
### confidence ellipses ####################################################
### COMPUTATIONS ###########################################################
if(is.list(conf)){
# simple ellipse to replace the function ellipse() from the car package
simple_ellipse <- function(center, a, b, n = 200L, border_col){
angle_t <- seq(0, 2*pi, length.out = n)[-1L]
polygon(center[1L] + a * cos(angle_t), center[2L] + b * sin(angle_t), lwd = 1.0, border = border_col)
}
# select items for which ellipses are drawn ## rh 2011-05-31
if(is.null(conf$which)) conf$which <- beta.subset#seq_along(beta.subset)
if(!all(conf$which %in% beta.subset)) stop("Incorrect item number(s) for which ellipses are to be drawn")
if(is.null(conf$col)){
conf$c <- rep("red", length.out = length(beta1))
} else if(!is.null(conf$which)){
# conf$c <- rep(NA,length.out=length(beta.subset))
conf$c <- rep(NA, length.out = length(conf$which))
if(length(conf$c)!=length(conf$which)){
stop('"which" and "col" must have the same length in specification of "conf"')
} else {
conf$c[conf$which] <- conf$col
}
}
conf$col <- conf$c
if(is.null(conf$gamma)) conf$gamma <- 0.95
if(is.null(conf$lty)) conf$lty <- "dotted"
if(is.null(conf$ia)) conf$ia <- FALSE
z <- qnorm((1.0-conf$gamma)/2.0, lower.tail = FALSE)
ci1u <- beta1 + z*s1
ci1l <- beta1 - z*s1
ci2u <- beta2 + z*s2
ci2l <- beta2 - z*s2
}
################################################################################
### 95% control lines (Wright) #############################################
### COMPUTATIONS ###########################################################
if(is.list(ctrline)){
if(is.null(ctrline$gamma)) ctrline$gamma <- 0.95
if(is.null(ctrline$col)) ctrline$col <- "blue"
if(is.null(ctrline$lty)) ctrline$lty <- "solid"
z <- qnorm((1.0 - ctrline$gamma)/2.0, lower.tail = FALSE)
d <- (beta1 + beta2)/2
se.d <- sqrt(v1 + v2)
d <- sort(d)
se.d <- se.d[order(d)]
upperx <- d - z*se.d/2
uppery <- d + z*se.d/2
}
################################################################################
################################################################################
### 95% smooth control lines (Wright) ######################################
### COMPUTATIONS ###########################################################
if(is.list(smooline)){
if(is.null(smooline$gamma)) smooline$gamma <- 0.95
if(is.null(smooline$col)) smooline$col <- "blue"
if(is.null(smooline$lty)) smooline$lty <- "solid"
if(is.null(smooline$spar)) smooline$spar <- 0.5
z <- qnorm((1.0 - smooline$gamma)/2.0, lower.tail = FALSE)
d <- (beta1 + beta2)/2
se.d <- sqrt(v1 + v2)
d <- sort(d)
se.d <- se.d[order(d)]
upperx <- d - z*se.d/2
uppery <- d + z*se.d/2
}
################################################################################
if(!exists("ci1l", inherits = FALSE)) ci1l <- NA
if(!exists("ci1u", inherits = FALSE)) ci1u <- NA
if(!exists("ci2l", inherits = FALSE)) ci2l <- NA
if(!exists("ci2u", inherits = FALSE)) ci2u <- NA
if(!exists("upperx", inherits = FALSE)) upperx <- NA
if(!exists("uppery", inherits = FALSE)) uppery <- NA
if(missing(xlim)){
xlim <- range(beta1[beta.subset], ci1l, ci1u, upperx, uppery, na.rm = TRUE)
}
if(missing(ylim)){
ylim <- range(beta2[beta.subset], ci2l, ci2u, upperx, uppery, na.rm = TRUE)
}
plot.new()
plot.window(xlim = xlim, ylim = ylim, asp = asp)
title(main = main, xlab = xlab, ylab = ylab)
if(x_axis) axis(1)
if(y_axis) axis(2)
abline(0, 1)
# confidence ellipses - if not interactive
if(is.list(conf) && !conf$ia){
# non-interactive: plot of all ellipses at once
x <- beta1
y <- beta2
for(i in beta.subset){
if(i %in% conf$which){
segments( x0 = c(x[i], ci1l[i]), y0 = c(ci2l[i], y[i]),
x1 = c(x[i], ci1u[i]), y1 = c(ci2u[i], y[i]),
col = conf$col[i], lty = conf$lty )
simple_ellipse( center = c(x[i],y[i]),
a = abs(diff(c(ci1u[i],ci1l[i])))/2,
b = abs(diff(c(ci2u[i],ci2l[i])))/2,
n = 200L, border_col = conf$col[i] )
}
}
}
# 95% control lines (Wright) - plotting
if(is.list(ctrline)){
lines(upperx, uppery, col = ctrline$col, lty = ctrline$lty)
lines(uppery, upperx, col = ctrline$col, lty = ctrline$lty)
}
# 95% smooth lines (Wright) - plotting
if(is.list(smooline)){
lines(smooth.spline(upperx, uppery, spar = smooline$spar), col = smooline$col, lty = smooline$lty)
lines(smooth.spline(uppery, upperx, spar = smooline$spar), col = smooline$col, lty = smooline$lty)
}
if(exists("textlab", inherits = FALSE)){
text(beta1[beta.subset], beta2[beta.subset], labels = textlab, pos = pos, ...)
}
points(x = beta1[beta.subset], y = beta2[beta.subset], type = type, ...)
if(exists("labs", inherits = FALSE)){
xycoords <- cbind(beta1[beta.subset], beta2[beta.subset])
nothing <- identify(xycoords, labels = labs, atpen = TRUE, offset = 1)
}
box()
# interactive confidence ellipses
if(is.list(conf) && conf$ia){
identifyEll <- function(x, y, ci1u, ci1l, ci2u,ci2l, v1, v2, conf, n=length(x), ...){
## source: example from help("identify")
## a function to use identify to select points, and overplot the
## points with a confidence ellipse as they are selected
xy <- xy.coords(x, y)
x <- xy$x
y <- xy$y
sel <- rep(FALSE, length(x))
res <- integer(0)
while(sum(sel) < n){
ans <- identify(x[!sel], y[!sel], n=1, plot=FALSE, ...)
if(!length(ans)) break
ans <- which(!sel)[ans]
i <- ans
segments( x0 = c(x[i], ci1l[i]), y0 = c(ci2l[i], y[i]),
x1 = c(x[i], ci1u[i]), y1 = c(ci2u[i], y[i]),
col = conf$col[i], lty = conf$lty )
simple_ellipse( center = c(x[i],y[i]),
a = abs(diff(c(ci1u[i],ci1l[i])))/2,
b = abs(diff(c(ci2u[i],ci2l[i])))/2,
n = 200L, border_col = conf$col[i] )
sel[ans] <- TRUE
res <- c(res, ans)
}
#res
}
identifyEll(beta1[beta.subset],beta2[beta.subset],
ci1u[beta.subset], ci1l[beta.subset], ci2u[beta.subset], ci2l[beta.subset],
v1[beta.subset], v2[beta.subset], conf)
}
}
|
