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
|
### summary.calibrateType1.R ---
##----------------------------------------------------------------------
## Author: Brice Ozenne
## Created: apr 23 2018 (12:58)
## Version:
## Last-Updated: Jan 11 2022 (16:48)
## By: Brice Ozenne
## Update #: 72
##----------------------------------------------------------------------
##
### Commentary:
##
### Change Log:
##----------------------------------------------------------------------
##
### Code:
## * method summary.modelsearch2
#' @title Display the Type 1 Error Rate
#' @description Display the type 1 error rate from the simulation results.
#'
#' @param object output of the \code{calibrateType1} function.
#' @param alpha [numeric, 0-1] the confidence levels.
#' @param robust [character] should the results be displayed for both model-based and robust standard errors (\code{TRUE}),
#' only model-based standard error (\code{FALSE}), or only robust standard error (\code{"only"})?
#' @param type [character] should the type 1 error rate be diplayed (\code{"type1error"}) or the bias (\code{"bias")}.
#' @param digits [integer >0] the number of decimal places to use when displaying the summary.
#' @param log.transform [logical] should the confidence intervals be computed on the logit scale.
#' @param print should the summary be printed in the terminal.
#' @param ... [internal] only used by the generic method.
#'
#' @method summary calibrateType1
#' @export
summary.calibrateType1 <- function(object, robust = FALSE, type = "type1error",
alpha = 0.05, log.transform = TRUE,
digits = 5, print = TRUE, ...){
type <- match.arg(type, c("type1error","bias"))
if(is.logical(robust)){robust <- as.character(robust)}
robust <- match.arg(robust, c("TRUE","FALSE","only"))
## ** compute bias
if(type == "bias"){
stop("not implemented yet!")
}
## ** compute type 1 error
if(type == "type1error"){
dfLong <- melt(object$p.value,
measure.vars = grep("^p.",names(object$p.value),value = TRUE),
value.name = "p.value",
variable.name = "method")
dfS <- stats::aggregate(dfLong$p.value,
by = list(n = dfLong$n, method = dfLong$method, link = dfLong$link),
FUN = function(x){c(n.rep = length(x), type1error = mean(x<=alpha, na.rm = TRUE))},
simplify = FALSE)
dfS <- cbind(dfS[,c("n","method","link")],
do.call(rbind,dfS[,"x"]))
## binom::binom.confint(x = round(dfS$type1error*dfS$n.rep), dfS$n.rep, method = "logit")
logit.p <- log(dfS$type1error/(1-dfS$type1error))
if(log.transform){
## delta method: ln(x/(1-x))' = ln(x)' - ln(1-x)' = 1/x + 1/(1-x) = 1/(x(1-x))
var.logit.p <- 1/(dfS$n.rep*dfS$type1error*(1-dfS$type1error))
## on logit scale
dfS$ci.inf <- logit.p + stats::qnorm(0.025) * sqrt(var.logit.p)
dfS$ci.sup <- logit.p + stats::qnorm(0.975) * sqrt(var.logit.p)
## on original scale
dfS$ci.inf <- 1/(1+exp(-dfS$ci.inf))
dfS$ci.sup <- 1/(1+exp(-dfS$ci.sup))
}else{
dfS$ci.inf <- dfS$type1error + stats::qnorm(0.025) * sqrt(dfS$type1error*(1-dfS$type1error)/dfS$n.rep)
dfS$ci.sup <- dfS$type1error + stats::qnorm(0.975) * sqrt(dfS$type1error*(1-dfS$type1error)/dfS$n.rep)
}
## names
rownames(dfS) <- NULL
dfS$correction <- sapply(as.character(dfS$method),switch,
p.Ztest = "Gaussian approx.",
p.Satt = "Satterthwaite approx.",
p.SSC = "small sample correction",
p.KR = "Satterthwaite approx. with small sample correction",
p.robustZtest = "Gaussian approx.",
p.robustSatt = "Satterthwaite approx.",
p.robustSSC = "small sample correction",
p.robustKR = "Satterthwaite approx. with small sample correction")
dfS$statistic <- sapply(as.character(dfS$method),switch,
p.Ztest = "Wald",
p.Satt = "Wald",
p.SSC = "Wald",
p.KR = "Wald",
p.robustZtest = "robust Wald",
p.robustSatt = "robust Wald",
p.robustSSC = "robust Wald",
p.robustKR = "robust Wald")
## display
if(print){
seqN <- unique(dfS$n)
seqRep <- stats::setNames(dfS$n.rep[duplicated(dfS$n) == FALSE],seqN)
vecTrans <- c("Gaus" = "Gaussian approx.",
"Satt" = "Satterthwaite approx.",
"SSC" = "small sample correction",
"SSC + Satt" = "Satterthwaite approx. with small sample correction")
ls.print <- lapply(seqN, function(iN){ # iN <- 73
df.tempo <- dfS[dfS$n==iN, c("link","statistic","correction","type1error","ci.inf","ci.sup")]
if(!is.null(digits)){
df.tempo$type1error <- round(df.tempo$type1error, digits = digits)
df.tempo$ci.inf <- round(df.tempo$ci.inf, digits = digits)
df.tempo$ci.sup <- round(df.tempo$ci.sup, digits = digits)
}
df.tempo$CI <- paste0("[",df.tempo$ci.inf," ; ",df.tempo$ci.sup,"]")
df.tempo$ci.inf <- NULL
df.tempo$ci.sup <- NULL
if(robust == "FALSE"){
df.tempo <- df.tempo[df.tempo$statistic=="Wald",,drop=FALSE]
}else if(robust == "only"){
df.tempo <- df.tempo[df.tempo$statistic=="robust Wald",,drop=FALSE]
}
df.tempo <- df.tempo[order(df.tempo$link,df.tempo$statistic),,drop=FALSE]
df.tempo$statistic[duplicated(cbind(df.tempo$link,df.tempo$statistic))] <- ""
df.tempo$link[duplicated(df.tempo$link)] <- ""
rownames(df.tempo) <- NULL
df.tempo$correction <- factor(df.tempo$correction,
levels = as.character(vecTrans),
labels = names(vecTrans))
## df.tempo$correction <- NULL
return(df.tempo)
})
names(ls.print) <- as.character(seqN)
cat("Estimated type 1 error rate [95% confidence interval] \n")
lapply(seqN, function(iN){
cat(" > sample size: ",iN," | number of simulations: ",seqRep[as.character(iN)],"\n",sep="")
print(ls.print[[as.character(iN)]],row.names = FALSE)
})
cat("\n")
cat("Corrections: Gaus = Gaussian approximation \n",
" SSC = small sample correction \n",
" Satt = Satterthwaite approximation \n",sep="")
}
}
return(invisible(dfS))
}
######################################################################
### summary.calibrateType1.R ends here
|
