cauchit(VGAM)
cauchit()所属R语言包：VGAM
Cauchit Link Function
Cauchit链接功能
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Computes the cauchit (tangent) link transformation, including its inverse and the first two derivatives.
计算的cauchit（正切值）的链接改造，包括逆和前两个衍生物。
用法----------Usage----------
cauchit(theta, earg = list(bvalue= .Machine$double.eps),
inverse = FALSE, deriv = 0, short = TRUE, tag = FALSE)
参数----------Arguments----------
参数：theta
Numeric or character. See below for further details.
数字或字符。请参阅下面进一步的细节。
参数：earg
List. Extra argument for passing in additional information. Values of theta which are less than or equal to 0 can be replaced by the bvalue component of the list earg before computing the link function value. Values of theta which are greater than or equal to 1 can be replaced by 1 minus the bvalue component of the list earg before computing the link function value. The component name bvalue stands for “boundary value”. See Links for general information about earg.
列表。额外的信息传递额外的参数。 theta的值是小于或等于0时，可以代替由bvalue组件的列表earg计算链接函数值之前。 theta是大于或等于1的值，可以由1代替减去bvalue组件列表earg之前计算的链接函数值。组件名称bvalue的意思是“边界值”。见Links的一般信息，关于earg。
参数：inverse
Logical. If TRUE the inverse function is computed.
逻辑。如果TRUE的逆函数计算。
参数：deriv
Order of the derivative. Integer with value 0, 1 or 2.
订购的衍生工具。值0，1或2的整数，带。
参数：short
Used for labelling the blurb slot of a vglmff-class object.
用于标签blurb插槽的vglmff-class对象。
参数：tag
Used for labelling the linear/additive predictor in the initialize slot of a vglmff-class object. Contains a little more information if TRUE.
用于标注线性/对添加剂的预测在initialize插槽的vglmff-class对象。如果TRUE包含了一些信息。
Details
详细信息----------Details----------
This link function is an alternative link function for parameters that lie in the unit interval. This type of link bears the same relation to the Cauchy distribution as the probit link bears to the Gaussian. One characteristic of this link function is that the tail is heavier relative to the other links (see examples below).
此链接功能是一种替代链接功能，参数，趴在单位的时间间隔。这种类型的链接负有相同的柯西分布的概率环节承担的高斯。此连结函数的特性之一是尾部是较重的相对于其他的链接（参见下面的示例）。
Numerical values of theta close to 0 or 1 or out of range result in Inf, -Inf, NA or NaN. The arguments short and tag are used only if theta is character.
数值theta接近0或1或范围的结果Inf，-Inf，NA或NaN。的参数short和tag只有theta是字符。
值----------Value----------
For deriv = 0, the tangent of theta, i.e., tan(pi * (theta-0.5)) when inverse = FALSE, and if inverse = TRUE then 0.5 + atan(theta)/pi.
对于deriv = 0，theta，即的切线tan(pi * (theta-0.5))inverse = FALSE，并如果inverse = TRUE0.5 + atan(theta)/pi的。
For deriv = 1, then the function returns d theta / d eta as a function of theta if inverse = FALSE, else if inverse = TRUE then it returns the reciprocal.
对于deriv = 1，则该函数返回Dtheta / Deta的函数，theta如果inverse = FALSE如果inverse = TRUE然后它返回的倒数。
注意----------Note----------
Numerical instability may occur when theta is close to 1 or 0. One way of overcoming this is to use earg.
数值不稳定时可能会出现theta是接近1或0。克服这一点的方法之一是使用earg。
As mentioned above, in terms of the threshold approach with cumulative probabilities for an ordinal response this link function corresponds to the Cauchy distribution (see cauchy1).
正如上面提到的，在序响应这个连接功能对应于柯西分布的累积概率的阈值方法（见cauchy1“）。
（作者）----------Author(s)----------
Thomas W. Yee
参考文献----------References----------
Generalized Linear Models, 2nd ed. London: Chapman & Hall.
参见----------See Also----------
logit, probit, cloglog, loge, cauchy, cauchy1.
logit，probit，cloglog，loge，cauchy，cauchy1。
实例----------Examples----------
p = seq(0.01, 0.99, by=0.01)
cauchit(p)
max(abs(cauchit(cauchit(p), inverse = TRUE) - p)) # Should be 0[应为0]
p = c(seq(-0.02, 0.02, by=0.01), seq(0.97, 1.02, by=0.01))
cauchit(p) # Has no NAs[有没有来港定居]
## Not run: [＃不运行：]
par(mfrow = c(2, 2), lwd = (mylwd <- 2))
y = seq(-4, 4, length = 100)
p = seq(0.01, 0.99, by = 0.01)
for(d in 0:1) {
matplot(p, cbind(logit(p, deriv = d), probit(p, deriv = d)),
type = "n", col = "purple", ylab = "transformation",
las=1, main = if (d == 0) "Some probability link functions"
else "First derivative")
lines(p, logit(p, deriv = d), col = "limegreen")
lines(p, probit(p, deriv = d), col = "purple")
lines(p, cloglog(p, deriv = d), col = "chocolate")
lines(p, cauchit(p, deriv = d), col = "tan")
if (d == 0) {
abline(v = 0.5, h = 0, lty = "dashed")
legend(0, 4.5, c("logit", "probit", "cloglog", "cauchit"), lwd = mylwd,
col = c("limegreen","purple","chocolate", "tan"))
} else
abline(v = 0.5, lty = "dashed")
}
for(d in 0) {
matplot(y, cbind( logit(y, deriv = d, inverse = TRUE),
probit(y, deriv = d, inverse = TRUE)),
type = "n", col = "purple", xlab = "transformation", ylab = "p",
main = if (d == 0) "Some inverse probability link functions"
else "First derivative", las=1)
lines(y, logit(y, deriv = d, inverse = TRUE), col = "limegreen")
lines(y, probit(y, deriv = d, inverse = TRUE), col = "purple")
lines(y, cloglog(y, deriv = d, inverse = TRUE), col = "chocolate")
lines(y, cauchit(y, deriv = d, inverse = TRUE), col = "tan")
if (d == 0) {
abline(h = 0.5, v = 0, lty = "dashed")
legend(-4, 1, c("logit", "probit", "cloglog", "cauchit"), lwd = mylwd,
col = c("limegreen","purple","chocolate", "tan"))
}
}
par(lwd = 1)
## End(Not run)[＃（不执行）]
转载请注明:出自 生物统计家园网(http://www.biostatistic.net)。
注：
注1：为了方便大家学习，本文档为生物统计家园网机器人LoveR翻译而成，仅供个人R语言学习参考使用，生物统计家园保留版权。
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发表于 2012-10-1 15:28:48
