dexpbinomial(VGAM)
dexpbinomial()所属R语言包：VGAM
Double Exponential Binomial Distribution Family Function
双指数二项分布家庭功能
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Fits a double exponential binomial distribution by maximum likelihood estimation. The two parameters here are the mean and dispersion parameter.
适用于双指数的二项式分布的最大似然估计。这里的两个参数是参数的平均值和分散。
用法----------Usage----------
dexpbinomial(lmean = "logit", ldispersion = "logit", emean = list(),
edispersion = list(), idispersion = 0.25, zero = 2)
参数----------Arguments----------
参数：lmean, ldispersion
Link functions applied to the two parameters, called mu and theta respectively below. See Links for more choices. The defaults cause the parameters to be restricted to (0,1).
链接功能适用于这两个参数，称为mu和theta下面分别。见Links更多的选择。缺省值导致的参数被限制到(0,1)。
参数：emean, edispersion
List. Extra argument for each of the links. See earg in Links for general information.
列表。每个环节的额外参数。见earg中Links的一般信息。
参数：idispersion
Initial value for the dispersion parameter. If given, it must be in range, and is recyled to the necessary length. Use this argument if convergence failure occurs.
分散参数的初始值。如果给出，则它必须是在范围内，，并recyled到必要的长度。使用此参数，如果出现收敛失败。
参数：zero
An integer specifying which linear/additive predictor is to be modelled as an intercept only. If assigned, the single value should be either 1 or 2. The default is to have a single dispersion parameter value. To model both parameters as functions of the covariates assign zero = NULL.
一个整数，指定线性/添加剂的预测中是被定义成仅截距。如果分配的，单值应该是1或2。默认情况下是有一个单一的分散参数值。为了模拟这两个参数作为协变量分配zero = NULL的功能，。
Details
详细信息----------Details----------
This distribution provides a way for handling overdispersion in a binary response. The double exponential binomial distribution belongs the family of double exponential distributions proposed by Efron (1986). Below, equation numbers refer to that original article. Briefly, the idea is that an ordinary one-parameter exponential family allows the addition of a second parameter theta which varies the dispersion of the family without changing the mean. The extended family behaves like the original family with sample size changed from n to n*theta. The extended family is an exponential family in mu when n and theta are fixed, and an exponential family in theta when n and mu are fixed. Having 0 < theta < 1 corresponds to overdispersion with respect to the binomial distribution. See Efron (1986) for full details.
这种分布偏大的二进制响应处理提供了一种方法。双指数的二项式分布，属于家庭·埃夫隆（1986）所提出的双指数分布。下面，方程的数字指的是原来的文章。简单地说，普通的单参数指数族的想法是，允许添加的第二个参数theta改变不改变的平均分散的家庭。像原来的家庭样本量从n到n*theta大家庭的行为。大家庭是一个指数家族中mun和theta是固定的，一个指数家族中thetan和mu是固定的。在0 < theta < 1偏大的二项分布。 ·埃夫隆（1986）的全部细节。
This VGAM family function implements an approximation (2.10) to the exact density (2.4). It replaces the normalizing constant by unity since the true value nearly equals 1. The default model fitted is eta1 =logit(mu) and eta2 = logit(theta). This restricts both parameters to lie between 0 and 1, although the dispersion parameter can be modelled over a larger parameter space by assigning the arguments ldispersion and edispersion.
这VGAM家庭功能实现了一个近似的确切密度（2.4）（2.10）。它取代了由统一的标准化常数，因为真正的价值约等于1。安装默认的模式是eta1 =logit(mu)和eta2 = logit(theta)。这限制了这两个参数都位于0和1之间，虽然可以被建模的分散参数在一个较大的参数空间中，通过分配的论据ldispersion和edispersion。
Approximately, the mean (of Y) is mu. The effective sample size is the dispersion parameter multiplied by the original sample size, i.e., n*theta. This family function uses Fisher scoring, and the two estimates are asymptotically independent because the expected information matrix is diagonal.
大约的意思（Y）mu。有效样本数是的分散参数乘以原始样本的大小，即，n*theta。这间家庭功能使用费舍尔得分，两个估计是渐近独立的，因为预期的信息矩阵是对角。
值----------Value----------
An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm.
类的一个对象"vglmff"（见vglmff-class）。该对象被用于建模功能如vglm。
警告----------Warning ----------
Numerical difficulties can occur; if so, try using idispersion.
数值困难可以发生，如果是的话，请尝试使用idispersion。
注意----------Note----------
This function processes the input in the same way as binomialff, however multivariate responses are not allowed (binomialff(mv = FALSE)).
此功能在相同的方式处理输入binomialff，但是多元响应不允许（binomialff(mv = FALSE)）。
（作者）----------Author(s)----------
T. W. Yee
参考文献----------References----------
Double exponential families and their use in generalized linear regression. Journal of the American Statistical Association, 81, 709–721.
参见----------See Also----------
binomialff, toxop.
binomialff，toxop。
实例----------Examples----------
# This example mimics the example in Efron (1986). The results here[此示例模仿埃夫隆（1986）的例子中。这里的结果]
# differ slightly.[略有不同。]
# Scale the variables[比例变量]
toxop = transform(toxop,
phat = positive / ssize,
srainfall = scale(rainfall), # (6.1)[（6.1）]
sN = scale(ssize)) # (6.2)[（6.2）]
# A fit similar (should be identical) to Section 6 of Efron (1986).[适合类似（应该是相同的）到第6埃弗龙（1986）。]
# But does not use poly(), and M=1.25 here, as in (5.3)[但不使用聚（），以及M = 1.25这里，在（5.3）]
cmlist = list("(Intercept)" = diag(2),
"I(srainfall)" = rbind(1,0),
"I(srainfall^2)" = rbind(1,0),
"I(srainfall^3)" = rbind(1,0),
"I(sN)" = rbind(0,1),
"I(sN^2)" = rbind(0,1))
dlist = list(min = 0, max = 1.25)
fit = vglm(cbind(phat, 1 - phat) * ssize ~
I(srainfall) + I(srainfall^2) + I(srainfall^3) +
I(sN) + I(sN^2),
dexpbinomial(ldisp = "elogit", idisp = 0.2,
edisp = dlist, zero = NULL),
toxop, trace = TRUE, constraints = cmlist)
# Now look at the results[现在看结果]
coef(fit, matrix = TRUE)
head(fitted(fit))
summary(fit)
vcov(fit)
sqrt(diag(vcov(fit))) # Standard errors[标准误差]
# Effective sample size (not quite the last column of Table 1)[有效样本量（不是很表1的最后一列）]
head(predict(fit))
Dispersion = elogit(predict(fit)[,2], earg = dlist, inverse = TRUE)
c(round(weights(fit, type = "prior") * Dispersion, dig = 1))
# Ordinary logistic regression (gives same results as (6.5))[普通logistic回归（（6.5）给出了相同的结果）]
ofit = vglm(cbind(phat, 1 - phat) * ssize ~
I(srainfall) + I(srainfall^2) + I(srainfall^3),
binomialff, toxop, trace = TRUE)
# Same as fit but it uses poly(), and can be plotted (cf. Figure 1)[相同适合，但是它使用了聚（），并且可以被绘制（参见图1）]
cmlist2 = list("(Intercept)" = diag(2),
"poly(srainfall, degree = 3)" = rbind(1, 0),
"poly(sN, degree = 2)" = rbind(0, 1))
fit2 = vglm(cbind(phat, 1 - phat) * ssize ~
poly(srainfall, degree = 3) + poly(sN, degree = 2),
dexpbinomial(ldisp = "elogit", idisp = 0.2,
edisp = dlist, zero = NULL),
toxop, trace = TRUE, constraints = cmlist2)
## Not run: par(mfrow = c(1, 2))[＃不运行：PAR（mfrow = C（1，2））]
plotvgam(fit2, se = TRUE, lcol = "blue", scol = "red") # Cf. Figure 1[比照。图1]
# Cf. Figure 1(a)[比照。图1（a）]
par(mfrow = c(1,2))
ooo = with(toxop, sort.list(rainfall))
with(toxop, plot(rainfall[ooo], fitted(fit2)[ooo], type = "l",
col = "blue", las = 1, ylim = c(0.3, 0.65)))
with(toxop, points(rainfall[ooo], fitted(ofit)[ooo], col = "red",
type = "b", pch = 19))
# Cf. Figure 1(b)[比照。图1（b）]
ooo = with(toxop, sort.list(ssize))
with(toxop, plot(ssize[ooo], Dispersion[ooo], type = "l", col = "blue",
las = 1, xlim = c(0, 100)))
## 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：
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发表于 2012-10-1 15:31:57
