betabinomial(VGAM)
betabinomial()所属R语言包：VGAM
Beta-binomial Distribution Family Function
β-二项分布的家庭功能
译者：生物统计家园网 机器人LoveR
描述----------Description----------
Fits a beta-binomial distribution by maximum likelihood estimation. The two parameters here are the mean and correlation coefficient.
适用于β-二项分布的最大似然估计。这里的两个参数的均值和相关系数。
用法----------Usage----------
betabinomial(lmu = "logit", lrho = "logit", emu = list(), erho = list(),
irho = NULL, imethod = 1, shrinkage.init = 0.95,
nsimEIM = NULL, zero = 2)
参数----------Arguments----------
参数：lmu, lrho
Link functions applied to the two parameters. See Links for more choices. The defaults ensure the parameters remain in (0,1), however, see the warning below.
链接功能施加到的两个参数。见Links更多的选择。默认的参数确保留在(0,1)，不过，看到下面的警告。
参数：emu, erho
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：irho
Optional initial value for the correlation parameter. If given, it must be in (0,1), and is recyled to the necessary length. Assign this argument a value if a convergence failure occurs. Having irho = NULL means an initial value is obtained internally, though this can give unsatisfactory results.
可选的初始值的相关参数。如果给出，则它必须是在(0,1)，，并recyled到必要的长度。指定这个参数的值，如果收敛发生故障。经irho = NULL意味着内部获得一个初始值，虽然这可以得到不能令人满意的结果。
参数：imethod
An integer with value 1 or 2 or ..., which specifies the initialization method for mu. If failure to converge occurs try the another value and/or else specify a value for irho.
一个整数，值1或2或的，指定初始化方法mu的。如果出现收敛失败尝试另一个值和/或其他指定的值irho。
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 correlation parameter. To model both parameters as functions of the covariates assign zero = NULL. See CommonVGAMffArguments for more information.
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相关参数。为了模拟这两个参数作为协变量分配zero = NULL的功能，。见CommonVGAMffArguments更多信息。
参数：shrinkage.init, nsimEIM
See CommonVGAMffArguments for more information. The argument shrinkage.init is used only if imethod = 2. Using the argument nsimEIM may offer large advantages for large values of N and/or large data sets.
见CommonVGAMffArguments更多信息。使用的参数shrinkage.init只有imethod = 2。使用参数nsimEIM可以提供大的优势，为大N和/或大型数据集的值。
Details
详细信息----------Details----------
There are several parameterizations of the beta-binomial distribution. This family function directly models the mean and correlation parameter, i.e., the probability of success. The model can be written T|P=p ~ Binomial(N,p) where P has a beta distribution with shape parameters alpha and beta. Here, N is the number of trials (e.g., litter size), T=NY is the number of successes, and p is the probability of a success (e.g., a malformation). That is, Y is the proportion of successes. Like binomialff, the fitted values are the estimated probability of success (i.e., E[Y] and not E[T]) and the prior weights N are attached separately on the object in a slot.
有几个参数化的β-二项分布。这间家庭功能的均值和相关参数，即成功的概率模型。该模型可以书面T|P=p ~ Binomial(N,p)其中P有β分布形状参数alpha和beta。在这里，N是试验次数（例如，产仔数），T=NY是成功的次数，和p是一个成功的概率（例如，一个畸形）。也就是说，Y是成功的比例。喜欢binomialff，拟合值的估计的成功概率（即，E[Y]而不是E[T]）和现有的权重N附着在对象上分开一个时隙中。
The probability function is
概率函数是
where t=0,1,…,N, and B is the beta function with shape parameters alpha and beta. Recall Y = T/N is the real response being modelled.
t=0,1,…,N，B是beta带形状参数的功能alpha和beta。回忆Y = T/N是真正的响应被建模。
The default model is eta1 =logit(mu) and eta2 = logit(rho) because both parameters lie between 0 and 1. The mean (of Y) is p = mu = alpha / (alpha + beta) and the variance (of Y) is mu(1-mu)(1+(N-1)rho)/N. Here, the correlation rho is given by 1/(1 + alpha + beta) and is the correlation between the N individuals within a litter. A litter effect is typically reflected by a positive value of rho. It is known as the over-dispersion parameter.
默认的模式是eta1 =logit(mu)和eta2 = logit(rho)，因为这两个参数介于0和1。平均（Y）p = mu = alpha / (alpha + beta)和方差（Y）mu(1-mu)(1+(N-1)rho)/N。 ，相关rho的1/(1 + alpha + beta)是的N内的枯枝落叶的个人之间的相关性。一胎效果典型地反映为正值的rho。这是被称为过度分散参数。
This family function uses Fisher scoring. Elements of the second-order expected derivatives with respect to alpha and beta are computed numerically, which may fail for large alpha, beta, N or else take a long time.
此的家庭功能使用费舍尔得分。元素的的二阶预期的衍生工具方面的alpha和beta数值计算，它可能会失败，大alpha，beta，N或其他需要很长的时间。
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。
Suppose fit is a fitted beta-binomial model. Then fit@y contains the sample proportions y, fitted(fit) returns estimates of E(Y), and weights(fit, type="prior") returns the number of trials N.
假设fit是一个装有β-二项式模型。然后fit@y包含的样本比例y，fitted(fit)E(Y)和weights(fit, type="prior")回报的估计返回的试验次数N。
警告----------Warning ----------
If the estimated rho parameter is close to zero then it pays to try lrho = "rhobit". One day this may become the default link function.
如果估计的rho沸石参数是接近于零，则它支付给尝试lrho = "rhobit"。有一天，这可能会成为默认链接的功能。
This family function is prone to numerical difficulties due to the expected information matrices not being positive-definite or ill-conditioned over some regions of the parameter space. If problems occur try setting irho to some numerical value, nsimEIM = 100, say, or else use etastart argument of vglm, etc.
这间家庭功能很容易由于预期的信息矩阵是正定的或病态的，在一些区域的参数空间的数值困难。如果出现问题，尝试设置irho一些数值，nsimEIM = 100，或者说其他人使用etastart参数vglm，等
注意----------Note----------
This function processes the input in the same way as binomialff. But it does not handle the case N=1 very well because there are two parameters to estimate, not one, for each row of the input. Cases where N=1 can be omitted via the subset argument of vglm.
此函数处理的输入相同的方式binomialff。但它不处理的情况下N=1非常好，因为有两个参数估计，而不是一个，每行的输入。其中N=1可以通过subset的vglm参数省略的情况。
The extended beta-binomial distribution of Prentice (1986) is currently not implemented in the VGAM package as it has range-restrictions for the correlation parameter that are currently too difficult to handle in this package. However, try lrho = "rhobit".
普伦蒂斯（1986）扩展的β-二项分布目前尚未实现在VGAM包，因为它有范围限制的相关参数，目前也很难处理这个包。然而，尝试lrho = "rhobit"。
（作者）----------Author(s)----------
T. W. Yee
参考文献----------References----------
Robust estimation of the variance in moment methods for extra-binomial and extra-Poisson variation. Biometrics, 47, 383–401.
Binary regression using an extended beta-binomial distribution, with discussion of correlation induced by covariate measurement errors. Journal of the American Statistical Association, 81, 321–327.
参见----------See Also----------
betabinomial.ab, Betabinom, binomialff, betaff, dirmultinomial, lirat.
betabinomial.ab，Betabinom，binomialff，betaff，dirmultinomial，lirat。
实例----------Examples----------
# Example 1[例1]
bdata = data.frame(N = 10, mu = 0.5, rho = 0.8)
bdata = transform(bdata,
y = rbetabinom(n=100, size = N, prob = mu, rho = rho))
fit = vglm(cbind(y, N-y) ~ 1, betabinomial, bdata, trace = TRUE)
coef(fit, matrix = TRUE)
Coef(fit)
head(cbind(fit@y, weights(fit, type = "prior")))
# Example 2[例2]
fit = vglm(cbind(R, N-R) ~ 1, betabinomial, lirat,
trace = TRUE, subset = N > 1)
coef(fit, matrix = TRUE)
Coef(fit)
t(fitted(fit))
t(fit@y)
t(weights(fit, type = "prior"))
# Example 3, which is more complicated[实施例3中，这是更复杂的]
lirat = transform(lirat, fgrp = factor(grp))
summary(lirat) # Only 5 litters in group 3[第3组只有5窝]
fit2 = vglm(cbind(R, N-R) ~ fgrp + hb, betabinomial(zero = 2),
data = lirat, trace = TRUE, subset = N > 1)
coef(fit2, matrix = TRUE)
## Not run: with(lirat, plot(hb[N > 1], fit2@misc$rho,[＃不运行：（lirat，图（HB [N> 1]，FIT2万方$ RHO，]
xlab = "Hemoglobin", ylab = "Estimated rho",
pch = as.character(grp[N > 1]), col = grp[N > 1]))
## End(Not run)[＃（不执行）]
## Not run: # cf. Figure 3 of Moore and Tsiatis (1991)[＃不运行：＃比照。图3 Moore和Tsiatis的（1991）]
with(lirat, plot(hb, R / N, pch = as.character(grp), col = grp, las = 1,
xlab = "Hemoglobin level", ylab = "Proportion Dead",
main = "Fitted values (lines)"))
smalldf = with(lirat, lirat[N > 1, ])
for(gp in 1:4) {
xx = with(smalldf, hb[grp == gp])
yy = with(smalldf, fitted(fit2)[grp == gp])
ooo = order(xx)
lines(xx[ooo], yy[ooo], col = gp) }
## 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。
注2：由于是机器人自动翻译，难免有不准确之处，使用时仔细对照中、英文内容进行反复理解，可以帮助R语言的学习。
注3：如遇到不准确之处，请在本贴的后面进行回帖，我们会逐渐进行修订。
|
发表于 2012-10-1 15:25:56
