pdNatural(nlme)
pdNatural()所属R语言包：nlme
General Positive-Definite Matrix in Natural Parametrization
在自然参数化的一般正定矩阵
译者：生物统计家园网 机器人LoveR
描述----------Description----------
This function is a constructor for the pdNatural class, representing a general positive-definite matrix, using a natural parametrization . If the matrix associated with object is of dimension n, it is represented by n*(n+1)/2 parameters. Letting S(i,j) denote the ij-th element of the underlying positive definite matrix and r(i,j) = S(i,j)/sqrt(S(i,i)S(j,j)), i not equal to j denote the associated "correlations", the "natural" parameters are given by sqrt(Sii), i=1,..,n and log((1+r(i,j))/(1-r(i,j))), i not equal to j. Note that all natural parameters are individually unrestricted, but not jointly unrestricted (meaning that not all unrestricted vectors would give positive-definite matrices). Therefore, this parametrization should NOT be used for optimization. It is mostly used for deriving approximate confidence intervals on parameters following the optimization of an objective function. When value is numeric(0), an uninitialized pdMat object, a one-sided formula, or a vector of character strings, object is returned as an uninitialized pdSymm object (with just some of its attributes and its class defined) and needs to have its coefficients assigned later, generally using the coef or matrix replacement functions. If value is an initialized pdMat object, object will be constructed from as.matrix(value). Finally, if value is a numeric vector, it is assumed to represent the natural parameters of the underlying positive-definite matrix.
此功能是为pdNatural类较一般的正定矩阵，利用自然的参数化的构造。 ，如果object相关的矩阵维n是，它是代表n*(n+1)/2参数。让S(i,j)指ij个元素的基础正定矩阵和r(i,j) = S(i,j)/sqrt(S(i,i)S(j,j)), i not equal to j表示相关的“关系”，“自然”参数sqrt(Sii), i=1,..,n的 log((1+r(i,j))/(1-r(i,j))), i not equal to j。请注意，所有的自然参数单独不受限制，但不能共同无限制（也就是说，不是所有的无限制向量将给正定矩阵）。因此，这不应该被用于参数化优化。它主要用于计算目标函数的优化后的参数近似置信区间。当value是numeric(0)，未初始化的pdMat对象，一种片面的公式，或一个字符串向量，object返回一个未初始化的pdSymm对象（只是它的一些属性和它的类中定义），都需要有它的系数分配后，一般使用coef或matrix更换功能。如果value是一个初始化pdMat对象，object将修建从as.matrix(value)。最后，如果value是一个数值向量，它被假定为代表的基础正定矩阵的自然参数。
用法----------Usage----------
pdNatural(value, form, nam, data)
参数----------Arguments----------
参数：value
an optional initialization value, which can be any of the following: a pdMat object, a positive-definite matrix, a one-sided linear formula (with variables separated by +), a vector of character strings, or a numeric vector. Defaults to numeric(0), corresponding to an uninitialized object.
一个可选的初始化值，它可以是下列任何一个pdMat对象，正定矩阵，一种片面的线性公式（与+分离变量），字符串向量或数字向量。 numeric(0)默认值，相应的未初始化的对象。
参数：form
an optional one-sided linear formula specifying the row/column names for the matrix represented by object. Because factors may be present in form, the formula needs to be evaluated on a data.frame to resolve the names it defines. This argument is ignored when value is a one-sided formula. Defaults to NULL.
一个可选的片面指定行/列名为object为代表的矩阵的线性公式。由于因素可能是在form目前，该公式需要评估数据框上，以解决它定义的名字。时value是一种片面的公式，则忽略此参数。 NULL默认。
参数：nam
an optional vector of character strings specifying the row/column names for the matrix represented by object. It must have length equal to the dimension of the underlying positive-definite matrix and unreplicated elements. This argument is ignored when value is a vector of character strings. Defaults to NULL.
由对象代表一个字符字符串指定为矩阵的行/列名的可选向量。它必须有长度等于底层正定矩阵和非复制的元素的尺寸。时value是一个字符串向量，则忽略此参数。 NULL默认。
参数：data
an optional data frame in which to evaluate the variables named in value and form. It is used to obtain the levels for factors, which affect the dimensions and the row/column names of the underlying matrix. If NULL, no attempt is made to obtain information on factors appearing in the formulas. Defaults to the parent frame from which the function was called.
在其中评估value和form命名的变量的可选数据框。用它来获得factors，这影响的尺寸和基础矩阵的行/列名的水平。如果NULL，没有尝试获得factors公式中出现的信息。默认从该函数被调用的父框架。
值----------Value----------
a pdNatural object representing a general positive-definite matrix in natural parametrization, also inheriting from class pdMat.
一个pdNatural对象代表自然参数化一般正定矩阵，也继承类pdMat。
作者（S）----------Author(s)----------
Jose Pinheiro and Douglas Bates <a href="mailto:bates@stat.wisc.edu">bates@stat.wisc.edu</a>
参考文献----------References----------
in S and S-PLUS", Springer, esp. p. 162.
参见----------See Also----------
as.matrix.pdMat, coef.pdMat, pdClasses,
as.matrix.pdMat，coef.pdMat，pdClasses
举例----------Examples----------
pdNatural(diag(1:3))
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。
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发表于 2012-2-16 18:53:42
