lme models as sparse, symmetric matrices

Description

A representation of a linear mixed-effects model using a combination of sparse, symmetric, column-oriented matrices and dense matrices.

Objects from the Class

Objects can be created by calls of the form new("ssclme", ...) or, more commonly, via the ssclme constructor function.

Slots

Gp:

integer vector of pointers to the beginning of each group of columns. Its length is 1 greater than the number of groups. Successive differences give the number of levels of each factor.

p:

as for "sscMatrix" objects.

i:

as for "sscMatrix" objects.

x:

as for "sscMatrix" objects.

Dim:

as for "sscMatrix" objects.

nc:

An integer vector of the number of columns in each model matrix. The last entry is p+1 where p is the number of columns in the fixed-effects model matrix.

ZtX:

A (dense) matrix equivalent to crossprod(Z,X).

XtX:

A (dense) matrix equivalent to the upper triangle of crossprod(X) where X has the response column appended.

Lp:

An integer vector of pointers to the beginnings of the columns of the unit lower triangular factor L in the LDL' decomposition of Z'Z+W.

Parent:

An integer vector from the symbolic analysis of the cross-tabulation. It is used to compute L efficiently.

Li:

Row indices of L.

D:

Diagonal of the diagonal matrix in the LDL' decomposition of Z'Z+W.

DIsqrt:

Square root of the inverse of the diagonal of D in LDL'.

Lx:

Non-zero elements in the (strict) lower triangle of L.

RZX:

A dense matrix corresponding to ZtX in the decomposition.

RXX:

A dense matrix corresponding to XtX in the decomposition.

LIp:

An integer vector of pointers to the columns of the unit lower triangular inverse of L.

LIi:

Row indices of L-inverse.

LIx:

Non-zero elements in the (strict) lower triangle of L-inverse.

status:

Logical vector of length 2 indicating if the object has been factored and if the factorization has been inverted.

deviance:

Numeric vector of length 2 containing the deviance corresponding to the maximum likelihood (ML) and REML criteria. This slot's contents are current if status$factored is TRUE.

devComp:

Numeric vector of length 4 giving the components used to calculate the deviance. This slot's contents are current if status$factored is TRUE.

bVar:

A list of numeric 3-dimensional arrays giving the conditional variances of the random effects. This slot's contents are current if status$inverted is TRUE.

Omega:

A list of numeric matrices providing the components of symmetric, positive-definite matrix Omega. Only the upper triangle of each component is used and stored.

Methods

coef

signature(object = "ssclme"): Extract the "coefficients" from the object as a numeric vector. If the optional argument unconst is FALSE (the default), the values in the upper triangles of the Omega matrices are concatenated. Within each matrix the diagonal is given first then the elements above the diagonal are given row-wise. If unconst is TRUE, an unconstrained parameterization based on the LDL decomposition (logarithms of diagonal elements of D followed by elements of the strict lower triangle of L column-wise) are given.

coef<-

signature(object = "ssclme", value = "numeric"): Assign the Omega matrices from a numeric vector. The assignment depends on the optional argument unconst as described above.

coerce

signature(from = "ssclme", to = "sscMatrix"): return the current Z'Z matrix as an sscMatrix object.

coerce

signature(from = "ssclme", to = "tscMatrix"): return the current L matrix from the LDL decomposition of Z'Z as a tscMatrix object.

See Also

sscCrosstab-class, sscMatrix-class, tscMatrix-class