Coef.qrrvglm-class {VGAM} | R Documentation |
The most pertinent matrices and other quantities pertaining to a QRR-VGLM (CQO model).
Objects can be created by calls of the form Coef(object,
...)
where object
is an object of class "qrrvglm"
(created by cqo
).
In this document, R is the rank, M is the number of linear predictors and n is the number of observations.
A
:"matrix"
, A, which are the
linear `coefficients' of the matrix of latent variables.
It is M by R. B1
:"matrix"
, B1.
These correspond to terms of the argument Norrr
. C
:"matrix"
, C, the
canonical coefficients. It has R columns. Constrained
:D
:"array"
,
D[,,j]
is an order-Rank
matrix, for
j
= 1,...,M.
Ideally, these are negative-definite in order to make the response
curves/surfaces bell-shaped.
Rank
:lv
:lvOrder
:"matrix"
, the permutation
returned when the function
order
is applied to each column of lv
.
This enables each column of lv
to be easily sorted.
Maximum
:"numeric"
, the
M maximum fitted values. That is, the fitted values
at the optima for Norrr = ~ 1
models.
If Norrr
is not ~ 1
then these will be NA
s. NOS
:Optimum
:"matrix"
, the values
of the latent variables where the optima are.
If the curves are not bell-shaped, then the value will
be NA
or NaN
.OptimumOrder
:"matrix"
, the permutation
returned when the function
order
is applied to each column of Optimum
.
This enables each row of Optimum
to be easily sorted.
bellshaped
:dispersion
:Dzero
:D[,,j]
equals O, for
j
= 1,...,M . Tolerance
:"array"
,
Tolerance[,,j]
is an order-Rank
matrix, for
j
= 1,...,M, being the matrix of
tolerances (squared if on the diagonal).
These are denoted by T in Yee (2004).
Ideally, these are positive-definite in order to make the response
curves/surfaces bell-shaped.
The tolerance matrices satisfy
T_s = -(0.5 D_s^(-1).
Thomas W. Yee
Yee, T. W. (2004) A new technique for maximum-likelihood canonical Gaussian ordination. Ecological Monographs, 74, 685–701.
Coef.qrrvglm
,
cqo
,
print.Coef.qrrvglm
.
x2 = rnorm(n <- 100) x3 = rnorm(n) x4 = rnorm(n) lv1 = 0 + x3 - 2*x4 lambda1 = exp(3 - 0.5 * (lv1-0)^2) lambda2 = exp(2 - 0.5 * (lv1-1)^2) lambda3 = exp(2 - 0.5 * ((lv1+4)/2)^2) y1 = rpois(n, lambda1) y2 = rpois(n, lambda2) y3 = rpois(n, lambda3) yy = cbind(y1,y2,y3) p1 = cqo(yy ~ x2 + x3 + x4, fam=poissonff, trace=FALSE) ## Not run: lvplot(p1, y=TRUE, lcol=1:3, pch=1:3, pcol=1:3) ## End(Not run) print(Coef(p1), digits=3)