Class “Coef.qrrvglm”
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:Of class "matrix", A, which are the
linear ‘coefficients’ of the matrix of latent variables.
It is M by R.
B1:Of class "matrix", B1.
These correspond to terms of the argument noRRR.
C:Of class "matrix", C, the
canonical coefficients. It has R columns.
Constrained:Logical. Whether the model is a constrained ordination model.
D:Of class "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:The rank (dimension, number of latent variables) of the RR-VGLM. Called R.
latvar:n by R matrix of latent variable values.
latvar.order:Of class "matrix", the permutation
returned when the function
order is applied to each column of latvar.
This enables each column of latvar to be easily sorted.
Maximum:Of class "numeric", the
M maximum fitted values. That is, the fitted values
at the optimums for noRRR = ~ 1 models.
If noRRR is not ~ 1 then these will be NAs.
NOS:Number of species.
Optimum:Of class "matrix", the values
of the latent variables where the optimums are.
If the curves are not bell-shaped, then the value will
be NA or NaN.
Optimum.order:Of class "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:Vector of logicals: is each response curve/surface bell-shaped?
dispersion:Dispersion parameter(s).
Dzero:Vector of logicals, is each of the
response curves linear in the latent variable(s)?
It will be if and only if
D[,,j] equals O, for
j = 1,...,M .
Tolerance:Object of class "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) latvar1 <- 0 + x3 - 2*x4 lambda1 <- exp(3 - 0.5 * ( latvar1-0)^2) lambda2 <- exp(2 - 0.5 * ( latvar1-1)^2) lambda3 <- exp(2 - 0.5 * ((latvar1+4)/2)^2) y1 <- rpois(n, lambda1) y2 <- rpois(n, lambda2) y3 <- rpois(n, lambda3) yy <- cbind(y1, y2, y3) # vvv 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) # vvv print(Coef(p1), digits = 3)
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