VGAM (version 1.1-14)

summary.drrvglm: Summarizing Reduced Rank Vector Generalized Linear Model (RR-VGLM) and Doubly constrained RR-VGLM Fits

Description

These functions are all methods for class "drrvglm" or "summary.drrvglm" objects, or for class "rrvglm" or "summary.rrvglm" objects.

Usage

# S3 method for drrvglm
summary(object, correlation = FALSE, dispersion = NULL,
    digits = NULL, numerical = TRUE, h.step = 0.005, omit123 = FALSE,
     omit13 = FALSE, fixA = FALSE, presid = FALSE,
    signif.stars = getOption("show.signif.stars"),
    nopredictors = FALSE, eval0 = TRUE, ...)
# S3 method for summary.drrvglm
show(x, digits = NULL,
    quote = TRUE, prefix = "", signif.stars = NULL)
# S3 method for rrvglm
summary(object, correlation = FALSE, dispersion = NULL,
    digits = NULL, numerical = TRUE, h.step = 0.005, omit123 = FALSE,
     omit13 = FALSE, fixA = TRUE, presid = FALSE,
    signif.stars = getOption("show.signif.stars"),
    nopredictors = FALSE, upgrade = FALSE, ...)
# S3 method for summary.rrvglm
show(x, digits = NULL,
    quote = TRUE, prefix = "", signif.stars = NULL, ...)

Value

summarydrrvglm returns an object of class "summary.drrvglm".

Details

Most of this document concerns DRR-VGLMs but also apply equally well to RR-VGLMs as a special case.

The overall variance-covariance matrix The overall variance-covariance matrix (called V below) is computed. Since the parameters comprise the elements of the matrices A, B1 and C (called here block matrices 1, 2, 3 respectively), and an alternating algorithm is used for estimation, then there are two overlapping submodels that are fitted within an IRLS algorithm. These have blocks 1 and 2, and 2 and 3, so that B1 is common to both. They are combined into one large overall variance-covariance matrix. Argument fixA specifies which submodel the B1 block is taken from. Block (1,3) is the most difficult to compute and numerical approximations based on first derivatives are used by default for this.

Sometimes the computed V is not positive-definite. If so, then the standard errors will be NA. To avoid this problem, try varying h.step or refitting the model with a different Index.corner. Argument omit13 and omit123 can also be used to give approximate answers. If V is not positive-definite then this may indicate that the model does not fit the data very well, e.g., Rank is not a good value. Potentially, there are many ways why the model may be ill-conditioned. Try several options and set trace = TRUE to monitor convergence---this is informative about how well the model and data agree.

How can one fit an ordinary RR-VGLM as a DRR-VGLM? If one uses corner constraints (default) then one should input H.A as a list containing Rank diag(M) matrices---one for each column of A. Then since Corner = TRUE by default, then [e-mail] has certain columns deleted due to corner constraints. In contrast, [e-mail] is the H.A that was inputted. FYI, the alt suffix indicates the alternating algorithm, while the suffix thy stands for theory.

References

Chapter 5 of: Yee, T. W. (2015). Vector Generalized Linear and Additive Models: With an Implementation in R. New York, USA: Springer. Sections 5.2.2 and 5.3 are particularly relevant.

See Also

rrvglm, rrvglm.control, vcovdrrvglm, CM.free, summaryvglm, summary.rrvglm-class, summary.drrvglm-class.

Examples

if (FALSE)   # Fit a rank-1 RR-VGLM as a DRR-VGLM.
set.seed(1); n <- 1000; S <- 6  # S must be even
myrank <- 1
rdata <- data.frame(x1 = runif(n), x2 = runif(n),
           x3 = runif(n), x4 = runif(n))
dval <- ncol(rdata)  # Number of covariates
# Involves x1, x2, ... a rank-1 model:
ymatrix <- with(rdata,
  matrix(rpois(n*S, exp(3 + x1 - 0.5*x2)), n, S))
H.C <- vector("list", dval)  # Ordinary "rrvglm"
for (i in 1:dval) H.C[[i]] <- CM.free(myrank)
names(H.C) <- paste0("x", 1:dval)
H.A <- list(CM.free(S))  # rank-1

rfit1 <- rrvglm(ymatrix ~ x1 + x2 + x3 + x4,
           poissonff, rdata, trace = TRUE)
class(rfit1)
dfit1 <- rrvglm(ymatrix ~ x1 + x2 + x3 + x4,
           poissonff, rdata, trace = TRUE,
           H.A = H.A,    # drrvglm
           H.C = H.C)    # drrvglm
class(dfit1)
Coef(rfit1)  # The RR-VGLM is the same as
Coef(dfit1)  # the DRR-VGLM.
max(abs(predict(rfit1) - predict(dfit1)))  # 0
abs(logLik(rfit1) - logLik(dfit1))  # 0
summary(rfit1)
summary(dfit1)