VGAM/man/cqo.Rd

7   \emph{canonical Gaussian ordination} or CGO) model is fitted using
16     coefstart = NULL, control = qrrvglm.control(...), offset = NULL,
25   The RHS of the formula is applied to each linear predictor. Different
33   describing what statistical model is to be fitted. This is called a
64    typically the environment from which \code{cqo} is called.
82   \code{NA}s.  The default is set by the \code{na.action} setting of
83   \code{\link[base]{options}}, and is \code{na.fail} if that is unset.
84   The ``factory-fresh'' default is \code{na.omit}.
90   It is a \eqn{M}-column matrix.
113   See \code{\link{qrrvglm.control}} for details.
143   Note the model matrix is the LM model matrix.
148 %    \code{vglmfit} is a \code{vglm} object.
166   If \code{constraints} is used it must contain \emph{all} the
167   terms; an incomplete list is not accepted.
181 %   VLM model matrix, is returned on the object.
190   further arguments passed into \code{\link{qrrvglm.control}}.
201   is the \emph{rank} or the number of ordination axes.  Each species'
202   response is then a regression of these latent variables using quadratic
204   for presence/absence responses).  The solution is obtained iteratively
209   The central formula (for Poisson and binomial species data) is
215   where \eqn{x_1}{x_1} is a vector (usually just a 1 for an intercept),
216   \eqn{x_2}{x_2} is a vector of environmental variables, \eqn{\nu=C^T
217   x_2}{nu=C^T x_2} is a \eqn{R}-vector of latent variables, \eqn{e_m} is
220   e.g., the \eqn{m}th element is \eqn{\eta_m = \log(E[Y_m])}{eta_m =
226   in \code{\link{qrrvglm.control}}, e.g., the argument \code{noRRR}
232   normal, and negative binomial distributions. The latter is a
238 % The Poisson is or should be catered for by
248   %For overdispersed Poisson data, using \code{\link{quasipoissonff}} is
249   %strongly recommended over \code{\link{negbinomial}}; the latter is
254   work reasonably well if the data is Poisson with species having equal
256   \code{Cinit} argument in \code{\link{qrrvglm.control}} can be used.
262   It is possible to relax the quadratic form to an additive model.  The
263   result is a data-driven approach rather than a model-driven approach,
264   so that CQO is extended to \emph{constrained additive ordination}
268   In this documentation, \eqn{M} is the number of linear predictors,
269   \eqn{S} is the number of responses (species). Then
279   For UQO, the response is the usual site-by-species matrix and
289   An object of class \code{"qrrvglm"}.
337   Here is a partial \bold{checklist}.
341   Feeding in 100+ species wholesale is a recipe for failure.
343   Using 10 well-chosen species is better than 100+ species thrown in
350   for presence/absence is the species totally absent or totally present
365   is it heavily skewed or are there outliers?
374   This is especially needed for \code{I.tolerance = TRUE}.
380   Only if the data is very good should a rank-2 model be attempted.
381   Usually a rank-1 model is all that is practically possible even
390   If the number of sites is large then choose a random sample of them.
398   if the inputted data set is large,
401   \code{eq.tolerance = TRUE}, is very memory hungry.
409   By default, a rank-1 equal-tolerances QRR-VGLM model is fitted
410   (see \code{\link{qrrvglm.control}} for the default control
414   By default, the argument \code{trace} is \code{TRUE} meaning a running
415   log is printed out while the computations are taking place.  This is
416   because the algorithm is computationally expensive, therefore users
420   The argument \code{Bestof} in \code{\link{qrrvglm.control}} controls
422   the data. This argument is important because convergence may be to a
427   arise because the optimization problem is highly nonlinear, and this is
432   %data. If this is so, then setting \code{I.tolerances = TRUE} or
434   %\eqn{n}, is small.
436   %If the negative binomial family function \code{\link{negbinomial}} is
438   %is necessary. This means to minimize the deviance, which the fast
456   \code{I.tolerances = FALSE}. This is because numerical problems can
459   slow down the computation considerably, however it is numerically
463   In Example 1 below, an unequal-tolerances rank-1 QRR-VGLM is fitted to the
465   Example 2 is the equal-tolerances version. The latter is less likely to
467   In Example 3 below, an equal-tolerances rank-2 QRR-VGLM is fitted to the
470   suggests a rank-1 model is probably preferable.
472   nomenclature, constrained Gaussian logit ordination) is fitted to some
476   indicate that the response (matrix) is multivariate. Otherwise, it is
479   This is useful as a diagnostic plot.
480   This is done by (re)regressing each species separately against the latent
492   of the argument \code{Bestof} in \code{\link{qrrvglm.control}}.
501   CQO is computationally expensive with memory and time.
507   be wide in order for the quadratics to fit the data well (bell-shaped
509   the response is linear on the transformed scale (e.g., log or logit)
510   and the ordination is called \emph{constrained linear ordination} or CLO.
513   Like many regression models, CQO is sensitive to outliers (in the
515   multicollinearity etc.  For these reasons, it is necessary to examine
520   be trusted.  Fitting a CAO is recommended first, then upon transformations
524   For binary data, it is necessary to have `enough' data.  In general,
529   and if the response data for each species is a string of all absences,
545   \code{\link{qrrvglm.control}},
546   \code{\link{Coef.qrrvglm}},
548   \code{\link{calibrate.qrrvglm}},
559   \code{\link{lvplot.qrrvglm}},
561   \code{\link{trplot.qrrvglm}},
608 aa <- aa[!is.na(aa)]  # Delete the species that is not unimodal
637 # This example is numerically fraught... need I.toler = TRUE too.