fbvevd(x, model = "log", start, ..., nsloc1 = NULL, nsloc2 = NULL,
std.err = TRUE, dsm = TRUE, corr = FALSE, method = "BFGS",
warn.inf = TRUE)"log" (the default), "alog", "hr",
"neglog", "aneglog", "bilog",
"negbilog" or "ct"start is omitted the routine attempts to find good
starting values using marginal maximum likelihood estimators.optim. If
parameters of the model are included they will be held fixed at
the values given (see Examples).x, for linear modelling of the location parameter on the
first/second margin (see Details).
The data frames are treated as covariate matrices, excluding the
intercept. A numeTRUE (the default), the standard
errors are returned.TRUE (the default), summaries of the
dependence structure are returned.TRUE, the correlation matrix is
returned.optim for
details).TRUE (the default), a warning is
given if the negative log-likelihood is infinite when evaluated at
the starting values.c("bvevd","evd"). The generic accessor functions fitted (or
fitted.values), std.errors,
deviance, logLik and
AIC extract various features of the
returned object.
The functions profile and profile2d can be
used to obtain deviance profiles.
The function anova compares nested models, and the
function AIC compares non-nested models.
The function plot produces diagnostic plots.
An object of class c("bvevd","evd") is a list containing
the following components
optim.x.nsloc1 and nsloc2.x.model.dep,
asy1, asy2, alpha and beta, depending on
the model selected (see rbvevd). The marginal parameter
names are loc1, scale1 and shape1 for the first
margin, and loc2, scale2 and shape2 for the
second margin.
If nsloc1 is not NULL, so that a linear model is
implemented for the first marginal location parameter, the parameter
names for the first margin are loc1, loc1x1,
..., loc1xn, scale and shape, where
x1, ..., xn are the column names of nsloc1,
so that loc1 is the intercept of the linear model, and
loc1x1, ..., loc1xn are the
ncol(nsloc1) coefficients.
When nsloc2 is not NULL, the parameter names for the
second margin are constructed similarly.
It is recommended that the covariates within the linear models for
the location parameters are (at least approximately) centered and
scaled (i.e. that the columns of nsloc1 and nsloc2
are centered and scaled), particularly if automatic starting values
are used, since the starting values for the associated parameters are
then zero. If dsm is TRUE, three values are returned which
summarize the dependence structure, based on the fitted
dependence function $A$ (see abvpar).
Two are measures of the strength of dependence.
The first (Dependence One) is given by $2(1-A(1/2))$.
The second (Dependence Two) is the integral of $4(1 - A(x))$,
taken over $0\leq x\leq1$.
Both measures are zero at independence and one at complete dependence.
The third value (Asymmetry) is a measure of asymmetry, given by
the integral of
$4(A(x) - A(1-x))/(3 - 2\sqrt2)$,
taken over $0 \leq x \leq 0.5$.
This lies in the closed interval [-1,1] (conjecture), with
larger absolute values representing stronger asymmetry.
For the logistic, Husler-Reiss and negative logistic models
$A(x) = A(1-x)$ for all $0 \leq x \leq 0.5$,
so the value will be zero.
For numerical reasons the parameters of each model are subject the artificial constraints given in Table 1 of the User's Guide.
anova.evd, optim,
plot.bvevd, profile.evd,
profile2d.evd, rbvevdbvdata <- rbvevd(100, dep = 0.6, model = "log", mar1 = c(1.2,1.4,0.4))
M1 <- fbvevd(bvdata, model = "log")
M2 <- fbvevd(bvdata, model = "log", dep = 0.75)
anova(M1, M2)
plot(M1)
plot(M1, mar = 1)
plot(M1, mar = 2)
plot(M2)
M1P <- profile(M1, which = "dep")
plot(M1P)
trend <- (-49:50)/100
rnd <- runif(100, min = -.5, max = .5)
fbvevd(bvdata, model = "log", nsloc1 = trend)
fbvevd(bvdata, model = "log", nsloc1 = trend, nsloc2 = data.frame(trend
= trend, random = rnd))
fbvevd(bvdata, model = "log", nsloc1 = trend, nsloc2 = data.frame(trend
= trend, random = rnd), loc2random = 0)Run the code above in your browser using DataLab