vglm  R Documentation 
vglm
fits vector generalized linear models (VGLMs).
This very large class of models includes
generalized linear models (GLMs) as a special case.
vglm(formula,
family = stop("argument 'family' needs to be assigned"),
data = list(), weights = NULL, subset = NULL,
na.action = na.fail, etastart = NULL, mustart = NULL,
coefstart = NULL, control = vglm.control(...), offset = NULL,
method = "vglm.fit", model = FALSE, x.arg = TRUE, y.arg = TRUE,
contrasts = NULL, constraints = NULL, extra = list(),
form2 = NULL, qr.arg = TRUE, smart = TRUE, ...)
formula 
a symbolic description of the model to be fit.
The RHS of the formula is applied to each linear
predictor.
The effect of different variables in each linear predictor
can be controlled by specifying constraint matrices—see

family 
a function of class 
data 
an optional data frame containing the variables in the model.
By default the variables are taken from

weights 
an optional vector or matrix of (prior fixed and known) weights
to be used in the fitting process.
If the VGAM family function handles multiple responses
( Currently the 
subset 
an optional logical vector specifying a subset of observations to be used in the fitting process. 
na.action 
a function which indicates what should happen when
the data contain 
etastart 
optional starting values for the linear predictors.
It is a 
mustart 
optional starting values for the fitted values.
It can be a vector or a matrix;
if a matrix, then it has the same number of rows
as the response.
Usually 
coefstart 
optional starting values for the coefficient vector.
The length and order must match that of 
control 
a list of parameters for controlling the fitting process.
See 
offset 
a vector or 
method 
the method to be used in fitting the model.
The default (and
presently only) method 
model 
a logical value indicating whether the
model frame
should be assigned in the 
x.arg, y.arg 
logical values indicating whether
the LM matrix and response vector/matrix used in the fitting
process should be assigned in the 
contrasts 
an optional list. See the 
constraints 
an optional If the Properties:
each constraint matrix must have As mentioned above, the labelling of each constraint matrix
must match exactly, e.g.,

extra 
an optional list with any extra information that might be needed by the VGAM family function. 
form2 
the second (optional) formula.
If argument 
qr.arg 
logical value indicating whether the slot 
smart 
logical value indicating whether smart prediction
( 
... 
further arguments passed into 
A vector generalized linear model (VGLM) is loosely defined
as a statistical model that is a function of M
linear
predictors and can be estimated by Fisher scoring.
The central formula is given by
\eta_j = \beta_j^T x
where x
is a vector of explanatory variables
(sometimes just a 1 for an intercept),
and
\beta_j
is a vector of regression coefficients
to be estimated.
Here, j=1,\ldots,M
, where M
is finite.
Then one can write
\eta=(\eta_1,\ldots,\eta_M)^T
as a vector of linear predictors.
Most users will find vglm
similar in flavour to
glm
.
The function vglm.fit
actually does the work.
An object of class "vglm"
, which has the
following slots. Some of these may not be assigned to save
space, and will be recreated if necessary later.
extra 
the list 
family 
the family function (of class 
iter 
the number of IRLS iterations used. 
predictors 
a 
assign 
a named list which matches the columns and the (LM) model matrix terms. 
call 
the matched call. 
coefficients 
a named vector of coefficients. 
constraints 
a named list of constraint matrices used in the fitting. 
contrasts 
the contrasts used (if any). 
control 
list of control parameter used in the fitting. 
criterion 
list of convergence criterion evaluated at the final IRLS iteration. 
df.residual 
the residual degrees of freedom. 
df.total 
the total degrees of freedom. 
dispersion 
the scaling parameter. 
effects 
the effects. 
fitted.values 
the fitted values, as a matrix. This is often the mean but may be quantiles, or the location parameter, e.g., in the Cauchy model. 
misc 
a list to hold miscellaneous parameters. 
model 
the model frame. 
na.action 
a list holding information about missing values. 
offset 
if nonzero, a 
post 
a list where postanalysis results may be put. 
preplot 
used by 
prior.weights 
initially supplied weights
(the 
qr 
the QR decomposition used in the fitting. 
R 
the R matrix in the QR decomposition used in the fitting. 
rank 
numerical rank of the fitted model. 
residuals 
the working residuals at the final IRLS iteration. 
ResSS 
residual sum of squares at the final IRLS iteration with the adjusted dependent vectors and weight matrices. 
smart.prediction 
a list of datadependent parameters (if any) that are used by smart prediction. 
terms 
the 
weights 
the working weight matrices at the final IRLS iteration. This is in matrixband form. 
x 
the model matrix (linear model LM, not VGLM). 
xlevels 
the levels of the factors, if any, used in fitting. 
y 
the response, in matrix form. 
This slot information is repeated at vglmclass
.
See warnings in vglm.control
.
Also, see warnings under weights
above regarding
sampling weights from complex sampling designs.
This function can fit a wide variety of
statistical models. Some of
these are harder to fit than others because
of inherent numerical
difficulties associated with some of them.
Successful model fitting
benefits from cumulative experience.
Varying the values of arguments
in the VGAM family function itself
is a good first step if
difficulties arise, especially if initial
values can be inputted.
A second, more general step, is to vary the
values of arguments in
vglm.control
.
A third step is to make use of arguments such
as etastart
,
coefstart
and mustart
.
Some VGAM family functions end in "ff"
to avoid
interference with other functions, e.g.,
binomialff
,
poissonff
.
This is because VGAM family
functions are incompatible with glm
(and also gam()
in gam and
gam
in the mgcv library).
The smart prediction (smartpred
)
library is incorporated
within the VGAM library.
The theory behind the scaling parameter is currently being made more rigorous, but it it should give the same value as the scale parameter for GLMs.
In Example 5 below, the xij
argument to
illustrate covariates
that are specific to a linear predictor.
Here, lop
/rop
are
the ocular pressures of the left/right eye
(artificial data).
Variables leye
and reye
might be
the presence/absence of
a particular disease on the LHS/RHS eye respectively.
See
vglm.control
and
fill1
for more details and examples.
Thomas W. Yee
Yee, T. W. (2015). Vector Generalized Linear and Additive Models: With an Implementation in R. New York, USA: Springer.
Yee, T. W. and Hastie, T. J. (2003). Reducedrank vector generalized linear models. Statistical Modelling, 3, 15–41.
Yee, T. W. and Wild, C. J. (1996). Vector generalized additive models. Journal of the Royal Statistical Society, Series B, Methodological, 58, 481–493.
Yee, T. W. (2014). Reducedrank vector generalized linear models with two linear predictors. Computational Statistics and Data Analysis, 71, 889–902.
Yee, T. W. (2008).
The VGAM
Package.
R News, 8, 28–39.
vglm.control
,
vglmclass
,
vglmffclass
,
smartpred
,
vglm.fit
,
fill1
,
rrvglm
,
vgam
.
Methods functions include
add1.vglm
,
anova.vglm
,
AICvlm
,
coefvlm
,
confintvglm
,
constraints.vlm
,
drop1.vglm
,
fittedvlm
,
hatvaluesvlm
,
hdeff.vglm
,
Influence.vglm
,
linkfunvlm
,
lrt.stat.vlm
,
score.stat.vlm
,
wald.stat.vlm
,
nobs.vlm
,
npred.vlm
,
plotvglm
,
predictvglm
,
residualsvglm
,
step4vglm
,
summaryvglm
,
lrtest_vglm
,
update
,
etc.
# Example 1. See help(glm)
(d.AD < data.frame(treatment = gl(3, 3),
outcome = gl(3, 1, 9),
counts = c(18,17,15,20,10,20,25,13,12)))
vglm.D93 < vglm(counts ~ outcome + treatment, poissonff,
data = d.AD, trace = TRUE)
summary(vglm.D93)
# Example 2. Multinomial logit model
pneumo < transform(pneumo, let = log(exposure.time))
vglm(cbind(normal, mild, severe) ~ let, multinomial, pneumo)
# Example 3. Proportional odds model
fit3 < vglm(cbind(normal, mild, severe) ~ let, propodds, pneumo)
coef(fit3, matrix = TRUE)
constraints(fit3)
model.matrix(fit3, type = "lm") # LM model matrix
model.matrix(fit3) # Larger VGLM (or VLM) matrix
# Example 4. Bivariate logistic model
fit4 < vglm(cbind(nBnW, nBW, BnW, BW) ~ age, binom2.or, coalminers)
coef(fit4, matrix = TRUE)
depvar(fit4) # Response are proportions
weights(fit4, type = "prior")
# Example 5. The use of the xij argument (simple case).
# The constraint matrix for 'op' has one column.
nn < 1000
eyesdat < round(data.frame(lop = runif(nn),
rop = runif(nn),
op = runif(nn)), digits = 2)
eyesdat < transform(eyesdat, eta1 = 1 + 2 * lop,
eta2 = 1 + 2 * lop)
eyesdat < transform(eyesdat,
leye = rbinom(nn, 1, prob = logitlink(eta1, inv = TRUE)),
reye = rbinom(nn, 1, prob = logitlink(eta2, inv = TRUE)))
head(eyesdat)
fit5 < vglm(cbind(leye, reye) ~ op,
binom2.or(exchangeable = TRUE, zero = 3),
data = eyesdat, trace = TRUE,
xij = list(op ~ lop + rop + fill1(lop)),
form2 = ~ op + lop + rop + fill1(lop))
coef(fit5)
coef(fit5, matrix = TRUE)
constraints(fit5)
fit5@control$xij
head(model.matrix(fit5))
# Example 6. The use of the 'constraints' argument.
as.character(~ bs(year,df=3)) # Get the white spaces right
clist < list("(Intercept)" = diag(3),
"bs(year, df = 3)" = rbind(1, 0, 0))
fit1 < vglm(r1 ~ bs(year,df=3), gev(zero = NULL),
data = venice, constraints = clist, trace = TRUE)
coef(fit1, matrix = TRUE) # Check
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