Description Usage Arguments Details Value Note References See Also Examples
Produces an object of class rsm
which is a regressionscale
model fit of the data.
1 2 3 4 5 6 
formula 
a formula expression as for other linear regression models, of the
form 
family 
a 
data 
an optional data frame in which to interpret the variables
occurring in the model formula, or in the 
dispersion 
if 
weights 
the optional weights for the fitting criterion. If supplied, the
response variable and the covariates are multiplied by the weights
in the IRLS algorithm. The length of the 
subset 
expression saying which subset of the rows of the data should be used in the fit. This can be a logical vector (which is replicated to have length equal to the number of observations), or a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included. All observations are included by default. 
na.action 
a function to filter missing data. This is applied to the model
frame after any 
offset 
this can be used to specify an a priori known component to
be included in the linear predictor during fitting. An

method 
the fitting method to be used; the default is 
control 
a list of iteration and algorithmic constants. See

model 
if 
x 
if 
y 
if 
contrasts 
a list of contrasts to be used for some or all of the factors appearing as variables in the model formula. The names of the list should be the names of the corresponding variables, and the elements should either be contrasttype matrices (matrices with as many rows as levels of the factor and with columns linearly independent of each other and of a column of one's), or else they should be functions that compute such contrast matrices. 
... 
absorbs any additional argument. 
The model is fitted using Iteratively Reweighted Least
Squares, IRLS for short (Green, 1984,
Jorgensen, 1984). The working response and iterative
weights are computed using the functions contained in the
family.rsm
object.
The two workhorses of rsm
are rsm.fit
and
rsm.surv
, which expect an X
and Y
argument rather then a formula. The first function is used for the
families student
with df
less than 3 and
Huber
;
the second one, based on the survreg.fit
routine for fitting parametric survival models, is used in case of
extreme
, logistic
, logWeibull
,
logExponential
, logRayleigh
and student
(with
df
> 2) error distributions. In the presence of a
userdefined error distribution the rsm.fit
routine is used.
The rsm.null
function is invoked to fit an empty (null)
model.
The details are given in Brazzale (2000, Section 6.3.1).
an object of class rsm
is returned which inherits from
glm
and lm
. See rsm.object
for details.
The output can be examined by print
,
summary
, rsm.diag.plots
and
anova
. Components can be extracted using
fitted
, residuals
,
formula
and family
. It can
be modified using update
. It has most of the
components of a glm
object, with a few more. Use
rsm.object
for further details.
In case of extreme
, logistic
, logWeibull
,
logExponential
, logRayleigh
and student
(with
df
> 2) error distributions, both methods,
rsm.fit
(default choice) and
rsm.surv
, can be used to fit the model.
There are, however, examples where one of the two algorithms (most
likely the one invoked by rsm.surv
) breaks
down. If this is the case, try and refit the model with the
alternative choice.
The message "negative iterative weights returned!"
is
returned if some of the iterative weights (q2
component of
the fitted rsm
object) are negative. These would be used by
default by the rsm.diag
routine for the definition of
residuals and regression diagnostics. In order to avoid missing
values (NA
s), the default weighting scheme "observed"
automatically switches to "score"
unless otherwise specified.
Brazzale, A. R. (2000) Practical SmallSample Parametric Inference. Ph.D. Thesis N. 2230, Department of Mathematics, Swiss Federal Institute of Technology Lausanne.
Green, P. J. (1984) Iteratively reweighted least squares for maximum likelihood estimation, and some robust and resistant alternatives (with Discussion). J. R. Statist. Soc. B, 46, 149–192.
Jorgensen, B. (1984) The delta algorithm and GLIM. Int. Stat. Rev., 52, 283–300.
rsm.object
, rsm.fit
,
rsm.surv
, rsm.null
,
rsm.families
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44  ## House Price Data
data(houses)
houses.rsm < rsm(price ~ ., family = student(5), data = houses)
## model fit including all covariates
houses.rsm < rsm(price ~ ., family = student(5), data = houses,
method = "rsm.fit", control = glm.control(trace = TRUE))
## prints information about the iterative procedure at each iteration
update(houses.rsm, ~ .  bdroom + offset(7 * bdroom))
## "bdroom" is included as offset variable with fixed (= 7) coefficient
## Sea Level Data
data(venice)
attach(venice)
Year < 1:51/51
venice.2.rsm < rsm(sea ~ Year + I(Year^2), family = extreme)
## quadratic model fitted to sea level data
venice.1.rsm < update(venice.2.rsm, ~.  I(Year^2))
## linear model fit
##
c11 < cos(2*pi*1:51/11) ; s11 < sin(2*pi*1:51/11)
c19 < cos(2*pi*1:51/18.62) ; s19 < sin(2*pi*1:51/18.62)
venice.rsm < rsm(sea ~ Year + I(Year^2) + c11 + s11 + c19 + s19,
family = extreme)
## includes 18.62year astronomical tidal cycle and 11year sunspot cycle
venice.11.rsm < rsm(sea ~ Year + I(Year^2) + c11 + s11, family = extreme)
venice.19.rsm < rsm(sea ~ Year + I(Year^2) + c19 + s19, family = extreme)
## includes either astronomical cycle
##
## comparison of linear, quadratic and periodic (11year, 19year) models
plot(year, sea, ylab = "sea level")
lines(year, fitted(venice.1.rsm))
lines(year, fitted(venice.2.rsm), col="red")
lines(year, fitted(venice.11.rsm), col="blue")
lines(year, fitted(venice.19.rsm), col="green")
##
detach()
## Darwin's Data on Growth Rates of Plants
data(darwin)
darwin.rsm < rsm(cross  self ~ pot  1, family = student(3),
data = darwin)
## Maximum likelihood estimates
darwin.rsm < rsm(cross  self ~ pot  1, family = Huber, data = darwin)
## Mestimates

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