Description Usage Arguments Details Value Examples
A GLDRM is a semiparametric generalized linear model. In contrast to a GLM, which assumes a particular exponential family distribution, the GLDRM uses a semiparametric likelihood to estimate the reference distribution. The reference distribution may be any discrete, continuous, or mixed exponential family distribution. The model parameters, which include both the regression coefficients and the cdf of the unspecified reference distribution, are estimated by maximizing a semiparametric likelihood. Regression coefficients are estimated with no loss of efficiency, i.e. the asymptotic variance is the same as if the true exponential family distribution were known.
1 2 3 4  gldrm(formula, data = NULL, link = "identity", mu0 = NULL,
offset = NULL, gldrmControl = gldrm.control(),
thetaControl = theta.control(), betaControl = beta.control(),
f0Control = f0.control())

formula 
An object of class "formula". 
data 
An optional data frame containing the variables in the model. 
link 
Link function. Can be a character string to be passed to the

mu0 
Mean of the reference distribution. The reference distribution is
not unique unless its mean is restricted to a specific value. This value can
be any number within the range of observed values, but values near the boundary
may cause numerical instability. This is an optional argument with 
offset 
Known component of the linear term. Offset must be passed through
this argument  offset terms in the formula will be ignored.
value and covariate values. If sampling weights are a function of both the
response value and covariates, then 
gldrmControl 
Optional control arguments.
Passed as an object of class "gldrmControl", which is constructed by the

thetaControl 
Optional control arguments for the theta update procedure.
Passed as an object of class "thetaControl", which is constructed by the

betaControl 
Optional control arguments for the beta update procedure.
Passed as an object of class "betaControl", which is constructed by the

f0Control 
Optional control arguments for the 
The arguments linkfun
, linkinv
, and mu.eta
mirror the "linkglm" class. Objects of this class can be created with the
stats::make.link
function.
The "gldrm" class is a list of the following items.
conv
Logical indicator for whether the gldrm algorithm
converged within the iteration limit.
iter
Number of iterations used. A single iteration is a beta
update, followed by an f0
update.
llik
Semiparametric loglikelihood of the fitted model.
beta
Vector containing the regression coefficient estimates.
mu
Vector containing the estimated mean response value for each
observation in the training data.
eta
Vector containing the estimated linear combination of
covariates for each observation.
f0
Vector containing the semiparametric estimate of the reference
distribution, evaluated at the observed response values. The values of correspond
to the support values, sorted in increasing order.
spt
Vector containing the unique observed response values, sorted in
increasing order.
mu0
Mean of the estimated semiparametric reference distribution.
The mean of the reference distribution must be fixed at a value in order for
the model to be identifiable. It can be fixed at any value within the range
of observed response values, but the gldrm
function assigns mu0
to be the mean of the observed response values.
varbeta
Estimated variance matrix of the regression coefficients.
seBeta
Standard errors for \hat{β}. Equal to
sqrt(diag(varbeta))
.
seMu
Standard errors for \hat{μ} computed from varbeta
.
seEta
Standard errors for \hat{η} computed from varbeta
.
theta
Vector containing the estimated tilt parameter for each observation.
The tilted density function of the response variable is given by
f(yx_i) = f_0(y) \exp(θ_i y) / \int f_0(u) \exp(θ_i u) du.
bPrime
is a vector containing the mean of the tilted distribution,
b'(θ_i), for each observation. bPrime
should match mu
,
except in cases where theta
is capped for numerical stability.
b'(θ_i) = \int u f(ux_i) du
bPrime2
is a vector containing the variance of the tilted
distribution, b''(θ_i), for each observation.
b''(θ_i) = \int (u  b'(θ_i))^2 f(ux_i) du
fTilt
is a vector containing the semiparametric fitted probability,
\hat{f}(y_i  x_i), for each observation. The semiparametric
loglikelihood is equal to
∑_{i=1}^n \log \hat{f}(y_i  x_i).
sampprobs
If sampling probabilities were passed through the
sampprobs
argument, then they are returned here in matrix form.
Each row corresponds to an observation.
llikNull
Loglikelihood of the null model with no covariates.
lr.stat
Likelihood ratio test statistic comparing fitted model to
the null model. It is calculated as 2 \times (llik  llik_0) / (p1).
The asymptotic distribution is F(p1, np) under the null hypothesis.
lr.pval
Pvalue of the likelihood ratio statistic.
fTiltMatrix
is a matrix containing the semiparametric density for
each observation, i.e. \hat{f}(y  x_i) for each unique y
value.
This is a matrix with nrow equal to the number of observations and ncol equal
to the number of unique response values observed.
Only returned if returnfTilt = TRUE
in the gldrmControl arguments.
score.logf0
Score function for log(f0)
.
Only returned if returnf0ScoreInfo = TRUE
in the gldrmControl arguments.
info.logf0
Information matrix for log(f0)
.
Only returned if returnf0ScoreInfo = TRUE
in the gldrmControl arguments.
formula
Model formula.
data
Model data frame.
link
Link function. If a character string was passed to the
link
argument, then this will be an object of class "linkglm".
Otherwise, it will be the list of three functions passed to the link
argument.
An S3 object of class "gldrm". See details.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  data(iris, package="datasets")
# Fit a gldrm with log link
fit < gldrm(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width + Species,
data=iris, link="log")
fit
# Fit a gldrm with custom link function
link < list()
link$linkfun < function(mu) log(mu)^3
link$linkinv < function(eta) exp(eta^(1/3))
link$mu.eta < function(eta) exp(eta^(1/3)) * 1/3 * eta^(2/3)
fit2 < gldrm(Sepal.Length ~ Sepal.Width + Petal.Length + Petal.Width + Species,
data=iris, link=link)
fit2

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