expo.brglmFit {brglm2}  R Documentation 
Estimate the exponential of parameters of generalized linear models using various methods
Description
The expo()
method uses the supplied "brglmFit"
or
"glm"
object to estimate the exponential of parameters of
generalized linear models with maximum likelihood or various mean
and median bias reduction methods. expo()
is useful for computing
(corrected) estimates of the multiplicative impact of a unit
increase on a covariate on the mean of a Poisson loglinear model
(family = poisson("log")
in glm()
) while adjusting for other
covariates, the odds ratio associated with a unit increase on a
covariate in a logistic regression model (family = binomial("logit")
in glm()
) while adjusting for other
covariates, the relative risk associated with a unit increase on a
covariate in a relative risk regression model (family = binomial("log")
in glm()
) while adjusting for other covariates,
among others.
Usage
## S3 method for class 'brglmFit'
expo(
object,
type = c("correction*", "correction+", "Lylesetal2012", "AS_median", "ML"),
level = 0.95
)
## S3 method for class 'glm'
expo(
object,
type = c("correction*", "correction+", "Lylesetal2012", "AS_median", "ML"),
level = 0.95
)
Arguments
object 
an object of class 
type 
the type of correction to be used. The available
options are 
level 
the confidence level required. Default is 
Details
The supported methods through the type
argument are:

"ML"
: the estimates of the exponentiated parameters are\exp(\hat\theta_j)
, where\theta_j
is the maximum likelihood estimates for thej
th regression parameter. 
"correction*"
: the estimates of the exponentiated parameters are\exp(\hat\theta_j) / (1 + \hat{v}_j / 2)
, where\hat\theta_j
is the estimate of thej
th regression parameter usingtype = "AS_mixed"
inbrglmFit()
. 
"correction+"
: the estimates of the exponentiated parameters are\exp(\hat\theta_j) (1  \hat{v}_j / 2)
, where\hat\theta_j
is the estimate of thej
th regression parameter usingtype = "AS_mixed"
inbrglmFit()
. 
"Lylesetal2012"
: the estimates of the exponentiated parameters are\exp(\hat\theta_j) exp( \hat{v}_j / 2)
, where\hat\theta_j
is the estimate of thej
th regression parameter usingtype = "AS_mixed"
inbrglmFit()
. This estimator has been proposed in Lyles et al. (2012). 
"AS_median"
: the estimates of the exponentiated parameters are\exp(\hat\theta_j)
, where\hat\theta_j
is the estimate of thej
th regression parameter usingtype = "AS_median"
inbrglmFit()
.
"correction*"
and "correction+"
are based on multiplicative and
additive adjustments, respectively, of the exponential of a
reducedbias estimator (like the ones coming from brglmFit()
with
type = "AS_mixed"
, type = "AS_mean"
, and type = "correction"
). The form of those adjustments results from the
expression of the firstterm in the mean bias expansion of the
exponential of a reducedbias estimator. See, for example, Di
Caterina & Kosmidis (2019, expression 12) for the general form of
the firstterm of the mean bias of a smooth transformation of a
reducedbias estimator.
The estimators from "correction+"
, "correction*"
,
"Lylesetal2012"
have asymptotic mean bias of order smaller than
than of the maximum likelihood estimator. The estimators from
"AS_median"
are asymptotically closed to being median unbiased
than the maximum likelihood estimator is.
Estimated standard errors are computed using the delta method, where both the Jacobin and the information matrix are evaluated at the logarithm of the estimates of the exponentiated parameters.
Confidence intervals results by taking the exponential of the limits of standard Waldtype intervals computed at the logarithm of the estimates of the exponentiated parameters.
Value
a list inheriting from class "brglmFit_expo"
with
components coef
(the estimates of the exponentiated
regression parameters), se
(the corresponding estimated
standard errors for the exponentiated parameters), ci
(confidence intervals of level level
for the exponentiated
parameters), and type
for the type
of correction that has
been requested.
Author(s)
Ioannis Kosmidis [aut, cre]
ioannis.kosmidis@warwick.ac.uk
References
Di Caterina C, Kosmidis I (2019). LocationAdjusted Wald Statistics for Scalar Parameters. Computational Statistics & Data Analysis, 138, 126142. doi:10.1016/j.csda.2019.04.004.
Kosmidis I, Kenne Pagui E C, Sartori N (2020). Mean and median bias reduction in generalized linear models. Statistics and Computing, 30, 4359. doi:10.1007/s11222019098606.
Cordeiro G M, McCullagh P (1991). Bias correction in generalized linear models. Journal of the Royal Statistical Society. Series B (Methodological), 53, 629643. doi:10.1111/j.25176161.1991.tb01852.x.
Lyles R H, Guo Y, Greenland S (2012). Reducing bias and mean squared error associated with regressionbased odds ratio estimators. Journal of Statistical Planning and Inference, 142 3235–3241. doi:10.1016/j.jspi.2012.05.005.
See Also
brglm_fit()
and and brglm_control()
Examples
## The lizards example from ?brglm::brglm
lizardsML < glm(cbind(grahami, opalinus) ~ height + diameter +
light + time, family = binomial(logit), data = lizards,
method = "glm.fit")
# Get estimates, standard errors, and confidence intervals of odds
# ratios with various methods
expo(lizardsML, type = "ML")
expo(lizardsML, type = "correction*")
expo(lizardsML, type = "Lylesetal2012")
expo(lizardsML, type = "correction+")
expo(lizardsML, type = "AS_median")
## Example from ?glm
## Dobson (1990) Page 93: Randomized Controlled Trial :
counts < c(18,17,15,20,10,20,25,13,12)
outcome < gl(3,1,9)
treatment < gl(3,3)
glm.D93 < glm(counts ~ outcome + treatment, family = poisson())
expo(glm.D93, type = "correction*")