plinks {glmx} | R Documentation |
Parametric Links for Binomial Generalized Linear Models
Description
Various symmetric and asymmetric parametric links for use as link function for binomial generalized linear models.
Usage
gj(phi, verbose = FALSE)
foldexp(phi, verbose = FALSE)
ao1(phi, verbose = FALSE)
ao2(phi, verbose = FALSE)
talpha(alpha, verbose = FALSE, splineinv = TRUE,
eps = 2 * .Machine$double.eps, maxit = 100)
rocke(shape1, shape2, verbose = FALSE)
gosset(nu, verbose = FALSE)
pregibon(a, b)
nblogit(theta)
angular(verbose = FALSE)
loglog()
Arguments
phi , a , b |
numeric. |
alpha |
numeric. Parameter in |
shape1 , shape2 , nu , theta |
numeric. Non-negative parameter. |
splineinv |
logical. Should a (quick and dirty) spline function be used for computing the inverse link function? Alternatively, a more precise but somewhat slower Newton algorithm is used. |
eps |
numeric. Desired convergence tolerance for Newton algorithm. |
maxit |
integer. Maximal number of steps for Newton algorithm. |
verbose |
logical. Should warnings about numerical issues be printed? |
Details
Symmetric and asymmetric families parametric link functions are available. Many families contain the logit for some value(s) of their parameter(s).
The symmetric Aranda-Ordaz (1981) transformation
and the asymmetric Aranda-Ordaz (1981) transformation
both contain the logit for and
respectively, where the latter also includes the
complementary log-log for
.
The Pregibon (1980) two parameter family is the link given by
For it is the logit. For
it is symmetric and
controls the skewness; the heavyness of the tails is controlled by
. The implementation uses the generalized lambda distribution
gl
.
The Guerrero-Johnson (1982) family
is symmetric and contains the logit for .
The Rocke (1993) family of links is, modulo a linear transformation, the
cumulative density function of the Beta distribution. If both parameters are
set to the logit link is obtained. If both parameters equal
the Rocke link is, modulo a linear transformation, identical to the
angular transformation. Also for
shape1
= shape2
, the
identity link is obtained. Note that the family can be used as a one and a two
parameter family.
The folded exponential family (Piepho, 2003) is symmetric and given by
The family (Doebler, Holling & Boehning, 2011) given by
is asymmetric and contains the logit for .
The Gosset family of links is given by the inverse of the cumulative
distribution function of the t-distribution. The degrees of freedom
control the heavyness of the tails and is restricted to values
. For
the Cauchy link is obtained and for
the link
converges to the probit. The implementation builds on
qf
and is
reliable for . Liu (2004) reports that the Gosset link
approximates the logit well for
.
Also the (parameterless) angular (arcsine) transformation
is available as a link
function.
Value
An object of the class link-glm
, see the documentation of make.link
.
References
Aranda-Ordaz F (1981). “On Two Families of Transformations to Additivity for Binary Response Data.” Biometrika, 68, 357–363.
Doebler P, Holling H, Boehning D (2012). “A Mixed Model Approach to Meta-Analysis of Diagnostic Studies with Binary Test Outcome.” Psychological Methods, 17(3), 418–436.
Guerrero V, Johnson R (1982). “Use of the Box-Cox Transformation with Binary Response Models.” Biometrika, 69, 309–314.
Koenker R (2006). “Parametric Links for Binary Response.” R News, 6(4), 32–34.
Koenker R, Yoon J (2009). “Parametric Links for Binary Choice Models: A Fisherian-Bayesian Colloquy.” Journal of Econometrics, 152, 120–130.
Liu C (2004). “Robit Regression: A Simple Robust Alternative to Logistic and Probit Regression.” In Gelman A, Meng X-L (Eds.), Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives, Chapter 21, pp. 227–238. John Wiley & Sons.
Piepho H (2003). The Folded Exponential Transformation for Proportions. Journal of the Royal Statistical Society D, 52, 575–589.
Pregibon D (1980). “Goodness of Link Tests for Generalized Linear Models.” Journal of the Royal Statistical Society C, 29, 15–23.
Rocke DM (1993). “On the Beta Transformation Family.” Technometrics, 35, 73–81.