logistic {VGAM} | R Documentation |
Logistic Distribution Family Function
Description
Estimates the location and scale parameters of the logistic distribution by maximum likelihood estimation.
Usage
logistic1(llocation = "identitylink", scale.arg = 1, imethod = 1)
logistic(llocation = "identitylink", lscale = "loglink",
ilocation = NULL, iscale = NULL, imethod = 1, zero = "scale")
Arguments
llocation , lscale |
Parameter link functions applied to the location parameter |
scale.arg |
Known positive scale parameter (called |
ilocation , iscale |
See |
imethod , zero |
See |
Details
The two-parameter logistic distribution has a density that can be written as
f(y;l,s) = \frac{\exp[-(y-l)/s]}{
s\left( 1 + \exp[-(y-l)/s] \right)^2}
where s > 0
is the scale parameter, and l
is the location
parameter. The response -\infty<y<\infty
. The mean
of Y
(which is the fitted value) is l
and its variance is
\pi^2 s^2 / 3
.
A logistic distribution with scale = 0.65
(see dlogis
)
resembles
dt
with df = 7
;
see logistic1
and studentt
.
logistic1
estimates the location parameter only while
logistic
estimates both parameters.
By default,
\eta_1 = l
and \eta_2 = \log(s)
for logistic
.
logistic
can handle multiple responses.
Value
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions
such as vglm
,
rrvglm
and vgam
.
Note
Fisher scoring is used, and the Fisher information matrix is diagonal.
Author(s)
T. W. Yee
References
Johnson, N. L. and Kotz, S. and Balakrishnan, N. (1994). Continuous Univariate Distributions, 2nd edition, Volume 1, New York: Wiley. Chapter 15.
Forbes, C., Evans, M., Hastings, N. and Peacock, B. (2011). Statistical Distributions, Hoboken, NJ, USA: John Wiley and Sons, Fourth edition.
Castillo, E., Hadi, A. S., Balakrishnan, N. and Sarabia, J. S. (2005). Extreme Value and Related Models with Applications in Engineering and Science, Hoboken, NJ, USA: Wiley-Interscience, p.130.
deCani, J. S. and Stine, R. A. (1986). A Note on Deriving the Information Matrix for a Logistic Distribution, The American Statistician, 40, 220–222.
See Also
rlogis
,
CommonVGAMffArguments
,
logitlink
,
gensh
,
cumulative
,
bilogistic
,
simulate.vlm
.
Examples
# Location unknown, scale known
ldata <- data.frame(x2 = runif(nn <- 500))
ldata <- transform(ldata, y1 = rlogis(nn, loc = 1+5*x2, sc = exp(2)))
fit1 <- vglm(y1 ~ x2, logistic1(scale = exp(2)), ldata, trace = TRUE)
coef(fit1, matrix = TRUE)
# Both location and scale unknown
ldata <- transform(ldata, y2 = rlogis(nn, loc = 1 + 5*x2, exp(x2)))
fit2 <- vglm(cbind(y1, y2) ~ x2, logistic, data = ldata, trace = TRUE)
coef(fit2, matrix = TRUE)
vcov(fit2)
summary(fit2)