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="identity", elocation=list(),
          scale.arg=1, method.init=1)
logistic2(llocation="identity", lscale="loge",
          elocation=list(), escale=list(),
          ilocation=NULL, iscale=NULL, method.init=1, zero=NULL)

Arguments

llocation Link function applied to the location parameter l. See Links for more choices.
elocation, escale List. Extra argument for each of the links. See earg in Links for general information.
scale.arg Known positive scale parameter (called s below).
lscale Parameter link function applied to the scale parameter s. See Links for more choices.
ilocation Initial value for the location l parameter. By default, an initial value is chosen internally using method.init. Assigning a value will override the argument method.init.
iscale Initial value for the scale s parameter. By default, an initial value is chosen internally using method.init. Assigning a value will override the argument method.init.
method.init An integer with value 1 or 2 which specifies the initialization method. If failure to converge occurs try the other value.
zero An integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. The default is none of them. If used, choose one value from the set {1,2}.

Details

The two-parameter logistic distribution has a density that can be written as

f(y;l,s) = exp[-(y-l)/s] / [s * ( 1 + exp[-(y-l)/s] )^2]

where s>0 is the scale parameter, and l is the location parameter. The response -Inf<y<Inf. The mean of Y (which is the fitted value) is l and its variance is pi^2 s^2 / 3.

logistic1 estimates the location parameter only while logistic2 estimates both parameters. By default, eta1=l and eta2=log(s) for logistic2.

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.

Evans, M., Hastings, N. and Peacock, B. (2000) Statistical Distributions, New York: Wiley-Interscience, Third edition.

Castillo, E., Hadi, A. S., Balakrishnan, N. Sarabia, J. S. (2005) Extreme Value and Related Models with Applications in Engineering and Science, Hoboken, N.J.: 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, bilogistic4.

Examples

# location unknown, scale known
n = 500
x = runif(n)
y = rlogis(n, loc=1+5*x, scale=4)
fit = vglm(y ~ x, logistic1(scale=4), trace=TRUE, crit="c")
coef(fit, matrix=TRUE)

# Both location and scale unknown
n = 2000
x = runif(n)
y = rlogis(n, loc=1+5*x, scale=exp(0+1*x))
fit = vglm(y ~ x, logistic2)
coef(fit, matrix=TRUE)
vcov(fit)
summary(fit)

[Package VGAM version 0.7-7 Index]