logistic {VGAM} | R Documentation |
Estimates the location and scale parameters of the logistic distribution by maximum likelihood estimation.
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)
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}.
|
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
.
An object of class "vglmff"
(see vglmff-class
).
The object is used by modelling functions such as vglm
,
rrvglm
and vgam
.
Fisher scoring is used, and the Fisher information matrix is diagonal.
T. W. Yee
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.
# 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)