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, imethod = 1) logistic2(llocation = "identity", lscale = "loge", elocation = list(), escale = list(), ilocation = NULL, iscale = NULL, imethod = 1, zero = NULL)
llocation, lscale |
Parameter link functions applied to the location parameter l
and scale parameter s.
See |
elocation, escale |
List. Extra argument for each of the links.
See |
scale.arg |
Known positive scale parameter (called s below). |
ilocation, iscale |
See |
imethod, zero |
See |
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.
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
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.
rlogis
,
logit
,
cumulative
,
bilogistic4
.
# location unknown, scale known ldat1 = data.frame(x = runif(nn <- 500)) ldat1 = transform(ldat1, y = rlogis(nn, loc = 1+5*x, scale = 4)) fit = vglm(y ~ x, logistic1(scale = 4), ldat1, trace = TRUE, crit = "c") coef(fit, matrix = TRUE) # Both location and scale unknown ldat2 = data.frame(x = runif(nn <- 2000)) ldat2 = transform(ldat2, y = rlogis(nn, loc = 1+5*x, scale = exp(0+1*x))) fit = vglm(y ~ x, logistic2, ldat2) coef(fit, matrix = TRUE) vcov(fit) summary(fit)