R: Logistic Distribution Family Function

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 l and scale parameter s. See `Links` for more choices, and `CommonVGAMffArguments` for more information.
`scale.arg` | Known positive scale parameter (called s below).
`ilocation, iscale` | See `CommonVGAMffArguments` for information.
`imethod, zero` | See `CommonVGAMffArguments` for information.

### 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.

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, eta1 = l and eta2 = 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. 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`, `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, scale = exp(2)))
    fit1 <- vglm(y1 ~ x2, logistic1(scale = exp(2)), data = ldata, trace = TRUE)
    coef(fit1, matrix = TRUE)

    # Both location and scale unknown
    ldata <- transform(ldata, y2 = rlogis(nn, loc = 1 + 5*x2, scale = exp(0 + 1*x2)))
    fit2 <- vglm(cbind(y1, y2) ~ x2, logistic, data = ldata, trace = TRUE)
    coef(fit2, matrix = TRUE)
    vcov(fit2)
    summary(fit2)

[Package VGAM version 1.1-3 Index]