cusp.logist {cusp}R Documentation

Fit a Logistic Surface Model to Data

Description

This function fits a logistic curve model to data using maximum likelihood under the assumption of normal errors (i.e., nonlinear least squares). Both the response variable may be modelled by a linear combination of variables and design factors, as well as the normal/asymmetry factor alpha and bifurction/splitting factor beta.

Usage

cusp.logist(formula, alpha, beta, data, ..., model = TRUE, x =
                 FALSE, y = TRUE)

Arguments

formula, alpha, beta formulas for the response variable and the regression variables (see below)
data data.frame containing n observations of all the variables named in the formulas
... named arguments that are passed to nlm
model, x, y logicals. If TRUE the corresponding components of the fit (the model frame, the model matrix, and the response are returned.

Details

A nonlinear regression is carried out of the model

y[i] = 1/(1+exp(-α[i]/β[i]^2)) + ε[i]

for i = 1, 2, ..., n, where

y[i] = w[0] + w[1] * Y[i,1] + cdots + w[p] * Y[i,p],

α[i] = a[0] + a[1] * X[i,1] + ... + a[p] * X[i,p],

β[i] = b[0] + b[1] * X[i,1] + ... + b[p] * X[i,p],

in which the a[j]'s, and b[j]'s, are estimated. The Y[i,j]'s are variables in the data set and specified by formula; the X[i,j]'s are variables in the data set and are specified in alpha and beta. Variables in alpha and beta need not be the same. The w[j]'s are estimated implicitely using concentrated likelihood methods, and are not returned explicitely.

Value

List with components

minimum Objective function value at minimum
estimate Coordinates of objective function minimum
gradient Gradient of objective function at minimum.
code Convergence code returned by optim
iterations Number of iterations used by optim
coefficients A named vector of estimates of a[j], b[j]'s
linear.predictors Estimates of α[i]'s and β[i]'s.
fitted.values Predicted values of y[i]'s as determined from the linear.predictors
residuals Residuals
rank Numerical rank of matrix of predictors for α[i]'s plus rank of matrix of predictors for β[i]'s plus rank of matrix of predictors for the y[i]'s.
deviance Residual sum of squares.
logLik Log of the likelihood at the minimum.
aic Akaike's information criterion
rsq R Squared (proportion of explained variance)
df.residual Degrees of freedom for the residual
df.null Degrees of freedom for the Null residual
rss Residual sum of squares
hessian Hessian matrix of objective function at the minimum if hessian=TRUE.
Hessian Hessian matrix of log-likelihood function at the minimum (currently unavailable)
qr QR decomposition of the hessian matrix
converged Boolean indicating if optimization convergence is proper (based on exit code optim, gradient, and, if hessian=TRUE eigen values of the hessian).
weights weights (currently unused)
call the matched call
y If requested (the default), the matrix of response variables used.
x If requested, the model matrix used.
null.deviance The sum of squared deviations from the mean of the estimated y[i]'s.

Author(s)

Raoul Grasman

References

Hartelman PAI (1997). Stochastic Catastrophe Theory. Amsterdam: University of Amsterdam, PhDthesis.

See Also

summary.cusp


[Package cusp version 2.2 Index]