cusp-package {cusp}

Cusp Catastrophe Modeling

Description

Fits cusp catastrophe to data using Cobb's maximum likelihood method with a different algorithm. The package contains utility functions for plotting, and for comparing the model to linear regression and logistic curve models. The package allows for multivariate response subspace modelling in the sense of the GEMCAT software of Oliva et al.

Details

Package:	cusp
Type:	Package
Version:	2.0
Date:	2008-02-14
License:	GNU GPL v2 (or higher)

This package helps fitting Cusp catastrophy models to data, as advanced in Cobb et al. (1985). The main functions are

cusp	Fit Cobb's Cusp catastrophe model; see example below.
summary.cusp	Summary statistics of cusp model fit.
confint.cusp	Confidence intervals for parameter estimates
plot.cusp	Diagnostic plots for cusp model fit
cusp3d	3D graphical display of cusp model fit (experimental).
dcusp	Density of Cobb's cusp distribtution
pcusp	Cumulative probability function of Cobb's cusp distribution
qcusp	Quantile function of Cobb's cusp distribution
rcusp	Sample from Cobb's cusp distribution.
cusp.logist	Fit logistic model for bifurctation testing (experimental)

Author(s)

Raoul Grasman <[e-mail]>

References

L. Cobb and S. Zacks (1985) Applications of Catastrophe Theory for Statistical Modeling in the Biosciences (article), Journal of the American Statistical Association, 392:793–802.

P. Hartelman (1996). Stochastic Catastrophy Theory. Unpublished PhD-thesis.

H. L. J. van der Maas, R. Kolstein, and J van der Pligt (2003). Sudden Transitions in Attitudes, Sociological Methods and Research, 32:125-152.

Oliva, DeSarbo, Day, and Jedidi. (1987) GEMCAT : A General Multivariate Methodology for Estimating Catastrophe Models, Behavioral Science, 32:121-137.

R. P. P. P. Grasman, H. L. J. van der Maas, and E-J. Wagenmakers (2009). Fitting the Cusp Catastrophe in R: A cusp Package Primer. Journal of Statistical Software 32(8), 1-28. URL https://www.jstatsoft.org/v32/i08/.

Examples

set.seed(123)
# fitting cusp to cusp data
x <- rcusp(100, alpha=0, beta=1)
fit <- cusp(y ~ x, alpha ~ 1, beta ~ 1)
print(fit)

# example with regressors
## Not run: 
x1 = runif(150)
x2 = runif(150)
z = Vectorize(rcusp)(1, 4*x1-2, 4*x2-1)
data <- data.frame(x1, x2, z)
fit <- cusp(y ~ z, alpha ~ x1+x2, beta ~ x1+x2, data)
print(fit)
summary(fit)
plot(fit)
cusp3d(fit)

## End(Not run)

# use of OK
npar <- length(fit$par)
## Not run: 
while(!fit$OK) # refit if necessary until convergence is OK
    fit <- cusp(y ~ z, alpha ~ x1+x2, beta ~ x1+x2, data, start=rnorm(npar))

## End(Not run)

## Not run: 
# example 1 from paper
data(attitudes)
data(attitudeStartingValues)
fit.attitudes <- cusp(y ~ Attitude, alpha ~ Orient + Involv, beta ~ Involv,
 data = attitudes, start=attitudeStartingValues)

summary(fit.attitudes)
plot(fit.attitudes)
cusp3d(fit.attitudes, B = 0.75, Y = 1.35, theta = 170, phi = 30, Yfloor = -9)

## End(Not run)