summary.cusp {cusp}R Documentation

Summarizing Cusp Catastrophe Model Fits

Description

summary method for class “cusp”

Usage

## S3 method for class 'cusp':
summary(object, correlation = FALSE, symbolic.cor = FALSE, logist = FALSE, ...)

## S3 method for class 'summary.cusp':
print(x, digits = max(3, getOption("digits") - 3), symbolic.cor = x$symbolic.cor, 
    signif.stars = getOption("show.signif.stars"), ...)

Arguments

object Object returned by cusp
x summary.cusp’ object
correlation logical; if TRUE the correlation matrix is returned
symbolic.cor logical; currently unused
logist logical. If TRUE a logistic model is fitted for cusp model assesment (see cusp.logist for details).
digits numeric; the number of significant digits to use when printing.
signif.stars logical. If TRUE, significance stars are printed for each coefficient.
... further arguments passed to or from other methods.

Details

print.summary.cusp tries to be smart about formatting the coefficients, standard errors, etc. and additionally gives significance stars if signif.stars is TRUE.

Correlations are printed to two decimal places (or symbolically): to see the actual correlations print summary(object)$correlation directly.

Value

The function summary.cusp computes and returns a list of summary statistics of the fitted linear model given in object, using the components (list elements) “call” and “terms” from its argument, plus

call the matched call
terms the terms object used.
deviance sum of squared residuals of cusp model fit
aic Akaike Information Criterion for cusp model fit
contrasts contrasts used
df.residual degrees of freedom for the residuals of the cusp model fit
null.deviance variance of canonical state variable
df.null degrees of freedom of constant model for state variable
iter number of optimization iterations
deviance.resid residuals computed by residuals.glm using type="deviance"
coefficients a p times 4 matrix with columns for the estimated coefficient, its standard error, t-statistic and corresponding (two-sided) p-value. Aliased coefficients are omitted.
aliased named logical vector showing if the original coefficients are aliased.
dispersion always 1
df 3-vector containing the rank of the model matrix, residual degrees of freedom, and model degrees of freedom.
resid.name string specifying the convention used in determining the residuals (i.e., "Delay" or "Maxwell").
cov.unscaled the unscaled (dispersion = 1) estimated covariance matrix of the estimated coefficients.
r2lin.r.squared R^2, the ‘fraction of variance explained’ by the linear regression model

w[0]+w[1]*Y[i,1] + ... + w[p]*Y[i,p] = β[0]+β[1]*X[i,1] + ... + β[q]*X[i,q] + ε[i],

where Y containes all explanatory variables for the behavioral states in the cusp model, and X containes all explanatory variables for the control parameters of the cusp model. This is computed from the largest canonical correlation.

r2lin.dev residual sums of squares of the linear model
r2lin.df degrees of freedom for the linear model
r2lin.logLik value of the log-likelihood for the linear model assuming normal errors
r2lin.npar number of parameters in the linear model
r2lin.aic AIC for the linear model
r2lin.aicc corrected AIC for the linear model
r2lin.bic BIC for the linear model
r2log.r.squared R^2, the ‘fraction of variance explained’ by the logistic model. See cusp.logist for details.
r2log.dev if logist = TRUE residual sums of square for the logistic model
r2log.df ditto, degrees of freedom for the logistic model
r2log.logLik ditto, value of log-likelihood function for the logistic model assuming normal errors.
r2log.npar ditto, number of parameters for the logistic model
r2log.aic ditto, AIC for logistic model
r2log.aicc ditto, corrected AIC for logistic model
r2log.bic ditto, BIC for logistic model
r2cusp.r.squared pseudo-R^2, the ‘fraction of variance explained by the cusp model’,

R^2 = 1 - Var(residuals[i])/Var(y[i]).

This value can be negative.

r2cusp.dev residual sums of squares for cusp model
r2cusp.df residual degrees of freedom for cusp model
r2cusp.logLik value of the log-likelihood function for the cusp model
r2cusp.npar number of parameters in the cusp model
r2cusp.aic AIC for cusp model fit
r2cusp.aicc corrected AIC for cusp model fit
r2cusp.bic BIC for cusp model fit.

Author(s)

Raoul Grasman

References

Cobb L, Zacks S (1985). Applications of Catastrophe Theory for Statistical Modeling in the Biosciences. Journal of the American Statistical Association, 80(392), 793–802.

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

Cobb L (1998). An Introduction to Cusp Surface Analysis.
http://www.aetheling.com/models/cusp/Intro.htm.

See Also

cusp, cusp.logist

Examples

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, logist=TRUE)

[Package cusp version 2.2 Index]