summary.cusp {cusp}

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_{i1} + \cdots + w_p Y_{ip} = \beta_0 + \beta_1 X_{i1} + \cdots + \beta_q X_{iq} + \epsilon_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 - \frac{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.
https://www.aetheling.com/models/cusp/Intro.htm.

See Also

cusp, cusp.logist

Examples

set.seed(97)
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=FALSE) # set logist to TRUE to compare to logistic fit