summary method for class “cusp”
# S3 method for cusp
summary(object, correlation = FALSE, symbolic.cor = FALSE, logist = FALSE, ...)# S3 method for summary.cusp
print(x, digits = max(3, getOption("digits") - 3), symbolic.cor = x$symbolic.cor,
signif.stars = getOption("show.signif.stars"), ...)
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
the matched call
the terms object used.
sum of squared residuals of cusp model fit
Akaike Information Criterion for cusp model fit
contrasts used
degrees of freedom for the residuals of the cusp model fit
variance of canonical state variable
degrees of freedom of constant model for state variable
number of optimization iterations
residuals computed by residuals.glm using type="deviance"
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.
named logical vector showing if the original coefficients are aliased.
always 1
3-vector containing the rank of the model matrix, residual degrees of freedom, and model degrees of freedom.
string specifying the convention used in determining the residuals (i.e., "Delay" or "Maxwell").
the unscaled (dispersion = 1) estimated covariance matrix of the estimated coefficients.
\(R^2\), 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 \(Y\) contains 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.
residual sums of squares of the linear model
degrees of freedom for the linear model
value of the log-likelihood for the linear model assuming normal errors
number of parameters in the linear model
AIC for the linear model
corrected AIC for the linear model
BIC for the linear model
\(R^2\), the ‘fraction of variance explained’ by the logistic model. See cusp.logist for details.
if logist = TRUE residual sums of square for the logistic model
ditto, degrees of freedom for the logistic model
ditto, value of log-likelihood function for the logistic model assuming normal errors.
ditto, number of parameters for the logistic model
ditto, AIC for logistic model
ditto, corrected AIC for logistic model
ditto, BIC for logistic model
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.
residual sums of squares for cusp model
residual degrees of freedom for cusp model
value of the log-likelihood function for the cusp model
number of parameters in the cusp model
AIC for cusp model fit
corrected AIC for cusp model fit
BIC for cusp model fit.
Object returned by cusp
‘summary.cusp’ object
logical; if TRUE the correlation matrix is returned
logical; currently unused
logical. If TRUE, a logistic model is fitted for cusp model assessment (see cusp.logist for details).
numeric; the number of significant digits to use when printing.
logical. If TRUE, significance stars are printed for each coefficient.
further arguments passed to or from other methods.
Raoul Grasman
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.
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, PhD thesis.
Cobb L (1998). An Introduction to Cusp Surface Analysis.
https://www.aetheling.com/models/cusp/Intro.htm.
cusp, cusp.logist
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
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