summary.cusp: Summarizing Cusp Catastrophe Model Fits

In cusp: Cusp-Catastrophe Model Fitting Using Maximum Likelihood

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

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

Example output

Call:  cusp(formula = y ~ z, alpha = alpha ~ x1 + x2, beta = beta ~      x1 + x2, data = data) 

Coefficients:
a[(Intercept)]           a[x1]           a[x2]  b[(Intercept)]           b[x1]  
      -2.06830         4.83825        -0.56044        -0.96232        -0.06032  
         b[x2]  w[(Intercept)]            w[z]  
       4.22968         0.08523         1.01154  

Degrees of Freedom: 149 Total (i.e. Null);  142 Residual
Null Deviance:	    253.7 
Delay Deviance:	 61.88 	AIC: 220.3 

Call:
cusp(formula = y ~ z, alpha = alpha ~ x1 + x2, beta = beta ~ 
    x1 + x2, data = data)

Deviance Residuals: 
     Min        1Q    Median        3Q       Max  
-2.03913  -0.28009   0.02592   0.34077   2.03444  

Coefficients:
               Estimate Std. Error z value Pr(>|z|)    
a[(Intercept)] -2.06830    0.40201  -5.145 2.68e-07 ***
a[x1]           4.83825    0.74779   6.470 9.79e-11 ***
a[x2]          -0.56044    0.38678  -1.449    0.147    
b[(Intercept)] -0.96232    0.62051  -1.551    0.121    
b[x1]          -0.06032    0.91266  -0.066    0.947    
b[x2]           4.22968    0.55419   7.632 2.31e-14 ***
w[(Intercept)]  0.08523    0.08253   1.033    0.302    
w[z]            1.01154    0.04372  23.137  < 2e-16 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


  Null deviance: 253.689  on 149  degrees of freedom
Linear deviance: 108.825  on 146  degrees of freedom
Logist deviance:      NA  on  NA  degrees of freedom
 Delay deviance:  61.879  on 142  degrees of freedom

             R.Squared    logLik npar     AIC     AICc      BIC
Linear model 0.5610693 -188.7735    4 385.547 385.8229 397.5896
Cusp model   0.7580366 -102.1295    8 220.259 221.2803 244.3441
---
Note: R.Squared for cusp model is Cobb's pseudo-R^2. This value
      can become negative.

	Chi-square test of linear vs. cusp model

X-squared = 173.3, df = 4, p-value = 0

Number of optimization iterations: 47

cusp documentation built on May 2, 2019, 6:51 p.m.