Description Usage Arguments Details Value Author(s) References See Also Examples
summary
method for class “cusp”
1 2 3 4 5 6 |
object |
Object returned by |
x |
‘ |
correlation |
logical; if |
symbolic.cor |
logical; currently unused |
logist |
logical. If |
digits |
numeric; the number of significant digits to use when printing. |
signif.stars |
logical. If |
... |
further arguments passed to or from other methods. |
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.
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 |
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 |
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 |
r2log.dev |
if |
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. |
Raoul Grasman
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.
1 2 3 4 5 6 7 8 |
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
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