summary/print method for class stepmented.
# S3 method for stepmented
summary(object, short = FALSE, var.diff = FALSE, p.df="p", .vcov=NULL, ...)# S3 method for summary.stepmented
print(x, short=x$short, var.diff=x$var.diff,
digits = max(3, getOption("digits") - 3),
signif.stars = getOption("show.signif.stars"),...)
# S3 method for stepmented
print(x, digits = max(3, getOption("digits") - 3),
...)
A list (similar to one returned by stepmented.lm or stepmented.glm) with additional components:
estimated break-points and relevant (approximate) standard errors
estimates and standard errors of the model parameters. This is similar
to the matrix coefficients returned by summary.lm or summary.glm,
but without the rows corresponding to the breakpoints. Even the p-values relevant to the
difference-in-slope parameters have been replaced by NA, since they are meaningless in
this case, see davies.test.
if var.diff=TRUE, the covaraince matrix accounting for heteroscedastic errors.
if var.diff=TRUE, the square root of the estimated error variances in each interval.
if var.diff=TRUE, the residual degrees of freedom in each interval.
Object of class "stepmented" or a summary.stepmented object produced by summary.stepmented().
logical indicating if the `short' summary should be printed.
logical indicating if different error variances should be computed
in each interval of the stepmented variable, see Details. If .vcov is provided, var.diff is set to FALSE.
A character as a function of 'p' (number of parameters) and 'K' (number of groups or segments) affecting computations of the group-specific variance (and the standard errors) if var.diff=TRUE, see Details.
Optional. The full covariance matrix for the parameter estimates. If provided, standard errors are computed (and displayed) according to this matrix.
controls number of digits printed in output.
logical, should stars be printed on summary tables of coefficients?
further arguments.
Vito M.R. Muggeo
If short=TRUE only coefficients of the stepmented relationships are printed.
If var.diff=TRUE and there is only one stepmented variable, different error variances are
computed in the intervals defined by the estimated breakpoints of the stepmented variable.
For the jth interval with \(n_j\) observations, the error variance is estimated via \(RSS_j/(n_j-p)\),
where \(RSS_j\) is the residual sum of squares in interval j, and \(p\) is the number of model parameters. This number to be subtracted from \(n_j\) can be changed via argument p.df. For instance p.df="0" uses \(RSS_j/(n_j)\), and p.df="p/K" leads to \(RSS_j/(n_j-p/K)\), where \(K\) is the number of groups (segments), and \(p/K\) can be interpreted as the average number of model parameter in that group.
Note var.diff=TRUE only affects the estimates covariance matrix. It does not affect the parameter estimates, neither the log likelihood and relevant measures, such as AIC or BIC. In other words, var.diff=TRUE just provides 'alternative' standard errors, probably appropriate when the error variances are different before/after the estimated breakpoints. Also \(p-values\) are computed using the t-distribution with 'naive' degrees of freedom (as reported in object$df.residual).
If var.diff=TRUE the variance-covariance matrix of the estimates is computed via the
sandwich formula,
$$(X^TX)^{-1}X^TVX(X^TX)^{-1}$$
where V is the diagonal matrix including the different group-specific error variance estimates. Standard errors are the square root of the main diagonal of this matrix.
pscore.test
##continues example from stepmented()
# summary(stepmented.model,short=TRUE)
## an heteroscedastic example..
# set.seed(123)
# n<-100
# x<-1:n/n
# y<- -x+1.5*pmax(x-.5,0)+rnorm(n,0,1)*ifelse(x<=.5,.4,.1)
# o<-lm(y~x)
# oseg<-stepmented(o,seg.Z=~x,psi=.6)
# summary(oseg,var.diff=TRUE)$sigma.new
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