summary.segmented: Summarizing model fits for segmented regression

In segmented: Regression Models with Break-Points / Change-Points Estimation (with Possibly Random Effects)

Summarizing model fits for segmented regression

Description

summary method for class segmented.

Usage

## S3 method for class 'segmented'
summary(object, short = FALSE, var.diff = FALSE, p.df="p", .vcov=NULL, ...)

## S3 method for class 'summary.segmented'
print(x, short=x$short, var.diff=x$var.diff, 
    digits = max(3, getOption("digits") - 3),
    signif.stars = getOption("show.signif.stars"),...)

Arguments

object	Object of class "segmented".
short	logical indicating if the ‘short’ summary should be printed.
var.diff	logical indicating if different error variances should be computed in each interval of the segmented variable, see Details. If .vcov is provided, var.diff is set to FALSE.
p.df	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.
.vcov	Optional. The full covariance matrix for the parameter estimates. If provided, standard errors are computed (and displayed) according to this matrix.
x	a summary.segmented object produced by summary.segmented().
digits	controls number of digits printed in output.
signif.stars	logical, should stars be printed on summary tables of coefficients?
...	further arguments.

Details

If short=TRUE only coefficients of the segmented relationships are printed. If var.diff=TRUE and there is only one segmented variable, different error variances are computed in the intervals defined by the estimated breakpoints of the segmented 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.

Value

A list (similar to one returned by segmented.lm or segmented.glm) with additional components:

psi	estimated break-points and relevant (approximate) standard errors
Ttable	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.
gap	estimated coefficients, standard errors and t-values for the ‘gap’ variables
cov.var.diff	if var.diff=TRUE, the covaraince matrix accounting for heteroscedastic errors.
sigma.new	if var.diff=TRUE, the square root of the estimated error variances in each interval.
df.new	if var.diff=TRUE, the residual degrees of freedom in each interval.

Author(s)

Vito M.R. Muggeo

See Also

print.segmented, davies.test

Examples

##continues example from segmented()
# summary(segmented.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<-segmented(o,seg.Z=~x,psi=.6)
# summary(oseg,var.diff=TRUE)$sigma.new

segmented documentation built on Nov. 28, 2023, 1:07 a.m.