summary.stepmented {segmented}

Summarizing model fits for stepmented regression

Description

summary/print method for class stepmented.

Usage

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

## S3 method for class '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 class 'stepmented'
print(x, digits = max(3, getOption("digits") - 3), 
    ...) 

Arguments

object, x

Object of class "stepmented" or a summary.stepmented object produced by summary.stepmented().

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 stepmented 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.

digits

controls number of digits printed in output.

signif.stars

logical, should stars be printed on summary tables of coefficients?

...

further arguments, notably type to be passed to vcov.stepmented to compute the standard errors. See vcov.stepmented.

Details

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.

Value

A list (similar to one returned by stepmented.lm or stepmented.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.

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.

Warning

If type is not specified in ... (which means type="standard"), no standard error will be computed (and returned) for the jumpoint.

Author(s)

Vito M.R. Muggeo

See Also

pscore.test

Examples

##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