The reference manual for the R strucchange package states:
As the maximum of a sequence of F statistics is equivalent to the minimum OLS estimator of the breakpoint in a 2-segment partition it can be extracted by breakpoints from an object of class "Fstats" as computed by Fstats.
Is the breakpoint extracted by the above approach always the same as the breakpoint extracted by applying coeftest to an object of class "breakpointsfull" when the "breaks" option is 1? In other words, is the breakpoint extracted by calling breakpoints on an Fstats object (minimum RSS) always equal to the breakpoint extracted by calling coeftest on a breakpointsfull object (minimum BIC) when breaks = 1?
library(lmtest)
library(strucchange)
data("Nile")
fs.nile <- Fstats(Nile ~ 1)
breakpoints(fs.nile)
bp.nile <- breakpoints(Nile ~ 1)
coeftest(bp.nile, breaks = 1)
Essentially yes. The breakpoint associated with the supF statistic (supWald or supLR) and the minimum RSS breakpoint in the linear regression model are identical.
Of course, the trimming/minimal segment size needs to be the same. The default is 15% in both breakpoints() (argument h) and Fstats() (arguments from and to). Also, no alternative covariance matrix estimator (vcov) must be used in Fstats().
However, breakpoints(Fstats(formula, ...)) just extracts a simple object of class "breakpoints" while breakpoints(formula, ...) sets up the whole "breakpointsfull" object from which confidence intervals, coefficient tests, information criteria etc. can be computed.