# Fitting segmented/stepmented regression `segreg` (`stepreg`) fits (generalized) linear segmented (stepmented) regression via a symbolic description of the linear predictor. This is an alternative but equivalent function, introduced since version 2.0-0 (segreg) and 2.1-0 (stepreg), to `segmented.(g)lm` or `stepmented.(g)lm`. ```r segreg(formula, data, subset, weights, na.action, family = lm, control = seg.control(), transf = NULL, contrasts = NULL, model = TRUE, x = FALSE, var.psi = TRUE, ...) stepreg(formula, data, subset, weights, na.action, family = lm, control = seg.control(), transf = NULL, contrasts = NULL, model = TRUE, x = FALSE, var.psi = FALSE, ...) ``` ## Arguments - `formula`: A standard model formula also including one or more 'segmented'/'stepmented' terms via the function `seg` - `data`: The possible dataframe where the variables are stored - `subset`: Possible subset, as in `lm` or `glm` - `weights`: Possible weight vector, see `weights` in `lm` or `glm` - `na.action`: a function which indicates what happen when the data contain NA values. See `na.action` in `lm` or `glm`. - `family`: The family specification, similar to `family` in `glm`. Default to `'lm'` for segmented/stepmented linear models. - `control`: See `seg.control` - `transf`: an optional character string (with "y" as argument) meaning a function to apply to the response variable before fitting - `contrasts`: see `contrasts` in `glm` - `model`: If `TRUE`, the model frame is returned. - `x`: If `TRUE`, the model matrix is returned. - `var.psi`: logical, meaning if the standard errors for the breakpoint estimates should be returned in the object fit. If `FALSE`, the standard errors will be computed by `vcov.segmented` or `summary.segmented`. Setting `var.psi=FALSE` could speed up model estimation for very large datasets. Default to `TRUE` for `segreg` and `FALSE` for `stepreg`. - ``...``: Ignored ## Details The function allows to fit segmented/stepmented (G)LM regression models using a formula interface. Results will be the same of those coming from the traditional `segmented.lm` and `segmented.glm` (or `stepmented.lm` or `stepmented.glm`), but there are some additional facilities: i) it is possible to estimate strightforwardly the segmented/stepmented relationships in each level of a categorical variable, see argument `by` in `seg`; ii) it is possible to constrain some slopes of the segmented relationship, see argument `est` or `R` in `seg`. ## Returns An object of class "segmented" (or "stepmented") which inherits from the class "lm" or "glm" depending on `family` specification. See `segmented.lm`. ## References Muggeo, V.M.R. (2003) Estimating regression models with unknown break-points. Statistics in Medicine 22, 3055-3071. ## Author(s) Vito Muggeo ## Note When the formula includes even a single segmented term with constraints (specified via the argument `est` in `seg()`), the relevant coefficients returned do not represent the slope differences as in `segmented.lm` or `segmented.glm`. The values depend on the constraints and are not usually interpretable. Use `slope` the recover the actual slopes of the segmented relationships. ## Warning Currently for fits returned by `segreg`, `confint.segmented` only works if `method="delta"`. Constraints on the mean levels (possibly via argument 'est' of `seg`) are not yet allowed when calling `stepreg`. ## See Also `seg`, `segmented`, `stepmented` ## Examples ```r ########################### #An example using segreg() ########################### set.seed(10) x<-1:100 z<-runif(100) w<-runif(100,-10,-5) y<-2+1.5*pmax(x-35,0)-1.5*pmax(x-70,0)+10*pmax(z-.5,0)+rnorm(100,0,2) ##the traditional approach out.lm<-lm(y~x+z+w) o<-segmented(out.lm, seg.Z=~x+z, psi=list(x=c(30,60),z=.4)) o1<-segreg(y ~ w+seg(x,npsi=2)+seg(z)) all.equal(fitted(o), fitted(o1)) #put some constraints on the slopes o2<-segreg(y ~ w+seg(x,npsi=2, est=c(0,1,0))+seg(z)) o3<-segreg(y ~ w+seg(x,npsi=2, est=c(0,1,0))+seg(z, est=c(0,1))) slope(o2) slope(o3) ##see ?plant for an additional example ########################### #An example using stepreg() ########################### ### Two stepmented covariates (with 1 and 2 breakpoints) n=100 x<-1:n/n z<-runif(n,2,5) w<-rnorm(n) mu<- 2+ 1*(x>.6)-2*(z>3)+3*(z>4) y<- mu + rnorm(n)*.8 os <-stepreg(y~seg(x)+seg(z,2)+w) #also includes 'w' as a possible linear term os summary(os) plot(os, "z", col=2:4) #plot the effect of z ```

segreg function