# S-Curve Fit Finds change(s) in mean. ```r fitS(dataIn,xColIndex=NULL,yColIndex=NULL,slopeIn=NULL,depth=1, family_wise_error_rate=0.05,autoTraverse=TRUE,plotTitle = '') ``` ## Arguments - `dataIn`: Data frame or equivalent. - `xColIndex`: Column number of "x" (typically time). - `yColIndex`: Column number of "y". - `slopeIn`: A fixed slope value for the model. Should be set to a large value for the abrupt-change case. If NULL, the algorithm will estimate the slope (gradual change case) - `depth`: Upper bound for the depth of the binary segmentation ; if this is 1, the algorithm models the situation of (at most) 1 changepoint. - `family_wise_error_rate`: Nominal alpha value for determining whether to proceed with the binary segmentations to the next split. Meaningful only if `depth` larger than 1. - `autoTraverse`: If TRUE, do automatic binary segmentation. Meaningful only of `depth` larger than 1. - `plotTitle`: Title for output plot, if any. ## Details Changepoint detection/estimation for changes in mean, performed by using an S-curve (logistic function) to approximate a step function. This enables asymptotic standard errors, and associated confidence intervals and tests for changepoint locations and change magnitudes. (However, in the multi-changepoint case, the alpha levels are only nominal.) Note: The location of a changepoint is considered to be a continuous numeric quantity, in contrast to packages such as `changepoints` where the location is integer-valued. ## Returns A `'fittedS'` object, containing estimates, standard errors and so on. ## Author(s) Lan Jiang, Collin Kennedy, Norm Matloff ## Examples ```r # real data # type ?Nile for background information nile <- data.frame(t=1871:1970, ht=Nile) fitS(nile,1,2,10) # abrupt change model # type ?cancerRates for background information data(cancerRates) fitS(cancerRates,1,2) # gradual change model # simulated data, changepoint at i = 367 n <- 500 x <- (1:n)/n y <- vector(length=n) trueChangePt <-round(n*2/3) y[1:trueChangePt] <- rnorm(trueChangePt,10,2) y[(trueChangePt+1):n] <- rnorm(n-trueChangePt,12.5,2) d <- data.frame(x=x,y=y) plot(d) fitS(d,1,2,10) # abrupt fitS(d, 1, 2) # gradual # simulated data, changepoints at i= 383, 855 n <- 1000 y <- vector(length = n) x <- seq(1,n,by = 1) idx <- c(383,855) part1 <- runif(n = length(x[1:(idx[1]-1)]), min = 0, max = 4) #mean of 2 part2 <- runif(n = length(x[idx[1]:(idx[2]-1)]), min = 0,max = 10) # mean of 5 part3 <- runif(n = length(x[idx[2]:n]), min = 0, max = 2) #mean of 1 y[1:(idx[1]-1)] <- part1 y[idx[1]:(idx[2]-1)] <- part2 y[idx[2]:n] <- part3 df <- data.frame(x = x, y = y) fitS(df, 1, 2, depth=2, autoTraverse = TRUE) ```

fitS function