Non-linear regression

tda_nlreg is TDA's nlreg command.

Usage

tda_nlreg(
  formula,
  data,
  expr = NULL,
  start = NULL,
  residuals = FALSE,
  control = NULL,
  options = list(),
  dir = tempfile("tda"),
  ...
)

# S3 method for class 'tda_nlreg'
predict(object, newdata = NULL, ...)

Arguments

formula

a two-sided formula. With expr, only the response and the predictor names it uses need to be present here – the functional form itself comes from expr, not from the formula's own right-hand side.

data

a data frame.

expr

optional nonlinear expression in TDA's language, written against formula's predictor names – e.g. "a * exp(b * x)" for \(y = a e^{bx}\). Names on the right that are neither predictors nor defined elsewhere are the parameters to be estimated. Without this, nlreg fits an ordinary (or orthogonal distance) linear predictor instead.

start

optional named list or vector of starting values, in the order expr introduces its parameters. TDA's default starting point is all 1s, which will not converge for every functional form.

residuals

for tda_nlreg and tda_lsreg1, ask TDA to write its per-case table (pres=) and return it as residuals: the case number, the response, the fitted value, the residual, then each predictor. TDA does not compute it unless asked.

control

convergence settings from tda_control.

options

a named list of further TDA options, passed through: opt = 1 (default) is ordinary least squares, opt = 2 orthogonal distance regression.

dir

working directory.

...

passed to tda_run.

Value

An object of class tda_fit.

Non-linear fits

nlreg takes an optional right-hand-side expression and starting values (xp=) to fit a non-linear function; without them it falls back to a linear predictor. That right-hand-side expression is reachable through expr/start: fitting \(y = a \, e^{bx}\) on data generated with \(a=2, b=0.5\) recovers both closely. options = list(opt = 2) additionally selects orthogonal distance regression (errors in both variables), which tda_lsreg has no equivalent for.

See also

Other regression: TDA_FAMILIES, TDA_QRMODELS, tda_freg(), tda_gdf(), tda_l1reg(), tda_lsreg(), tda_mlrc_design(), tda_mreg(), tda_npreg(), tda_zreg()

Examples

set.seed(25)
d <- data.frame(x = round(rnorm(60, sd = 2), 3))
d$y <- round(1.5 + 0.9 * d$x + rnorm(60, sd = 1.5), 3)
reg <- tda_nlreg(y ~ x, d, options = list(opt = 1))  # ordinary least squares
coef(reg)
#> Intercept         x 
#> 1.2121419 0.7990406 
coef(tda_nlreg(y ~ x, d, options = list(opt = 2)))  # orthogonal distance
#> Intercept         x 
#>  1.328604  1.066289 
head(fitted(reg))     # no newdata needed
#> [1]  0.8733487 -0.4522596 -0.6312447  1.7259250 -1.1849799  0.5001967
predict(reg, newdata = data.frame(x = c(0, 1, 2)))
#> [1] 1.212142 2.011182 2.810223

# a nonlinear fit: y = a * exp(b * x), true a = 2, b = 0.5
set.seed(1)
d2 <- data.frame(x = round(runif(40, 0, 5), 2))
d2$y <- round(2 * exp(0.5 * d2$x) + rnorm(40, sd = 0.5), 3)
nl <- tda_nlreg(y ~ x, d2, expr = "a * exp(b * x)", start = c(1, 1))
coef(nl)
#>         a         b 
#> 2.0685764 0.4912572 
# predict()/fitted() for this case evaluate the fitted expression
# itself (in R, not TDA) rather than X %*% coefficients, which would
# be meaningless for a nonlinear model
head(fitted(nl))
#> [1]  3.975827  5.158259  8.430501 19.243404  3.397468 18.776489
predict(nl, newdata = data.frame(x = c(0, 1, 2, 5)))
#> [1]  2.068576  3.380819  5.525507 24.122540