Monotone regression

Rather than assume the response is already on an interval scale, mreg finds the monotone rescaling of it that fits a linear model best – Kruskal's non-metric approach, the same idea non-metric MDS uses. It reports a coefficient table but no standard errors: mreg does not compute them (no pcov= in its own TDA implementation), so vcov() and confint() are always NA here, honestly reflecting what TDA itself reports rather than a parsing gap.

Usage

tda_mreg(
  formula,
  data,
  ties = c("ignore", "primary", "secondary"),
  control = NULL,
  options = list(),
  dir = tempfile("tda"),
  ...
)

Arguments

formula

a two-sided formula.

data

a data frame.

ties

how to handle tied response values: "ignore" (default), or Kruskal's "primary" or "secondary" approach to them; mreg's opt=. On data with ties, "ignore" and "secondary" converge to a different final stress, not the same value under two names.

control

convergence settings from tda_control (mxit=/tolf=/tolsp=).

options

a named list of further TDA options, passed through.

dir

working directory.

...

passed to tda_run.

Value

An object of class tda_fit.

Details

predict() (and fitted(), its default with no newdata) is well defined here – the coefficients describe a linear model, just of the rescaled response rather than the original one – but the numbers it returns are on that rescaled (“disparity”) scale, not the original response's units or levels. This is the same idea as predict.glm(type = "link") returning the linear predictor rather than a probability.

See also

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

Examples

set.seed(52)
d <- data.frame(x = round(rnorm(50), 2))
# y is an ordinal rank (1-5), not an interval scale, driven by a linear
# score plus noise -- exactly the case mreg is meant for
score <- 1 + 2 * d$x + rnorm(50, sd = 0.4)
d$y <- as.integer(cut(score, quantile(score, seq(0, 1, 0.2)),
                      include.lowest = TRUE))
fit <- tda_mreg(y ~ x, d)
coef(fit)
#> Intercept         x 
#>  2.895386  1.604513 

# y is heavily tied by construction (5 ordinal ranks) -- ties= selects
# how mreg's algorithm resolves that; see Details for a directly
# verified case where it changes the fit's stress
coef(tda_mreg(y ~ x, d, ties = "secondary"))
#> Intercept         x 
#>  2.895386  1.604513 

# fitted values, on the rescaled response -- not the original 1-5 scale,
# but increasing with x the way the underlying score was
predict(fit)
#>  [1]  1.3069175  2.2696255  4.9972983  4.4196735 -0.5222278  4.6122151
#>  [7]  0.7934732  3.7778681  1.2748272  4.1469062  3.0397919  1.4513237
#> [13]  3.1841981  2.0770839  4.8849823  2.2214901  4.2431770  5.9439612
#> [19]  2.2054450  2.7188893  3.0879273  4.7887115  3.6815973  0.1356227
#> [25]  3.6976424  3.2644238  1.2908723  3.5853265  2.2535804  1.9166326
#> [31]  2.1733547  1.6599104  3.0718822  4.0025000  2.5423928  4.4196735
#> [37]  2.8632955  2.3658963  4.3234027  3.2323335  4.9491629  3.9062292
#> [43]  2.7670247  2.4621671  1.5315493  6.6339020  2.8953857  2.4942574
#> [49]  3.1681530  1.7882715
predict(fit, newdata = data.frame(x = c(-1, 0, 1)))
#> [1] 1.290872 2.895386 4.499899