MonotoneRegression function

Weighted Isotonic Regression (Weighted Monotone Regression)

Performs weighted isotonic (monotone) regression using the non-negative weights in w. The function is a direct translation of the matlab function lsqisotonic.

MonotoneRegression(x, y, w = NULL)

Arguments

• x: The independent variable vector
• y: The dependent variable vector
• w: A vector of weigths

Details

YHAT = MonotoneRegression(X,Y) returns a vector of values that minimize the sum of squares (Y - YHAT).^2 under the monotonicity constraint that X(I) > X(J) => YHAT(I) >= YHAT(J), i.e., the values in YHAT are monotonically non-decreasing with respect to X (sometimes referred to as "weak monotonicity"). LSQISOTONIC uses the "pool adjacent violators" algorithm.

If X(I) == X(J), then YHAT(I) may be <, ==, or > YHAT(J) (sometimes referred to as the "primary approach"). If ties do occur in X, a plot of YHAT vs. X may appear to be non-monotonic at those points. In fact, the above monotonicity constraint is not violated, and a reordering within each group of ties, by ascending YHAT, will produce the desired appearance in the plot.

Returns

The fitted values after the monotone regression

References

Kruskal, J.B. (1964) "Nonmetric multidimensional scaling: a numerical method", Psychometrika 29:115-129.

Cox, R.F. and Cox, M.A.A. (1994) Multidimensional Scaling, Chapman&Hall.

Author(s)

Jose L. Vicente Villardon (from a matlab functiom)

Note

The function is a direct translation of the matlab function lsqisotonic.

Examples

## Used inside MDS