loessmt#

Purpose#

Computes coefficients of locally weighted regression.

Format#

{ yhat, ys, xs } = loessmt(depvar, indvars[, l_ctl])#

Parameters:

depvar (Nx1 vector) – dependent variable.
indvars (NxK matrix) – independent variables.

l_ctl (struct) –

Optional input, an instance of a loessmtControl structure containing the following members:

l_ctl.Span	scalar, degree of smoothing. Must be greater than 2/N. Default = .67777.
l_ctl.NumEval	scalar, number of points in ys and xs. Default = 50.
l_ctl.Degree	scalar, if 2, quadratic fit, otherwise linear. Default = 1.
l_ctl.WgtType	scalar, type of weights. If 1, robust, symmetric weights, otherwise Gaussian. Default = 1.
l_ctl.output	scalar, if 1, iteration information and results are printed, otherwise nothing is printed.

Returns:

yhat (Nx1 vector) – predicted depvar given indvars.
ys (l_ctl.numEval x 1 vector) – ordinate values given abscissae values in xs.
xs (l_ctl.numEval x 1 vector) – equally spaced abscissae values.

Examples#

Example 1: Basic usage#

// Load dataset
fname = getGAUSSHome("examples/lowess1.dta");
data = loadd(fname, "h1 + depth");

// Define dependent variable
depvar = data[., 1];

// Define independent variable
indvars = data[., 2];

{ yhat, ys, xs } = loessmt(depvar, indvars);

After the above code, the first few lines of the printed results will be:

Obs        X       Y  Fitted Y    Weights  Residuals
  0.000   6.642     6.169      0.985      0.473
  4.040   5.705     6.218      0.982     -0.514
  8.081   4.698     6.267      0.837     -1.569
 12.121   7.164     6.316      0.951      0.848

Example 2: Set options#

// Load dataset
fname = getGAUSSHome("examples/lowess1.dta");
data = loadd(fname, "h1 + depth");

// Control structure
struct loessmtControl l_ctl;
l_ctl = loessmtControlCreate;

// Quadratic fit
l_ctl.Degree = 2;

// Do not print output to screen
l_ctl.output = 0;


// Define dependent variable
depvar = data[., 1];

// Define independent variable
indvars = data[., 2];

{ yhat, ys, xs } = loessmt(depvar, indvars, l_ctl);

Remarks#

Based on Cleveland, William S. ‘’Robust Locally Weighted Regression and Smoothing Scatterplots.’’ JASA, Vol. 74, 1979, 829-836.

For backward compatibility, you may still call loessmt() like this:

{ yhat, ys, xs } = loessmt(l_ctl, depvar, indvars);

though this is not recommended for new code.

Source#

loessmt.src