Overview (WLS command)

WLS (weighted least squares) estimates regression models with different weights for different cases. Weighted least squares should be used when errors from an ordinary regression are heteroscedastic—that is, when the size of the residual is a function of the magnitude of some variable, termed the source.

The WLS model is a simple regression model in which the residual variance is a function of the source variable, up to some power transform indicated by a delta value. For fuller regression results, save the weights produced by WLS and specify that weight variable on the REGWGT subcommand in REGRESSION.

Options

Calculated and Specified Weights. WLS can calculate the weights based on a source variable and delta values (subcommands SOURCE and DELTA), or it can apply existing weights contained in a series (subcommand WEIGHT). If weights are calculated, each weight value is calculated as the source series value raised to the negative delta value.

New Variables. You can change NEWVAR settings on the TSET command prior to WLS to evaluate the regression coefficients and log-likelihood function without saving the weight variable, or save the new values to replace the values saved earlier, or save the new values without erasing values saved earlier (see the TSET command). You can also use the SAVE subcommand on WLS to override the NONE or the default CURRENT settings on NEWVAR for the current procedure.

Statistical Output. You can change the PRINT setting on the TSET command prior to WLS to display regression coefficients or the list of log-likelihood functions at each delta value, or to limit the output to only the regression statistics for the delta value at which the log-likelihood function is maximized (see the TSET command). You can also use the PRINT subcommand to override the PRINT setting on the TSET command for the current procedure and obtain regression coefficients at each value of delta in addition to the default output.

Basic Specification

  • The basic specification is the VARIABLES subcommand specifying one dependent variable, the keyword WITH, and one or more independent variables. Weights are calculated using the first independent variable as the source variable and a default delta value of 1.
  • The default output for calculated weights displays the log-likelihood function for each value of delta. For the value of delta at which the log-likelihood function is maximized, the displayed summary regression statistics include R, R 2, adjusted R 2, standard errors, analysis of variance, and t tests of the individual coefficients. A variable named WGT#1 containing the calculated weights is automatically created, labeled, and added to the active dataset.

Syntax Rules

  • VARIABLES can be specified only once.
  • DELTA can be specified more than once. Each specification will be executed.
  • If other subcommands are specified more than once, only the last specification of each one is executed.
  • You can specify either SOURCE and DELTA, or just the WEIGHT subcommand. You cannot specify all three, and you cannot specify WEIGHT with SOURCE or with DELTA.

Subcommand Order

  • Subcommands can be specified in any order.

Operations

  • If neither the WEIGHT subcommand nor the SOURCE and DELTA subcommands are specified, a warning is issued and weights are calculated using the default source and delta value.
  • Only one WGT#1 variable is created per procedure. If more than one delta value is specified, the weights used when the log-likelihood function is maximized are the ones saved as WGT#1.
  • WGT#1 is not created when the WEIGHT subcommand is used.
  • The WEIGHT command specifies case replication weights, which are not the same as the weights used in weighted least squares. If the WEIGHT command and WLS WEIGHT subcommand are both specified, both types of weights are incorporated in WLS.
  • WLS uses listwise deletion of missing values. Whenever one variable is missing a value for a particular observation, that observation will not be included in any computations.

Limitations

  • Maximum one VARIABLES subcommand.
  • Maximum one dependent variable on the VARIABLES subcommand. There is no limit on the number of independent variables.
  • Maximum 150 values specified on the DELTA subcommand.