Robust LTS Linear Regression

Robust regression models are useful for fitting linear relationships when the random variation in the data is not Gaussian (normal) or when the data contain significant outliers. In such situations, standard linear regression may return inaccurate estimates.

The robust LTS regression method performs least-trimmed squares regression. It has less detailed plots and summaries than standard linear regression and robust MM regression.

To perform robust regression

Choose Statistics __image\arrow5.gif Regression __image\arrow5.gif Robust LTS. The dialog shown below appears.

Model Page

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In the Robust LTS Linear Regression dialog, the Model page has the following options:

Data

Data Set

Select a data set from the dropdown list or type the name of a data set. You can also type into the Data Set edit field any expression that evaluates to a data set.

Weights

Enter the column that specifies weights to be applied to all observations used in the analysis. To weight all rows equally, leave this blank.

Subset Rows

Enter an S-PLUS expression that identifies the rows to use in the analysis. To use all the rows in the data set, leave this field blank.

Omit Rows with Missing Values

Select this box to omit from the analysis any rows in the data set that contain missing values for any of the variables in the model.

Variables

Dependent Variables

Select a variable as the dependent variable in the formula. The variable name will appear in the formula field below, followed by a '~'.

Independent Variables

Select one or more variables as the independent variables, or predictor, in the formula. To select more than one variable, Ctrl-click the variables.

Formula

In the Formula field, enter a formula specifying the desired model. In its simplest form a formula consists of the response variable, a tilde (~), and a list of predictor variables separated by "+"s. An intercept is automatically included by default.

Save Model Object

In the Save As field, enter the name for the object in which to save the results of the analysis. If an object with this name already exists, its contents are overwritten. The model object can be used in later functions such as plotting.

Options Page

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In the Robust LTS Linear Regression dialog, the Options page has the following option:

Number of Residuals in SS to Minimize

Enter the number of squared residuals whose sum will be minimized. The default is floor((n+p+1)/2) where n is the number of observations and p is the number of predictors in the model.

Results page

On the Results page, choose the type of printed results and how you would like the results of the analysis saved. To select or clear an option, click the check box.

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In the Robust LTS Linear Regression dialog, the Results page has the following options:

Printed Results

Short Output for Robust LTS Regression

Display a short summary of the model fit. This includes the model formula, the estimates of regression coefficients, the scale estimates of residuals, and the number of observations used in the estimate.

Long Output for Robust LTS Regression

Display a detailed summary of the model fit. This includes the model formula, the estimates of regression coefficients, the scale estimates of residuals, the robust multiple R-squared value, the number of observations used in the estimate, the residuals, and the weights.

Saved Results

Save In

Enter the name of a data set in which a part of the analysis, such as fitted values and residuals, predictions, confidence intervals, or standard errors, is saved.

Fitted Values

Save the fitted values from the model in the object specified in Save In.

Residuals

Save the residuals from the model in the object specified in Save In. These are the ordinary residuals (the response minus the fitted value).

LTS Weights (0's, 1's)

Select this to save weights with a value of 1 for observations having reasonably small residuals and a value of 0 for observations having large residuals. These weights can later be used in an ordinary least squares regression.

Plot Page

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In the Robust LTS Linear Regression dialog, the Plot page has the following options:

Plots

Residuals vs Fit

Select this to display a plot of the residuals versus the fitted values.

Residuals vs Index

Select this to display a plot of the standardized residuals versus the index of the observations.

Residuals Normal QQ

Display a normal quantile-quantile plot of the residuals.

Residuals vs Robust Distance

Select this to display a plot of the LTS residuals versus Robust Distances of 'x'-rows.

Options

Number of Extreme Points to Identify

Enter the number of extreme points that are identified on the Residuals vs Fit, Sqrt Abs Residuals vs Fit, Residuals Normal QQ, and Cook's Distance plots. The row names from the data set specified on the model page are used to identify the points.

S-Plus language functions related to Least Trimmed Squares Robust Regression

ltsreg, ltsreg.formula, ltsreg.default, plot.lts, summary.lts

Other related S-Plus language functions

lm, lmsreg, rreg