leverage (Statistics Toolbox)

Leverage values for a regression.

Syntax

h = leverage(DATA)
h = leverage(DATA,'model')

Description

h = leverage(DATA) finds the leverage of each row (point) in the matrix, DATA for a linear additive regression model.

h = leverage(DATA,'model') finds the leverage on a regression, using a specified model type. 'model' can be one of these strings:

'interaction' - includes constant, linear, and cross product terms.
'quadratic' - interactions plus squared terms.
'purequadratic' - includes constant, linear and squared terms.

Leverage is a measure of the influence of a given observation on a regression due to its location in the space of the inputs.

Example

One rule of thumb is to compare the leverage to 2p/n where n is the number of observations and p is the number of parameters in the model. For the Hald dataset this value is 0.7692.

load hald
h = max(leverage(ingredients,'linear'))

h =

    0.7004

Since 0.7004 < 0.7692, there are no high leverage points using this rule.

Algorithm

[Q,R] = qr(x2fx(DATA,'model'));

leverage = (sum(Q'.*Q'))'

Reference

Goodall, C. R. (1993). Computation using the QR decomposition. Handbook in Statistics, Volume 9. Statistical Computing (C. R. Rao, ed.). Amsterdam, NL Elsevier/North-Holland.