Weighted Hat Matrix

I understand that the trace of the projection matrix also known as the hat matrix XInvXXX in linear regression is equal to the rank of X.

Weighted hat matrix. Regression diagnostics are geared toward identifying individual points or groups of points that have an important influence on a fitted model. The matrix H is called the hat matrix because it maps the vector of observed values into a vector of fitted values. A matrix Hwith H2 His called idempotent.

The weighted decision matrix helps you to plan and to communicate your decisions. When fitting a model with survey data the sources of influence are the response variable Y the predictor variables X and the survey weights W. The airfocus Scoring Board allows you to combine different.

Long J Scott and Laurie H Ervin. For a given model with independent variables and a dependent variable the hat matrix is the projection matrix to. In hindsight it is geometrically obvious that we should have had H2 H.

Where H XXT X 1XT is an n nmatrix which puts the hat on y and is therefore referred to as the hat matrix. By writing H 2 HHout fully and cancelling we nd H H. 15-24 Statistics Canada Catalogue No.

Survey Weighted Hat Matrix and Leverages Survey Methodology 35 1. In this case the weight matrix should ideally be equal to the inverse of the variance-covariance matrix of the observations. Weighted Criteria Matrix Description The weighted criteria matrix is a valuable decision-making tool that is used to evaluate program alternatives based on specific evaluation criteria weighted by importance.

Survey weighted hat matrix and leverages Survey Methodology 351. Q1. This article discusses the use of the hat matrix and leverages to identify points that may be influential.