Design matrix

Design matrix

In statistics, a design matrix is a matrix of explanatory variables, often denoted by X, that is used in certain statistical models, e.g., the general linear model.[1][2] It can contain indicator variables (ones and zeros) that indicate group membership in an ANOVA.

The design matrix represents the independent variables in statistical models which describe observed data (often called dependent variables) in terms of other known variables (explanatory variables). The theory relating to such models makes substantial use of matrix manipulations involving the design matrix: see for example linear regression. A notable feature of the concept of a design matrix is that it is able to represent a number of different experimental designs and statistical models, e.g., ANOVA, ANCOVA, and linear regression.

Contents

Example

One-way ANOVA

Example with a one-way analysis of variance (ANOVA) with 3 groups and 7 observations. The first column in the design matrix models the grand [global] mean of the ys, while the 3 remaining columns indicate the group membership of each observation. Here the first group consists of the 3 first observations and the next two groups each consist of two observations.


\begin{bmatrix}y_1 \\ y_2 \\ y_3 \\ y_4 \\ y_5 \\ y_6 \\ y_7 \end{bmatrix} = 
\begin{bmatrix}1 & 1 &0 &0 \\1 &1 &0  &0 \\ 1 & 1 & 0 & 0 \\ 1 & 0 & 1 & 0 \\ 1 & 0 & 1 & 0 \\ 1 & 0 & 0 & 1 \\ 1 & 0 & 0 & 1\end{bmatrix}
\begin{bmatrix}\mu \\ \tau_1 \\ \tau_2 \\ \tau_3 \end{bmatrix}
+ 
\begin{bmatrix}u_1 \\ u_2 \\ u_3 \\ u_4 \\ u_5 \\ u_6 \\ u_7 \end{bmatrix}

See also

References

  1. ^ Everitt,B.S. (2002) Cambridge Dictionary of Statistics, CUP. ISBN 0-521-91099-x
  2. ^ Box, G.E.P., Tiao, G.C. (1973) Bayesian Inference in Statistical Analysis, Wiley. ISBN 0-471-57427-7 (Section 8.1.1)

Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Design knowledge — There is a large body of knowledge that designers call upon and use during the design process to match the ever increasing complexity of design problems.[1] Design knowledge can be classified into two categories [2]: product knowledge and design… …   Wikipedia

  • Matrix of Leadership — Plot element from the Transformers franchise Publisher Marvel Comics (introduction only) First appearance Transformers issue 10 (November 1985) Created by Bob Budiansky …   Wikipedia

  • Matrix molding — or matrix transfer molding is a technique often used during molding. The person doing the assembly will first create the rigid outer shell and then he or she will introduce the softer and more fluid molding material between the shell and the… …   Wikipedia

  • Design Structure Matrix — Die Design Structure Matrix (DSM) ist eine Methode zur Erfassung, Modellierung, Analyse und Synthese (in gewissen Grenzen) der Vernetzung von Elementen in hochvernetzten Systemen. Typische Beispiele für solche Systeme sind komplexe… …   Deutsch Wikipedia

  • Design structure matrix — The design structure matrix (DSM) (also referred to as dependency structure method, dependency structure matrix, problem solving matrix (PSM), incidence matrix, n square matrix or design precedence matrix) is a compact, matrix representation of a …   Wikipedia

  • Design Structure Matrix — The design structure matrix (DSM) is a system modeling tool. It has two main strengths. First, it can represent a large number of system elements and their relationships in a compact way that highlights important patterns in the data (such as… …   Wikipedia

  • Matrix (numismatics) — In numismatics, a matrix is an intermediate used in the process of manufacturing coins. A matrix has its design in the same sense as a die. The design is engraved convex into the matrix, which is used to create punches. The matrix step was… …   Wikipedia

  • Design of experiments — In general usage, design of experiments (DOE) or experimental design is the design of any information gathering exercises where variation is present, whether under the full control of the experimenter or not. However, in statistics, these terms… …   Wikipedia

  • Matrix — Contents 1 Science and mathematics 2 Technology 3 Arts and entertainment …   Wikipedia

  • Matrix-assisted laser desorption/ionization — MALDI TOF mass spectrometer Matrix assisted laser desorption/ionization (MALDI) is a soft ionization technique used in mass spectrometry, allowing the analysis of biomolecules (biopolymers such as DNA, proteins, peptides and sugars) and large… …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”