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Leverage matrix

A leverage matrix is used to rank the level of influence stakeholders have on each other. This comes in handy when, for instance, you need to move a stakeholder s support level from opposed to supportive, and you realize that another stakeholder can help move this person in the right direction. [Pg.49]

In particular, the leverage matrix H, also called influence matrix, is an important tool in regression diagnostics, containing information on the independent variables on which the model is built. [Pg.62]

Let X be a matrix with n rows and p columns, where p is the number of model parameters. The leverage matrix H is a symmetric nxn matrix defined as ... [Pg.62]

The leverage matrix is related to the response vector y by the following relationship ... [Pg.63]

A study of a - leverage matrix obtained from the - molecular matrix M of the atomic coordinates (hydrogen atoms included), i.e. a matrix with A rows (the atoms) and three columns (the x, y, z geometric coordinates), is in progress [Authors, This Book]. This symmetric Ax A matrix H, called the molecular v uence matrix (MIM), is calculated on the atom coordinates after their centring ... [Pg.302]

As the values of the leverage matrix are sensitive to the whole molecule structure, they automatically contain information about the molecular complexity, which is a function of the size, symmetry, elemental molecular composition, molecular branching, and centricity. Thus, 3D complexity descriptors can be obtained from this matrix as total and standardized information content ... [Pg.302]

Hat matrix and leverages in charge density refinements example of atomic net charges determination in a natural zeolite, the scolecite... [Pg.296]

Table 4. Diagonal elements (leverages H,) of the hat matrix and weighted residues ( F / - Fc /c(F )) of the pertinent data in the determination of the atomic net charges in scolecite. [Pg.308]

The scores and loadings are used to detect samples and X-variables (respectively) that have a very high importance in the PCA model. This detection is accomplished through leverage statistics, which are derived from the scores and loadings matrices. Sample leverage is calculated from the scores matrix by the following equation ... [Pg.279]

The leverage, / , of the z th calibration sample is the z th diagonal of the hat matrix, H. The leverage is a measure of how far the z th calibration sample lies from the other n - 1 calibration samples in X-space. The matrix H is called the hat matrix because it is a projection matrix that projects the vector y into the space spanned by the X matrix, thus producing y-hat. Notice the similarity between leverage and the Mahalanobis distance described in Chapter 4. [Pg.128]

Note that the most commonly used diagnostics to flag leverage points have traditionally been the diagonal elements / of the hat matrix H = X(X7X) X f These are equivalent to the Mahalanobis distances M/Xx,) because of the monotone relation... [Pg.182]

When only one factor is involved in the experiment, the predictive ability is often visualised by confidence bands. The size of these confidence bands depends on the magnitude of the experimental error. The shape , however, depends on the experimental design, and can be obtained from the design matrix (Section 2.2.3) and is influenced by the arrangement of experiments, replication procedure and mathematical model. The concept of leverage is used as a measure of such confidence. The mathematical definition is given by... [Pg.47]


See other pages where Leverage matrix is mentioned: [Pg.49]    [Pg.49]    [Pg.366]    [Pg.63]    [Pg.262]    [Pg.126]    [Pg.328]    [Pg.444]    [Pg.750]    [Pg.115]    [Pg.30]    [Pg.49]    [Pg.49]    [Pg.366]    [Pg.63]    [Pg.262]    [Pg.126]    [Pg.328]    [Pg.444]    [Pg.750]    [Pg.115]    [Pg.30]    [Pg.202]    [Pg.299]    [Pg.306]    [Pg.309]    [Pg.23]    [Pg.149]    [Pg.150]    [Pg.442]    [Pg.109]    [Pg.227]    [Pg.231]    [Pg.425]    [Pg.294]    [Pg.164]    [Pg.47]    [Pg.47]    [Pg.51]    [Pg.316]    [Pg.249]    [Pg.86]    [Pg.75]    [Pg.40]   
See also in sourсe #XX -- [ Pg.49 ]




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