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Development of factor analysis as a statistical procedure proceeds from the generalized least squares (GLS) model used in regression and other least squares analyses Assuming all variables to be in Z score form for convenience, the model is based on this set of equations: X i1 = w1A Ai + w1B Bi + w1C Ci + w1D Di + + u i1 X i2 = w2A Ai + w2B Bi + w2C Ci + w2D D2 + + u i2 X i3 = w3A Ai + w3B Bi + w3C Ci + w3D Di + + u i3 X iv = wv A Ai + wv B Bi + wvC Ci + wv D Di + + u iv (6.

In this methodology, the lowest order O[1] device p-cells can be dc and RF characterized The basic device library is constructed of the devices, which are fully quanti ed; both passive and active elements are placed into dc pad sets for dc measurements and within Sparameter pad sets for RF characterization Additionally, the ESD testing can be completed on the base library of elements using wafer-level transmission line pulse (TLP) and human body model (HBM) testing Note that the circuit characterization and ESD testing can be done on both the primitive O[1] p-cell elements or the O[n] hierarchical p-cell To provide RF ESD design cosynthesis, it is desirable to have both the ability to vary physical size or circuit topology In this method, schematics and symbology of both the primitive and the higher order O[n] ESD p-cell networks is possible with the generation of design layout..

Figure 10-8

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1) where, for the rst line, X is the score for person i on variable 1, w is the weight for variable 1 for factor A, and A is the score for person i on factor A The equation shows factors A through D and indicates that there may be more Additional variables are indicated, for a total of v variables in the analysis The last element of each equation, u, is that which is unique to that particular variable, often called error or residual Each u is in a separate column to indicate that each is distinct from any other u There are as many distinct us as there are variables It is important to note that each variable s uniqueness (us) includes two sources of variance First is random error due to unreliability and second is that variance in the variable that is not estimable from the factors.

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by gene-environment interactions (Khoury, Beaty, & Cohen, 1993) While no one has yet demonstrated the presence of speci c gene-environment interactions on tobacco use in humans, because of insuf cient study sample sizes, interactions have been demonstrated in biometric models of twin similarity for alcohol use (Koopmans, Heath, Neale, & Boomsma, 1997) It has been speculated that if such interactions exist, they could emerge as potentially powerful determinants of susceptibility and maintenance of tobacco dependence (Kendler, 1999; Swan, 1999) De nition of Phenotypes In most behavior genetic and genetic epidemiologic studies, smoking has been assessed as a static phenotype (ie, as if the behavior is a trait that remains constant over time) (See next section for a review of these studies.

When the preceding equation is solved for each dependent variable, the multiple correlation of the factors with that variable can be computed In factor analysis, the square of that multiple correlation is called the communality (h2) because it is an index of how much that variable has in common with the factors How high can the communality be The absolute maximum is 10, because then all the variation of the variable would be reproduced by the factor But the psychometric maximum is the variable s reliability coef cient, which by de nition is the maximum proportion of the variable that can be.

Let denote modulo 2 addition. Thus, X X = 1 is equivalent to X = X. We do not minimize I (X; X) directly; instead, we nd a lower bound and then show that this lower bound is achievable. For any joint distribution satisfying the distortion constraint, we have I (X; X) = H (X) H (X|X) = H (p) H (X X|X) H (p) H (X X) H (p) H (D), (10.15) (10.16) (10.17) (10.18)

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