Search Results for Matrix Calculus

..., standard deviation, variance, Theil’s index, mean logarithmic deviation, and interquartile range). We derive each of these indices from an absorbing Markov chain formulation of the life table, and use matrix calculus to obtain the sensitivity and the elasticity (i.e., the proportional sensitivity...

... . (3) The theory of matrix calculus is detailed in Magnus and Neudecker (2019) and the calculation procedure can be found in the online appendix . Similarly, the derivative in the survival matrix in Eq. (1) for values of x ≥ α is l ˙ x   = l ˙ α ∏ k...

... 8y to be a vector of changes, iJH/iJY to be the (non- singular) Jacobian matrix of partial de- rivatives of each H with respect to each y, and the differentiais 8H to be assem- bled in vector form. The same expres- sion then holds. Example 4. To illustrate this method, let us assess the change...

... for why one should focus on preserving the cross- product ratios of a marriage matrix. The "standardized rank-and-file" model developed by Schoen (1977) in- Harmonic Mean as Basis of Realistic Two-Sex Marriage Model 203 troduced the notion of a "rectangular" population, one which had the same num- ber...

...- fitz (1968) provide the most complete and accessible accounts of the theory, but they draw on mathematics ranging from number theory and matrix algebra to Laplace transforms, integral equa- tions, and esoteric theorems in complex analysis. Lopez (1961, pp. 72-76) does give a "heuristic view" of part...

... mpact A ssessment) that implements this approach. 28 6 2012 10 10 2012 © Population Association of America 2012 2012 Health impact assessment Markov models Matrix exponential Micro-simulation Chronic disease modeling In medical demography, demographic techniques...

... des Sciences MatMma- tiques (Paris: Gauthier-Villars, 1906), Book I, IV, 127-60; A. S. Householder, Principles of Numerical Analysis (New York: McGraw-Hill Book ce., 1953), p. 188. 532 DEMOGRAPHY The condition that the tP's might serve in this capacity is that the matrix of their zeroth to second...

... demografiá y a la teoría matemática del desarrollo de la población. Summary This article presents an elementary approach to the study of the population projection-matrix, the reverse (or inverse) projection-matrix, the process of population growth generated by the projection-matrix, the “prior” process...

... is based on an absorbing Markov chain formulation of the life table and matrix calculus (see Caswell 2001 : chapter 10). The second general method, the stepwise replacement algorithm (Andreev et al. 2002 ), extends Das Gupta’s logic by presenting the total change in the dependent index as a sum...

... this difference in the two meth- ods of analysis: in the discrete approach we project the entire age structure from one step to the next by means of the per- tinent transition matrix, whereas the key variable in the continuous model is the birth function at any moment of time. This birth function can be expressed...

... and Consequences . Journal of Marriage and Family , 67 , 53 – 67 . 10.1111/j.0022-2445.2005.00005.x White , H. ( 1980 ). A Heteroskedasticity-Consistent Covariance Matrix Estimator of a Direct Test of Heteroskedasticity . Econometrica , 48 , 417 – 30 . Wu , Z. ( 1995 ). The Stability...

... . American Sociological Review , 57 , 661 – 678 . 10.2307/2095919 Todaro M. ( 1976 ). Internal migration in developing countries . Geneva : International Labor Office . White H. ( 1980 ). A heteroskedastic-consistent covariance matrix estimator and a direct test...

... is a vector of parameters describing the influence on q of the variables contained in the matrix X.lO In our case, X contains Breastfeeding, Infant Mortality, Married Sex Ratio, Income, and a vector of unity. Therefore M can be written as M = mX(TMY). (2) Researchers offer a wealth of hypotheses about...

... of the independent effects of each ofthe variables will lack precision, although they will be unbiased. Hanushek and Jackson (1977:90) recommend using a threshold value of 0.70 for identification of "high" correlations. As indicated by the correlation matrix shown in table 2, none of the correlations for the main...

... of the data. Conse- quently, j = 1, 2, 3, , J , which is a system of J linear equations in the unknown ~r i amenable to a routine computer solution. In a matrix form this system is where (28) N (ap )Bm = L(P*i - Pi) - . i=1 arm i Details that concern the partial deriva- tives ap/ arm are given in the Appendix...