By Michael J. Panik
Domestic / arithmetic & facts / facts research / Longitudinal Analysis
Growth Curve Modeling: conception and Applications
Michael J. Panik
Growth Curve Modeling: conception and functions (1118764048) conceal image
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Features fresh traits and advances within the thought and methods used to competently degree and version growth
Growth Curve Modeling: thought and functions gains an obtainable advent to progress curve modeling and addresses the right way to visual display unit the swap in variables through the years considering there is not any “one dimension suits all” method of development dimension. A assessment of the needful arithmetic for progress modeling and the statistical strategies wanted for estimating progress versions are supplied, and an outline of renowned progress curves, reminiscent of linear, logarithmic, reciprocal, logistic, Gompertz, Weibull, adverse exponential, and log-logistic, between others, is included.
In addition, the publication discusses key program parts together with financial, plant, inhabitants, woodland, and enterprise progress and is acceptable as a source for assessing contemporary development modeling traits within the scientific box. SAS is applied all through to research and version progress curves, assisting readers in estimating really expert progress premiums and curves. together with derivations of almost all the significant development curves and types, progress Curve Modeling: concept and purposes additionally features:
• Statistical distribution research because it relates to progress modeling
• pattern estimations
• Dynamic web site equations bought from progress models
• Nonlinear regression
• Yield-density curves
• Nonlinear combined results types for repeated measurements data
Growth Curve Modeling: conception and functions is a superb source for statisticians, public overall healthiness analysts, biologists, botanists, economists, and demographers who require a contemporary evaluation of statistical tools for modeling progress curves and interpreting longitudinal info. The ebook is additionally precious for upper-undergraduate and graduate classes on development modeling.
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Additional resources for Growth Curve Modeling: Theory and Applications
Here RY, RA, RL, and RK are the respective RGRs of output, technical progress, labor, and capital. 44 indicates that the RGR of output is a weighted sum of the RGRs of technical progress (wA = 1), labor, and capital. Moreover, the weights wL and wK are the output elasticities of the labor and capital inputs, respectively. 42 FUNDAMENTALS OF GROWTH Next, we may express (via Eq. 46) = (1 − wK ) RK − RA − wL RL . 47a) dwK 1 dK / dt = FKK + RK − R. 48) where A(t) = A(0)egt is the level of (neutral) technical progress in period t (here (1/A) dA/dt = RA = g (>0) is constant or technology growth is exogenous) and 1 − α = wL and α = wK are the output elasticities with respect to L and K, respectively.
3 could possibly lead one to conclude otherwise). 3 Comparing Two Time Series: Indexing Data to a Common Starting Point In order to compare the performance of two time series data sets, say Xt and Yt, we need to index the data to a common starting point. Hence, the initial values of X and Y must be set equal to each other so that differences over time between the X and Y variables can be highlighted. Once indexing to a common starting point is accomplished, we can readily determine their rates of growth, especially when the Xt and Yt series are stated in different units.
R(t) = r* = constant over [t1, t2]. 56) (Y increases exponentially in (t2 – t1)). 57) that is, if the instantaneous growth rate is constant over the time interval [t1, t2], then its value r* is obtained simply by knowing the value of Y at the beginning and at the end of the interval. 57 yield the same result. Why? 2. r(t) = αt over [t1, t2], α a constant. Then α t2 Y2 = Y1e ∫t1 α tdt = Y1e 2 ( t22 − t12 ) (Y increases exponentially in t22 t12 for α > 0) and thus ln(Y2 / Y1 ) α t22 − t12 . 58) 3.