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An alternative method of growth curve analysis is latent growth curve modeling using structural equation modeling (SEM). This approach will provide the same estimates as the multilevel modeling approach, provided that the model is specified identically in SEM. However, there are circumstances in which either MLM or SEM are preferable: [4] [6]
Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards , who proposed the general form for the family of models in 1959.
An UpSet plot showing three sets, and the corresponding venn diagram. UpSet plots visualize intersections between sets in a matrix. In a vertical UpSet plot, the columns of the matrix correspond to the sets, the rows correspond to the intersections. For each row, the cells that are part of an intersection are filled in.
The Gompertz curve or Gompertz function is a type of mathematical model for a time series, named after Benjamin Gompertz (1779–1865). It is a sigmoid function which describes growth as being slowest at the start and end of a given time period.
The diagram juxtaposes a graph which has input price ratios as its horizontal axis, endowment ratios as its positive vertical axis, and output price ratios as its negative vertical axis. The diagram is named after economists Roy F. Harrod and Harry G. Johnson ; the Samuelson-Harrod-Johnson name is in reference to economist Paul Samuelson . [ 3 ]
The Bass diffusion model is used to estimate the size and growth rate of these social networks. The work by Christian Bauckhage and co-authors [ 10 ] shows that the Bass model provides a more pessimistic picture of the future than alternative model(s) such as the Weibull distribution and the shifted Gompertz distribution.
The Ramsey–Cass–Koopmans model (also Ramsey growth model or neoclassical growth model) is a neoclassical model of economic growth based primarily on the work of Frank P. Ramsey in 1928, [1] with significant extensions by David Cass and Tjalling Koopmans in 1965.
Latent growth modeling is a statistical technique used in the structural equation modeling (SEM) framework to estimate growth trajectories. It is a longitudinal analysis technique to estimate growth over a period of time. It is widely used in the field of psychology, behavioral science, education and social science.