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[4]: 114 A DataFrame is a 2-dimensional data structure of rows and columns, similar to a spreadsheet, and analogous to a Python dictionary mapping column names (keys) to Series (values), with each Series sharing an index. [4]: 115 DataFrames can be concatenated together or "merged" on columns or indices in a manner similar to joins in SQL.
One application of multilevel modeling (MLM) is the analysis of repeated measures data. Multilevel modeling for repeated measures data is most often discussed in the context of modeling change over time (i.e. growth curve modeling for longitudinal designs); however, it may also be used for repeated measures data in which time is not a factor.
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.
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]
Growth curve model: [2] Let X be a p×n random matrix corresponding to the observations, A a p×q within design matrix with q ≤ p, B a q×k parameter matrix, C a k×n between individual design matrix with rank(C) + p ≤ n and let Σ be a positive-definite p×p matrix. Then
Phase diagram of the Ramsey model, for the case of () =, and ,,, =,,,. Phase space graph (or phase diagram) of the Ramsey model. The blue line represents the economy's dynamic adjustment (or saddle) path in which all the constraints present in the model are satisfied.
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.
Uzawa's theorem, also known as the steady-state growth theorem, is a theorem in economic growth that identifies the necessary functional form of technological change for achieving a balanced growth path in the Solow–Swan and Ramsey–Cass–Koopmans growth models. It was proved by Japanese economist Hirofumi Uzawa in 1961. [1]