LINEAR AND NONLINEAR MODELS

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Presentation transcript:

LINEAR AND NONLINEAR MODELS The decisive criterion is position of parameters, not type of regression line! Examples of linear models (paramerers are in linear position): y = a + bx - přímka y = a + bx + cx2 - parabola y = a + (b/x) - hyperbola curves !! Examples of nonlinear models (paramerers are in nonlinear position): y = axb y = aebx Pros – they can model complicated real processes, e.g. growth, with real prediction. Cons – relatively complicated calculus

NONLINEAR MODEL ESTIMATION OF PARAMETERS (arbitrally selected) 1. aproximation 2. estimation of param (first computed) 2. aproximation 3. estimstion of param (second computed)

NONLINEAR MODEL ESTIMATION OF PARAMETERS local min. (there are not optimal solution) global minimum (optimal solution)

ESTIMATION OF REGRESSION MODEL QUALITY Akaike information criterion (AIC) RSS residual sum of squares m number of parameters The AIC is smaller, the model is better.