Guess value

A guess value is more commonly called a starting value or initial value. These are necessary for most nonlinear regression search algorithms, because those algorithms are mainly deterministic and iterative, and they need to start somewhere. The quality of the initial values can have a considerable impact on the success or lack of such of the search algorithm. This is because the fitness function (in this case the SSE) has a (conjectured) unique shape about the global minimum, similar to the shape that objective functions in Operations Research problems often have. To one "side" the SSE simply increases exponentially. To the other "side" the SSE increases parabolically and then asymptotes to the plateau of the sum of squares of the observations. Starting values that fall in the exponential region can lead to algorithm failure because of overflow. Starting values that fall in the asymptotic plateau region can lead to algorithm failure because of "dithering". Deterministic NLR algorithms use a slope function to go to a minimum. If the slope is very small, then underflow errors can cause the algorithm to wander, seemingly aimlessly; this is dithering.

Guess values can be determined a number of ways. Guessing is one of them. If one is familiar with the type of problem, then this is an educated guess or guesstimate. Other techniques include linearization, solving simultaneous equations, reducing dimensions, treating the problem as a time series, converting the problem to a (hopefully) linear differential equation, and using mean values.

Other methods for determining starting values and optimal values in their own right come from stochastic methods, the most commonly known of these being evolutionary algorithms and particularly genetic algorithms. There is also stochastic funneling where interesting work is currently being done.