Ridge Estimate Application to Growth Function

抄録

Growth functions are often used to describe longitudinal growth processes. In growth analysis, it is first necessary to estimate the parameters included in the growth function based on real life data. During the numerical estimation process, this is often accomplished using iterative algorithm. The initial value setting is the key to this iterative algorithm process. An improper setting of the initial value is risky, because it may lead to non-convergence. Another element of risk is the “convergence of an improper solution” without an error message. Under such a scenario, because the estimation process is correctly completed, it is difficult to identify the source of the error. To resolve this problem, we focus our attention to ridge estimation and how it applies to growth analysis. Ridge estimation method can be used to stabilize the estimation process by imposing the ℓ₂ -norm condition as a constraint. In this paper we evaluated the performance of the ridge estimation technique using two cases of numerical experiments. Under several settings of the initial value, we were able to evaluate the behavior of the estimate, especially for dispersion. We concluded that the estimate from the ridge estimation process is more stable compared to the residual sum of square approach. Actually the mean squared error value in ridge estimate is smaller than the residual sum of square. Although ridge estimation method is not universal, this paper has shown us that it is possible to extend the range of setting initial values that converge to a proper estimate.