DETERMINISTIC AND PROBABILISTIC MODELS WITH APPLICATIONS TO MODELING FERTILITY DATA

摘要

Inefficient registration of vital events and geographically remote areas in many developing countries often hinder the regular availability of data. Hence its mathematical modeling is of utmost importance. Here three deterministic nonlinear models: Gamma, Hadwiger and Gompertz models as well as their nonlinear mixed effect forms, called probabilistic models, are studied, analyzed for their accuracy and compared for their performance. To examine these models, their goodness of fit and accuracy, first these deterministic models are fitted to the fertility data of Nepal for the period 1971-2001. Then their nonlinear mixed effect forms are fitted to the same data. The resulted fits obtained from these models are analyzed for their accuracy and are compared for their goodness of fit. It is observed that whereas the deterministic non linear models are more effective with very low residual sum of squares, the variation of these sums of squares is very high among the various years. In contrast, their nonlinear mixed effects counterparts, in addition to having low residual sum of square, have consistent values. It is thus concluded that non linear mixed effect models would statistically describe the unreliable base population data such as fertility of many developing countries like Nepal more effectively.