STAGES IN MODELLING

Modelling requires through review of what is known and what is not known. Then the process to be modelled is analysed and represented in the form of mathematical equations, statistical relationships and/or probability distributions. The equations would contain some unknown characteristics of the population to be modelled. They are estimated using an appropriate method of fitting. This is followed by testing whether the model reproduced the old data accurately. If it did, then the model can be used for predictions or theorising. Thus modelling is done in four steps:

• specification of model;

• estimation of parameters;

• validation; and

• forecasting.

SPECIFICATION

Specification refers to the process of expressing relationships between dependent and independent variables in the form of mathematical or statistical equations. These relationships contain variables and some constants. The constants of the equations are called parameters. Specification requires a sound understanding of the field of study and a thorough review of works done in the field, understanding of assumptions on which past models were based, how sound they are, and the researcher's judgement. Suppose in a particular field, such as the study of waiting time in fertility, past researchers have used mostly Poisson distribution and the researcher thinks that the population being heterogeneous, a mixture of Poisson distributions will fit better. Then the researcher has to specify the waiting time as a linear combination of two Poisson distributions containing different parameters.