Estimation of the Predictive Ability of Ecological Models

The conventional criteria for predictive model selection do not indicate the absolute goodness of models. For example, the quantity of Akaike Information Criterion (AIC) has meanings only when we compare AIC of different models for a given amount of data. Thus, the existing criteria do not tell us whether the quantity and quality of data is satisfactory, and hence we cannot judge whether we should collect more data to further improve the model or not. To solve such a practical problem, we propose a criterion RD that lies between 0 and 1. RD is an asymptotic estimate of the proportion of improvement in the predictive ability under a given error structure, where the predictive ability is defined by the expected logarithmic probability by which the next data set (2nd data set) occurs under a model constructed from the current data set (1st data set). That is, the predictive ability is defined by the expected logarithmic probability of the 2nd data set evaluated at the model constructed from the 1st data set. Appropriate choice of error structures is important in the calculation of RD. We illustrate examples of calculations of RD by using a small data set about the moth abundance.