Age-at-death estimation based on algorithms for multi-class discriminant analysis using binary and ordinal predictors

Abstract

Objective

The objective of this study is to develop algorithms for multi-class discriminant analysis using binary and/or ordinal predictors that can be used effectively to age-at-death estimation when expressed in terms of binary/ordinal age markers.

Method

The algorithms examined are based on the crude assumption that the predictors are uncorrelated or on the latent model which assumes that the discrete predictors code an underlying multivariate normal distribution. The tetrachoric/polychoric correlations of this distribution are either estimated from the training dataset and used without or with correction to fall within feasible correlation bounds or are extracted from algorithms used to generate correlated binary/ordinal data.

Results

It was found that, irrespective of the origin of the dataset analyzed, the crude algorithms may give poor results only when applied to ordinal datasets with very strong intercorrelated predictors. In what concerns the classification performance of the algorithms based on the latent model, we did not detect any statistically significant differences; they all perform similarly. The application of the algorithms to age-at-death estimation showed that the total classification accuracy is overall satisfactory even in datasets with small sample sizes, but the cross-validated accuracy is low when sample sizes are small.

Conclusion

In age-at-death estimations we can use any algorithm from those we studied except for the crude algorithms. However, to increase the classification accuracy, we should increase the size of the classes. Under this prerequisite, we may achieve very high cross-validated classification accuracies, in most cases higher than 90 %.