A model for clustering of longitudinal data sets of infant mortality rates in India

Cluster analysis is used to assign a set of observations into clusters that have similar characteristics as measured by a set of classifying variables. There have been few studies on clusters of longitudinal datasets or the mathematical and statistical modeling of partitioning of time trends. We present a model to cluster the infant mortality rate trends for 14 major states of India from 1972 to 1998.

Each state is represented as an nth degree polynomial using the curvilinear regression method. The total difference in the rate of change from time t1 (1972) to tn (1998) for each state is obtained by summing the differences in velocity between two adjacent time points (1), and the Euclidean distance of the trend from the base is calculated objectively by dividing the trend into the optimum number of divisions (2). By adding these two (1 & 2), the measure of dissimilarity coefficient is obtained, which is finally used to cluster the trends.

In this case, all three methods, i.e. complete linkage, average between groups, and Ward's linkage method (using SPSS 10.0), suggested the same number and type of clusters. Cluster I has only one state, Cluster II consists of four states, Cluster III has eight states, and Cluster IV has only one state.

Such clustering and grouping gives much more confidence to planners in devising strategies for the control of infant mortality and resource allocation at the national level.