Abstract

In mixture modeling, it is assumed that the data set shows a heterogeneous structure. This heterogeneity is defined as unobservable heterogeneity. The data set’s heterogeneity produces serious deviations in the parameter estimates and the standard deviations. Heterogeneity is overcome when the data set divides itself into homogeneous sub-populations. Thus, while homogeneity is attained for sub-populations, the heterogeneity between the sub-populations is tried to be put forward. Akaike’s information criteria (AIC), Bayesian information criteria (BIC), and Entropy classification criteria are used to determine the number of sub-populations. After the number of sub-populations is determined, the model determines the probability that each observation will fall within a particular sub-population. In this study, the classification of districts based on fruit traits is achieved by applying mixture modeling to walnut fruits collected from eight districts. According to the AIC, BIC, and entropy criteria, a model with five sub-populations was chosen where the data set is the most distributed. Therefore, it was determined that each district does not form a different population according to the studied walnut fruit traits, but are distributed into five sub-populations. The fourth sub-population had the most desirable traits for walnut improvement, and the highest proportion of these traits came from the naturally grown populations of Adilcevaz and Ahlat districts.

Key words: Mixture model, classification, EM algorithm, latent class analysis, Walnut.