Use of mixture model approach for classification

Mixture modelling is identification of the amount of homogeneous subsets by determining the unobservable heterogeneity in that data set. Thus, homogeneity within subgroups and heterogeneity among subgroups are achieved. Akaiki, Bayesian and entropy information criteria are used to determine the number of subgroups. In mixture modelling, the parameter estimations are obtained by the maximum likelihood method using the EM algorithm. Mixture modelling is used to define relationships between variables, to reduce the size, and to estimate the individual parameters for each subset obtained. This method gives more explanatory results than clustering and factor analysis. Mixture modelling is applied to both discrete and continuous data. Normal mixture modelling is used when the data show normal distribution. In this study, the happiness map of the provinces in Turkey (2013) was obtained by using variables such as children, spouse, parents, the individual himself, grandchildren, health, love, success, money and job as a source of happiness. In other words, by using the normal mixture model, provinces were formed as 6 subgroups. This is applied according to the defined criteria of happiness; homogeneous within themselves, and yet heterogeneous among themselves. For each subgroup, the parameter estimation values were also obtained. Mardin is the first among the provinces that does not consider children as a source of happiness. This province is followed by the provinces in Eastern Anatolia, South-eastern Anatolia and the Black Sea Region. The provinces that take the spouse as a source of happiness with the highest average are Ağrı, Bitlis and Muş. It is found that generally, Eastern Anatolia and South-eastern Anatolia regions do not consider health status as a source of happiness and they consider love as a source of happiness when compared to other regions. Keywords: Akaike, Bayesian, Entropy, Mixture Model, Normal Mixture Model.