Binary variable extraction using nonlinear principal component analysis in classical location model

Location model is a predictive classification model that determines the groups of objects which contain mixed categorical and continuous variables. The simplest location model is known as classical location model, which can be constructed easily using maximum likelihood estimation. This model performs ideally with few binary variables. However, there is an issue of many empty cells when it involves a large number of binary variables, b due to the exponential growth of multinomial cells by 2b. This issue affects the classification accuracy badly when no information can be obtained from the empty cells to estimate the required parameters. This issue can be solved by implementing the dimensionality reduction approach into the classical location model. Thus, the objective of this study is to propose a new
classification strategy to reduce the large binary variables. This can be done by integrating classical location model and nonlinear principal component analysis where the binary variables reduction is based on variance accounted for, VAF. The proposed location model was tested and compared to the classical location model using leave-one-out method. The results proved that the proposed location model could reduce the number of empty cells and has better performance in term of
misclassification rate than the classical location model. The proposed model was also validated using a real data. The findings showed that this model was comparable or even better than the existing classification methods. In conclusion, this study demonstrated that the new proposed location model can be an alternative method in solving the mixed variable classification problem, mainly when facing
with a large number of binary variables.