Karesel Olumsallık Tablolarında Model Uyumunun Sapma Ölçüsü ile Belirlenmesi

Abstract

The joint distribution of categorical variables is summarized by the contingency table. The R × R dimensional contingency tables in which the variables are cross classified according to the same criteria with the number of row variables R and the number of column variable R in contingency tables are called the square contingency table. If a square contingency table has a very small frequency or sample zero, this table is called a sparse contingency table. The most basic model used to analyze the square contingency tables is the full symmetry model. The goodness-of-fit tests are used to decide whether the structure of the table is appropriate for the given model. The power-divergence family of statistics consists of well-known goodness-of-fits statistics, such as Pearson’s χ2, likelihood ratio G2, Freeman-Tukey’s T2, modified G2 and Neyman’s modified χ2. According to the different values that the parameter contains, the function including the goodness-of-fit test statistics following asymptotically chi-square distribution is defined as power-divergence family of statistics. In cases where the symmetry model does not hold, it is studied with non-symmetric models or departure measures. Departure measures represent the degree of departure from the unfitted model as a percentage. Two different departure measures were used in the literature. The first one is a measure of departure obtained from a single result calculated without depending on the parameter. The second one which is also used in the thesis study, is based on the power divergence function and gives different results depending on the parameter. In this thesis study, a two-stage simulation is carried out. In the first stage, the chi-square approach of the test statistics for sparse and non-sparse square contingency tables is evaluated. In the second stage, the relation between the departure measures and the test statistics corresponding to the values of the parameters are examined and, the departure measure is graded to decide the model fitting. It is illustrated on the example that the grading system can be used to decide the model fitting in sparse square contingency tables. All results are discussed on various numerical examples.