VALIDATION OF MEXICAN FOOD SECURITY SCALE THROUGH TETRACHORIC CORRELATION BASED ON BIVARIATE SKEW NORMAL DISTRIBUTION

Abstract

Food security in Mexico is evaluated using the Mexican Food Security Scale (EMSA), composed of dichotomous-response items that measure access to food in households with and without children (members under 18 years-old). One way to validate EMSA is through Confirmatory Factor Analysis (CFA), by comparing the structures of latent variables with the observed data. The correlation between EMSA items is obtained using tetrachoric correlation on a double-entry contingency table, which assumes latent variables with a normal distribution. However, the symmetry assumption does restrict the admission of variables that do not satisfy this assumption, such as economic variables, which are characterized by a skewed distribution. The aim of this research was to propose an estimator of the tetrachoric correlation for different levels of skewness. This coefficient was denoted ρ_tSN, which minimizes the difference between the proportion of coincidences of the dichotomous variables under study and the probability of the Bivariate Skew Normal distribution. ρ_tSN was characterized by its statistical consistency and robustness at the different levels of skewness considered. The CFA models with EMSA 2014 data confirmed the theoretical structure of the scale for adults. In households with children, the CFA suggested a confusion in the comprehension of items related to hunger experiences. The model suggests that a lack of money or resources limits the variety of food and forces either adults or children to skip one meal. These findings were only visible by the CFA with the inclusion of the proposed coefficient ρ_tSN. The proposed estimation method helps analyze the correlation between dichotomous variables with a certain level of skewness, which can be defined with knowledge of the topic under study.