ABSTRACT Background: Child undernutrition is a global health concern. Infants and young children are the most vulnerable to undernutrition due to their high nutritional requirements for growth and development. Many studies have focused on the association of childhood undernutrition indicators with their predictors. A few studies have looked at relationship between the undernutrition indicators. Several cross-sectional studies have used the three anthropometric indicators separately to identify the factors associated to undernutrition of children. This study aimed at investigating the possible association structures of childhood undernutrition indicators; and identifying the factors associated with undernutrition of children using a single composite index of anthropometric indicators. Methods: The data set used in the analysis was Children's Data set from 2016 Ethiopia Demographic and Health Survey. Log-linear models were used to fit the cell counts of a three-way table of stunting, wasting, and underweight and comparisons of models were made. A single composite index of undernutrition indicators was created using principal component analysis and recode into ordinal outcome. For this ordinal outcome, partial proportional odds model was fitted to identify significant determinants of undernutrition and its relative performance was compared with some other ordinal regression models. Results: The saturated log-linear model fitted the three-way contingency table well compared to the rest of the unsaturated log-linear models. The fitted log-linear model revealed that underweight is associated with both stunting and wasting, whereas there is no association between stunting and wasting; and there is no three-way interaction among stunting, wasting, and underweight. The Brant test of proportional odds model indicated that the null hypothesis that states the model parameters are equal across categories was rejected. Based on Akaike information criterion, partial proportional odds model suggested an improved fit compared to ordinal regression models that do not need parallel regression assumption. Hence, the fitted partial proportional odds model revealed child’s age, maternal education, region, source of drinking water, number of children under five years, wealth index, anemic status of child, multiple birth, child’s sex, fever, mother’s age at birth, body mass index of mother and husband’s education were significantly associated with children undernutrition. Conclusion and recommendation: The lack of three-way interaction of stunting, wasting, and underweight confirms that the three anthropometric indicators of children are not redundant of each other. Thus, the concerned body should consider the three undernutrition indicators simultaneously to estimate the actual burden of childhood undernourishment. The results of this study, using national data provides evidence to the ministry of health and policy makers about the contributor’s factors of child undernutrition. Some of the interventions that should be taken, so as to have healthy and wellnourished children in Ethiopia, are improving household wealth index and food security, educating mothers and their partners, improving maternal nutritional status and increase access to health care. Key words: Log-linear model, stunting, underweight, wasting, partial proportional odds model