Background: Ethiopia is one of the developing countries where child under-nutrition is prevalent. Prior studies employed three anthropometric indicators for identifying factors of children’s under-nutrition. This study aimed at identifying factors of child under-nutrition using a single composite index of anthropometric indicator. Methods: Data from Ethiopia’s Demographic and Health Survey 2016 was the base for studying under-nutrition in a sample of 9494 children below 59 months. A single composite index of under-nutrition was created from three anthropometric indices through principal component analysis recoded into an ordinal outcome. In line with WHO 2006 Child Growth Standards, the three anthropometric indices involve z-score of height-for-age (stunting), weight-for-height (wasting) and weight-for-age (underweight). To identify significant determinants of under-nutrition , partial proportional odds model was fitted and its relative performance compared with some other ordinal regression models. Results: The single composite index of anthropometric indicators showed that 49.0% (19.8% moderately and 29.2% severely) of sampled children were undernourished. In the Brant-test of proportional odds model, the null hypothesis that the model parameters equal across categories was rejected. Compared to ordinal regression models that do not involve parallel regression assumption, and Akaike information criterion, partial proportional odds model showed an improved fit. A child with mother of body mass index less than 18.5 kg, from poorest family, a husband without education and male to be in a severe under-nutrition status was 1.4, 1.8 1.2 and 1.2 times more likely to be in worse under-nutrition status compared to its reference group respectively. Conclusion: The authors conclude that the fitted partial proportional odds model indicated that age and sex of the child, maternal education, region, source of drinking water, number of under five children, mother’s body mass index, wealth index, anemic status, multiple birth, fever before two months of survey, mother’s age at first birth, and husband’s education were significantly associated with child under-nutrition. Thus, it is argued that interventions focus on improving household wealth index, food security, educating mothers and their spouses, improving maternal nutritional status, and increasing mothers’ health care access.