Box–Cox t random intercept model for estimating usual nutrient intake distributions
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The issue of estimating usual nutrient intake distributions and prevalence of inadequate nutrient intakes is of interest in nutrition studies. Box–Cox transformations coupled with the normal distribution are usually employed for modeling nutrient intake data. When the data present highly asymmetric distribution or include outliers, this approach may lead to implausible estimates. Additionally, it does not allow interpretation of the parameters in terms of characteristics of the original data and requires back transformation of the transformed data to the original scale. This paper proposes an alternative approach for estimating usual nutrient intake distributions and prevalence of inadequate nutrient intakes through a Box–Cox t model with random intercept. The proposed model is flexible enough for modeling highly asymmetric data even when outliers are present. Unlike the usual approach, the proposed model does not require a transformation of the data. A simulation study suggests that the Box–Cox t model with random intercept estimates the usual intake distribution satisfactorily, and that it should be preferable to the usual approach particularly in cases of highly asymmetric heavy-tailed data. In applications to data sets on intake of 19 micronutrients, the Box–Cox t models provided better fit than its competitors in most of the cases.
KeywordsBox–Cox Cole–Green distribution Box–Cox t distribution Box–Cox transformation NCI method Nutrient intake
We thank the reviewers for their valuable comments and suggestions on an earlier version of the paper. We gratefully acknowledge the financial support of the Brazilian agencies FAPESP (grants 2008/10261-8 and 2012/21788-2) and CNPq (grant 304388/20149).
- Carriquiry AL (1998) Assessing the prevalence of nutrient inadequacy. Public Health Nutr 2:23–33Google Scholar
- Institute of Medicine, Food and Nutrition Board (2003) Dietary reference intakes: applications in dietary planning. National Academies Press, Washington. [Acessed in 31 May, 2017], Subcommittee on interpretation and uses of dietary reference intakes and the standing committee on the scientific evaluation of dietary reference intakes. Available at https://www.ncbi.nlm.nih.gov/books/NBK221369/pdf/Bookshelf_NBK221369.pdf
- Nutrition Coordenating Center (2012) Nutrition data system for research. NDS-R. Features. http://www.ncc.umn.edu/products/. Accessed 31 May 2017
- Pinheiro JC, Bates DM (1995) Approximations to the log-likelihood function in the nonlinear mixed-effects model. J Comput Graph Stat 4:12–35Google Scholar
- R Core Team (2008) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN: 3-900051-07-0Google Scholar
- SAS Institute Inc. (2012) SAS/STAT 12.1 user’s guide. SAS Institute Inc., CaryGoogle Scholar