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).
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