In this study, we evaluated the lettuce accumulated evapotranspiration (ET) across four levels of irrigation, using a nonlinear mixed‐effects model. The plants were grown in protected environments and monitored over 23 consecutive days. When the moisture of the substrate in the vessels reached 50% of their maximum retention capacity, the water levels were elevated according to four treatments: W 1 = 62.5 %, W 2 = 75.0 %, W 3 = 87.5 %, and W 4 = 100.0 %. The model appeared to provide a good fit to the data and showed that the estimates of the maximum amount of accumulated ET were similar for the three treatments with soil water deficit and lower for W 4. The results of the study supported the idea that optimization of the ET of lettuce plants could be achieved through irrigation with deficit, also indicating that the economical use of water was the most efficient way to boost agricultural production. Recommendations for resource managers The continued growth of the world population will result in a decrease of quality and availability of water and also an increase in demand for food. Therefore, sustainability will depend on high agricultural productivity with rational use of water. Considered the most efficient technology for boosting agricultural productivity, irrigation is also the largest water consumer in the world. With any kind of irrigation in the vegetable production area, the water intake for the plants must be treated with great caution. Both a lack or excess in water can decrease plant productivity. The amount of water available in the soil should be enough to maximize production. It is shown that high levels of irrigation are not necessary for this. It is important to balance the amount of irrigated water for an optimal level, in order that the production has its the production is maximized and valuable water resources are not wasted.
Occasionally, the behavior of a response variable monitored over time can be influenced by an intervention performed during the experimental period. With this perspective, this study proposes a simple methodology based on the fitting of two mixed effects models in longitudinal profiles, before and after an intervention, to verify significant differences. The notoriety of this methodology consists of using all repeated observations from the response variable regarding the intervention. This proposed method was motivated by two real datasets. Linear mixed models were fitted in the first dataset, which refers to the CD4 cells count in HIV-positive patients whom, over 30 consecutive days, received a glutamine based food supplement. For the second dataset, nonlinear mixed effects models were fitted for the body mass measurements of preterm newborns whose initial diet was based on breast milk and was subsequently replaced by a commercial food supplement. The proposed methodology was able to identify differences in the growth trend of the CD4 cells count after the observed patients took glutamine based supplementation. Moreover, it provided evidences suggesting the commercial food supplement as an alternative to a breast milk diet in preterm newborns by maintaining the body mass growth trend.
Data sets with complex structures is increasingly common in dental research. As consequences, statistical methods to analyze and interpret these data must be efficient and robust. Hierarchical structures is one of the most common kind of complex structures, and a proper approach is required. The multilevel modeling used to study hierarchical structures is a powerful tool which allows the collected data to be analyzes in several levels. This study has as objective to make a literature review on multilevel linear models and to illustrate a three level model through a matrix procedure, without the use of specific software to estimate the parameters. With this model, we analyzed the vertical gingival retraction when using the substances: Naphazoline Chloridrate, Aluminium Chloride and without any substance. The intraclass correlation coefficient on dental level within patients showed that the hierarchical structure was important to accommodate the dependence within clusters.
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