A Bayesian Approach to Unit Lindley Mixed Model

In the applied filed of many areas such as Business and Economics, Physical, Biological, Medical, Environmental, and Social Sciences, Psychology, and Educations outcome measurements like rates, proportions, and fractions are common. Researchers have proven that using normal linear regression to analyze the relationship between outcome measurements such as rates and proportions and a set of independent variables can violates key assumptions of the method. Transformation techniques are usually applied to correct the assumptions, but this practice can violate the probability property of bounded nature of outcome variables. Even though beta regression was one of the popular methods to analyze bounded data situations, the latest development of unit-Lindley distribution and its associate regression was found to be superior. Unit-Lindley regression requires uncorrelated response variables; but in real applied fields, researchers may encounter clustered or correlated response variables. Thus, mixed models that are capable to handle correlated and clustered response variables are required. Therefore, unit-Lindley mixed model, that is capable to analyze correlated and bounded response variable and a set of independent variables is one of the suitable model choices. It is widely accepted and proven by researchers that the Bayesian parameter estimation approach is more advantageous over a classical approach in the case of mixed models in several ways. Despite the several advantages of the Bayesian approach, it has not been applied to the unit-Lindley mixed model. Therefore, this dissertation aims to develop a Bayesian approach to unit-Lindley mixed model. Additionally, the assumption of normality for random effects may not be appropriate when dealing with skewed data. Thus, this dissertation also aims to apply three distributional assumptions for random effects: normal, skew-normal, and skew-t. To achieve the research aims outlined in this dissertation, a Bayesian unit-Lindley mixed model with distributional assumptions of normal, skew-normal, and skew-t for random effects was developed. To implement them, a STAN program code was also developed and presented in this dissertation. A variety of simulated data situations were used to test all models in R. Leave-One-Out Cross-Validation Information Criterion (LOOIC) and Watanabe-Akaike Information Criterion (WAIC) were used to compare the modes. In addition, bias and RMSE of intercept and its variance were also used to support the results of LOOIC and WAIC. The results confirmed that a Bayesian unit-Lindley model with normal assumption of random effects performed better as compered to the model with two other assumptions when the data situation was approximately normal with normal random effects. However, when the response variable is skewed with a skewed random effects, model with the normal assumption was less robust than the model with skew-normal and skew-t random effects. While comparing the model with skew-normal and skew-t random effects, the model with skew-normal produced slightly less biased parameter estimation and RMSE and smaller LOOIC and WAIC. Finally, all the models were applied to analyze the child mortality rates across the countries of South Asia, and their performance was compared. After testing the models by using the simulation method and applying to a real data situation, it was confirmed that a Bayesian unit-Lindley model is ready to apply in any fields of the applied areas where measurement of outcome variable is clustered and bounded within unit interval

Impacts of Altered Precipitation Frequency, Clipping, and Competition on Perennial Grasses Mediated Through Belowground Bud Bank in Northern Mixed-Grass Prairie

Perennial grasslands are remarkably resilient to severe natural and anthropogenic disturbances. Such resiliency largely depends on successful tiller recruitment and establishment from belowground bud banks. In the northern Great Plains, introduced perennial smooth bromegrass (Bromus inermis) has been rapidly invading and transforming larger tracts of native prairies by replacing native perennial species, such as western wheatgrass (Pascopyrum smithii), reducing biodiversity and quality of habitats, and increasing vulnerability of grasslands to other environmental disturbances. In this study, we evaluated the response of belowground bud production, tiller and rhizome recruitment, and plant establishment between the native P. smithii and the non-native B. inermis to altered precipitation frequency, clipping, and competition with two different controlled greenhouse experiments over two growing seasons. In the first experiment, the treatments consisted of combinations of three precipitation frequencies (every 2d, 8d, and 16d) representing high, medium, and low, two levels of clipping (clipping vs. no-clipping), and two species with 40 replicates for each treatment. One single-leaf seedling of each species was transplanted into individual potting-soil filled pots in mid-June. We initiated precipitation frequency treatments and applied a clipping treatment two weeks after transplanting. Plants were harvested 20 weeks after the treatments had been initiated. The number of tillers and rhizomes based on generation, number of tillers based on location (crown vs. rhizome), and rhizome length were recorded. Three randomly sub-sampled tillers and rhizomes from each generation were dissected to record the number of buds and propagule development. We found B. inermis significantly decreased their number of tillers, rhizomes, rhizome length, and live propagules at the low precipitation frequency, but increased propagule development at medium precipitation frequency. However, P. smithii significantly increased the traits described above under medium precipitation frequency, except for the number of tillers and propagule development, which were not affected at medium and low precipitation frequency. The clipping significantly reduced tiller production for both species and the number of rhizomes for B. inermis. The results indicate that non-native B. inermis may be more susceptible to the altered precipitation frequency and clipping compared to native P. smithii. Native P. smithii may be able to resist the soil moisture variability and clipping effects mediated via the belowground bud banks. The second competition experiment consisted of five treatments including single B. smithii, single P. smithii, pairwise monoculture of B. inermis, pairwise monoculture of P. smithii, and pairwise mixed-culture of B. inermis and P. smithii with 30 replicates for each treatment under every 2d precipitation frequency regime. Double-leaf seedlings of each species were transplanted into individual potting soil-filled pots based on designated treatments. Plants were harvested 12 weeks after the treatments had been initiated. The data collection followed the same protocol as the first experiment. In addition, biomass and relative interaction index (RII) were calculated to determine intra- and inter-specific competition between P. smithii and B. inermis. We found that the presence of B. inermis as a neighbor significantly decreased the number of live propagules, tillers, and aboveground biomass of the native P. smithii. However, the presence of P. smithii as a neighbor significantly increased the number of live propagules and had significantly less negative effect on tiller production and aboveground biomass of B. inermis. Also, investment in dual phalanx and guerilla growth by B. inermis while competing with P. smithii indicates possible phenotypic plasticity trait. All results demonstrated a strong competitive ability of the non-native B. inermis against P. smithii during the establishment phase when environmental conditions are favorable (i.e. lack of water stress and grazing). Overall, we can conclude that species establishment and interaction between these two key perennial grasses in northern mixed-grass prairies is environmentally dependent and species specific. The outcomes are mediated by the response of the belowground bud bank. The findings from this study can help us to better understanding the mechanisms of bud banks in maintaining tiller population, regulating vegetation dynamics, productivity, and response to climate change in the context of grazing practices and invasion by nonnative perennial grasses. They could form the basis for a long-term effective grassland management plan

Judicial Partisanship in a Partisan Era: A Reply to Professor Robertson

Professor Cassandra Burke Robertson’s outstanding article, Judicial Impartiality in A Partisan Era, is timely given the increasing politicization of the judiciary. The political debate and controversy around the Judge Garland nomination and the Justice Kavanaugh confirmation to the United States Supreme Court, only served to reaffirm that the judiciary is not immune from the growing political polarization in America. And it is not just senate judicial confirmation battles that have become highly bitter and partisan. Scholars writing about the substantive work of the Court have argued that it is more akin to a political body than a judicial one, and others have called for constitutional issues to be taken away from the Court. The recent spate of 5–4 decisions upholding President Trump’s immigration policies will further convince many people that Supreme Court justices are nothing more than politicians in robes

School of Law_Dean Update_March 17, 2020

Email update from Dmitry Bam, Interim Dean and Professor of Law, University of Maine School of Law regarding COVID-19