Bayesian Analysis of Population Health Data

Bayesian multilevel logistic regression models: a case study applied to the results of two questionnaires administered to university students

Bayesian multilevel models—also known as hierarchical or mixed models—are used in situations in which the aim is to model the random effect of groups or levels. In this paper, we conduct a simulation study to compare the predictive ability of 1-level Bayesian multilevel logistic regression models with that of 2-level Bayesian multilevel logistic regression models by using the prior Scaled Beta2 and inverse-gamma distributions to model the standard deviation in the 2-level. Then, these models are employed to estimate the correct answers in two questionnaires administered to university students throughout the first academic semester of 2018. The results show that 2-level models have a better predictive ability and provide more precise probability intervals than 1-level models, particularly when the prior Scaled Beta2 distribution is used to model the standard deviation in the second level. Moreover, the probability intervals of 1-level Bayesian multilevel logistic regression models proved to be more precise when Scaled Beta2 distributions, rather than an inverse-gamma distribution, are employed to model the standard deviation or when 1-level Bayesian multilevel logistic regression models, are used.

Survival with Random Effect

The article focuses on mortality models with a random effect applied in order to evaluate human mortality more precisely. Such models are called frailty or Cox models. The main assertion of the paper shows that each positive random effect transforms the initial hazard rate (or density function) to a new absolutely continuous survival function. In particular, well-known Weibull and Gompertz hazard rates and corresponding survival functions are analyzed with different random effects. These specific models are presented with detailed calculations of hazard rates and corresponding survival functions. Six specific models with a random effect are applied to the same data set. The results indicate that the accuracy of the model depends on the data under consideration.

ML-LME: A Plant Growth Situation Analysis Model Using the Hierarchical Effect of Fractal Dimension

Rice plays an essential role in agricultural production as the most significant food crop. Automated supervision in the process of crop growth is the future development direction of agriculture, and it is also a problem that needs to be solved urgently. Productive cultivation, production and research of crops are attributed to increased automation of supervision in the growth. In this article, for the first time, we propose the concept of rice fractal dimension heterogeneity and define it as rice varieties with different fractal dimension values having various correlations between their traits. To make a comprehensive prediction of the rice growth, Machine Learning and Linear Mixed Effect (ML-LME) model is proposed to model and analyze this heterogeneity, which is based on the existing automatic measurement system RAP and introduces statistical characteristics of fractal dimensions as novel features. Machine learning algorithms are applied to distinguish the rice growth stages with a high degree of accuracy and to excavate the heterogeneity of rice fractal dimensions with statistical meaning. According to the information of growth stage and fractal dimension heterogeneity, a precise prediction of key rice phenotype traits can be received by ML-LME using a Linear Mixed Effect model. In this process, the value of the fractal dimension is divided into groups and then rices of different levels are respectively fitted to improve the accuracy of the subsequent prediction, that is, the heterogeneity of the fractal dimension. Afterwards, we apply the model to analyze the rice pot image. The research results show that the ML-LME model, which possesses the hierarchical effect of fractal dimension, performs more excellently in predicting the growth situation of plants than the traditional regression model does. Further comparison confirmed that the model we proposed is the first to consider the hierarchy structure of plant fractal dimension, and that consideration obviously strengthens the model on the ability of variation interpretation and prediction precision.