Academic literature on the topic 'Finite mixture of quantile regression model spatial data'

This paper studies a quantile regression spatial dynamic Durbin panel data (SDDPD) model with fixed effects. Conventional fixed effects estimators of quantile regression specification are usually biased in the presentation of lagged response variables in spatial and time as regressors. To reduce this bias, we propose the instrumental variable quantile regression (IVQR) estimator with lagged covariates in spatial and time as instruments. Under some regular conditions, the consistency and asymptotic normalityof the estimators are derived. Monte Carlo simulations show that our estimators not only perform well in finite sample cases at different quantiles but also have robustness for different spatial weights matrices and for different disturbance term distributions. The proposed method is used to analyze the influencing factors of international tourism foreign exchange earnings of 31 provinces in China from 2011 to 2017.

In the last decade, the usage of advanced statistical models is growing rapidly in many different disciplines. However, the Quantile Regression Mixture Model (QRMIX), which is a developed approach of the Finite Mixture Model (FMM), is an applicable new method in the educational literature. The aim of the proposed study was to determine factors affecting students' science achievement using the QRMIX approach. To reach this aim, data of the Programme for International Student Assessment (PISA) survey, which has been conducted by the Organization Economic for Co-Operation and Development (OECD) every 3 years, was used. Dataset used in the research is composed of 6,115 students from Singapore, which is the top-performer country among the participant countries, and 5,895 students from Turkey. The results showed that the factors affecting students' science achievement and its importance on the achievement differentiated according to the achievement levels of the students. In conclusion, it was revealed that Turkish students with the lowest science achievement level should be supported with home possessions, perceived feedback, and environmental awareness and Singaporean students with the lowest achievement level should be supported with perceived feedback, enjoyment of science, and epistemological beliefs. Keywords: finite mixture models, Programme for International Student Assessment, quantile regression mixture models, science performance.

Abstract Thorson, J. T., Stewart, I. J., and Punt, A. E. 2012. Development and application of an agent-based model to evaluate methods for estimating relative abundance indices for shoaling fish such as Pacific rockfish (Sebastes spp.). – ICES Journal of Marine Science, 69: 635–647. Many marine fish, including Pacific rockfish (Sebastes spp.), exhibit habitat-selective and shoaling behaviours, which can lead to imprecision when using survey data to estimate an annual index of stock abundance. We develop a spatial agent-based model (ABM) for Pacific rockfish, which generates data similar to those observed in existing bottom-trawl surveys and can represent various spatial and shoaling behaviours. We use the ABM to evaluate the performance of a model that uses mixture distribution methods to account for fish shoals and delta-methods to account for range expansion or contraction. This delta-mixture model is compared with conventional delta-generalized linear models (delta-GLMs) and a quantile regression delta-model. The delta-mixture increases precision by 15% relative to delta-GLMs in estimated abundance indices when shoaling behaviours are present, whereas precision is similar between delta-GLM and delta-mixture models when shoals are absent. The delta-quantile method has similar improvements over conventional delta-GLM methods, and the improved precision from delta-mixture and delta-quantile methods is decreased but not eliminated by decreased sampling intensities. These simulations represent the first evaluation of delta-mixture models for index standardization and show a substantial improvement over conventional delta-GLMs for shoaling species such as Pacific rockfish.

This article develops a two-part finite mixture quantile regression model for semi-continuous longitudinal data. The proposed methodology allows heterogeneity sources that influence the model for the binary response variable to also influence the distribution of the positive outcomes. As is common in the quantile regression literature, estimation and inference on the model parameters are based on the asymmetric Laplace distribution. Maximum likelihood estimates are obtained through the EM algorithm without parametric assumptions on the random effects distribution. In addition, a penalized version of the EM algorithm is presented to tackle the problem of variable selection. The proposed statistical method is applied to the well-known RAND Health Insurance Experiment dataset which gives further insights on its empirical behaviour.

Observed data are frequently characterized by a spatial dependence; that is the observed values can be influenced by the "geographical" position. In such a context it is possible to assume that the values observed in a given area are similar to those recorded in neighboring areas. Such data is frequently referred to as spatial data and they are frequently met in epidemiological, environmental and social studies, for a discussion see Haining, (1990). Spatial data can be multilevel, with samples being composed of lower level units (population, buildings) nested within higher level units (census tracts, municipalities, regions) in a geographical area. Green and Richardson (2002) proposed a general approach to modelling spatial data based on finite mixtures with spatial constraints, where the prior probabilities are modelled through a Markov Random Field (MRF) via a Potts representation (Kindermann and Snell, 1999, Strauss, 1977). This model was defined in a Bayesian context, assuming that the interaction parameter for the Potts model is fixed over the entire analyzed region. Geman and Geman (1984) have shown that this class process can be modelled by a Markov Random Field (MRF). As proved by the Hammersley-Clifford theorem, modelling the process through a MRF is equivalent to using a Gibbs distribution for the membership vector. In other words, the spatial dependence between component indicators is captured by a Gibbs distribution, using a representation similar to the Potts model discussed by Strauss (1977). In this work, a Gibbs distribution, with a component specific intercept and a constant interaction parameter, as in Green and Richardson (2002), is proposed to model effect of neighboring areas. This formulation allows to have a parameter specific to each component and a constant spatial dependence in the whole area, extending to quantile and m-quantile regression the proposed by Alfò et al. (2009) who suggested to have both intercept and interaction parameters depending on the mixture component, allowing for different prior probability and varying strength of spatial dependence. We propose, in the current dissertation to adopt this prior distribution to define a Finite mixture of quantile regression model (FMQRSP) and a Finite mixture of M-quantile regression model (FMMQSP), for spatial data.