Semiparametric transformation models with Bayesian P-splines

Transformation latent variable models are proposed in this study to analyze multivariate censored data. The proposed models generalize conventional linear transformation models to semiparametric transformation models that accommodate latent variables. The characteristics of the latent variables were assessed based on several correlated observed indicators through measurement equations. A Bayesian approach was developed with Bayesian P-splines technique and the Markov chain Monte Carlo algorithm to estimate the unknown parameters and transformation functions. Simulation shows that the performance of the proposed methodology is satisfactory. The proposed method was applied to analyze a cardiovascular disease data set.

A general multivariate non-linear regression model is considered, including as special cases linear regression when the regression matrix is of less than full rank, simultaneous equations systems and regression on an unobservable predetermined variable. Given a time-series of observations at unit intervals we consider the estimation of the parameters, subject to non-linear constraints, by minimizing a criterion based on the Fourier-transformed model. We allow the residuals to be generated by a stationary, linear, process and establish asymptotic properties of our estimates.

Field‐chamber measurements of soil respiration from 17 different forest and shrubland sites in Europe and North America were summarized and analyzed with the goal to develop a model describing seasonal, interannual and spatial variability of soil respiration as affected by water availability, temperature, and site properties. The analysis was performed at a daily and at a monthly time step. With the daily time step, the relative soil water content in the upper soil layer expressed as a fraction of field capacity was a good predictor of soil respiration at all sites. Among the site variables tested, those related to site productivity (e.g., leaf area index) correlated significantly with soil respiration, while carbon pool variables like standing biomass or the litter and soil carbon stocks did not show a clear relationship with soil respiration. Furthermore, it was evidenced that the effect of precipitation on soil respiration stretched beyond its direct effect via soil moisture. A general statistical nonlinear regression model was developed to describe soil respiration as dependent on soil temperature, soil water content, and site‐specific maximum leaf area index. The model explained nearly two thirds of the temporal and intersite variability of soil respiration with a mean absolute error of 0.82 μmol m−2 s−1. The parameterized model exhibits the following principal properties: (1) At a relative amount of upper‐layer soil water of 16% of field capacity, half‐maximal soil respiration rates are reached. (2) The apparent temperature sensitivity of soil respiration measured as Q10 varies between 1 and 5 depending on soil temperature and water content. (3) Soil respiration under reference moisture and temperature conditions is linearly related to maximum site leaf area index. At a monthly timescale, we employed the approach by Raich et al. [2002] that used monthly precipitation and air temperature to globally predict soil respiration (T&P model). While this model was able to explain some of the month‐to‐month variability of soil respiration, it failed to capture the intersite variability, regardless of whether the original or a new optimized model parameterization was used. In both cases, the residuals were strongly related to maximum site leaf area index. Thus, for a monthly timescale, we developed a simple T&P&LAI model that includes leaf area index as an additional predictor of soil respiration. This extended but still simple model performed nearly as well as the more detailed time step model and explained 50% of the overall and 65% of the site‐to‐site variability. Consequently, better estimates of globally distributed soil respiration should be obtained with the new model driven by satellite estimates of leaf area index. Before application at the continental or global scale, this approach should be further tested in boreal, cold‐temperate, and tropical biomes as well as for non‐woody vegetation.

This paper considers specification testing for regression models with errors-in-variables and proposes a test statistic comparing the distance between the parametric and nonparametric fits based on deconvolution techniques. In contrast to the methods proposed by Hall and Ma (2007, Annals of Statistics, 35, 2620–2638) and Song (2008, Journal of Multivariate Analysis, 99, 2406–2443), our test allows general nonlinear regression models and possesses complementary local power properties. We establish the asymptotic properties of our test statistic for the ordinary and supersmooth measurement error densities. Simulation results endorse our theoretical findings: our test has advantages in detecting high-frequency alternatives and dominates the existing tests under certain specifications.

In this paper, fuzzified Choquet integral and fuzzy-valued integrand with respect to separate measures like fuzzy measure, signed fuzzy measure and intuitionistic fuzzy measure are used to develop regression model for forecasting. Fuzzified Choquet integral is used to build a regression model for forecasting time series with multiple attributes as predictor attributes. Linear regression based forecasting models are suffering from low accuracy and unable to approximate the non-linearity in time series. Whereas Choquet integral can be used as a general non-linear regression model with respect to non classical measures. In the Choquet integral based regression model parameters are optimized by using a real coded genetic algorithm (GA). In these forecasting models, fuzzified integrands denote the participation of an individual attribute or a group of attributes to predict the current situation. Here, more generalized Choquet integral,i.e., fuzzified Choquet integral is used in case of non-linear time series forecasting models. Three different real stock exchange data are used to predict the time series forecasting model. It is observed that the accuracy of prediction models highly depends on the non-linearity of the time series.

A general nonlinear regression model is considered in the form of fitting a sum of damped sinusoids to a series of non-uniform observations. The problem of parameter estimation in this model is important in many applications like signal processing. The corresponding continuous optimization problem is typically difficult due to the high multiextremal character of the objective function. It is shown how Lipschitz-based deterministic methods can be well-suited for studying these challenging global optimization problems, when a limited computational budget is given and some guarantee of the found solution is required.

Bayesian analysis relies heavily on the Markov chain Monte Carlo (MCMC) algorithm to obtain random samples from posterior distributions. In this study, we compare the performance of MCMC stopping rules and provide a guideline for determining the termination point of the MCMC algorithm in latent variable models. In simulation studies, we examine the performance of four different MCMC stopping rules: potential scale reduction factor (PSRF), fixed‐width stopping rule, Geweke's diagnostic, and effective sample size. Specifically, we evaluate these stopping rules in the context of the DINA model and the bifactor item response theory model, two commonly used latent variable models in educational and psychological measurement. Our simulation study findings suggest that single‐chain approaches outperform multiple‐chain approaches in terms of item parameter accuracy. However, when it comes to person parameter estimates, the effect of stopping rules diminishes. We caution against relying solely on the univariate PSRF, which is the most popular method, as it may terminate the algorithm prematurely and produce biased item parameter estimates if the cut‐off value is not chosen carefully. Our research offers guidance to practitioners on choosing suitable stopping rules to improve the precision of the MCMC algorithm in models involving latent variables.

TAO-robust backpropagation learning algorithm

Recently, interest has grown in the use of instrumental variables (IVs) in estimating factor analysis and latent variable models such as structural equations models. Bollen (1996) suggested a two-stage least squares (2SLS) technique that makes use of model-implied IVs in estimating the measurement and latent variable models. Model-implied instrumental variables are the observed variables in the model that can serve as instrumental variables in a given equation. One difficulty inhibiting the practical use of the 2SLS estimator is identifying the model-implied IVs. The authors provide a simple procedure that identifies the model-implied IVs and a computer algorithm that can easily be implemented to automate the selection of IVs for simultaneous equations, factor analysis, and latent variable models.

It is common to model responses to surveys within latent variable frameworks (e.g., item response theory [IRT], confirmatory factor analysis [CFA]) and use model fit indices to evaluate model-data congruence. Unfortunately, research shows that people occasionally engage in careless responding (CR) when completing online surveys. While CR has the potential to negatively impact model fit, this issue has not been systematically explored. To better understand the CR-fit linkage, two studies were conducted. In study 1, participants' response behaviors were experimentally shaped and used to embed aspects of a comprehensive simulation (study 2) with empirically informed data. For this simulation, 144 unique conditions (which varied the sample size, number of items, CR prevalence, CR severity, and CR type), two latent variable models (IRT, CFA), and six model fit indices (χ2, RMSEA, SRMSR [CFA] and M2, RMSEA, SRMSR [IRT]), were examined. The results indicated that CR deteriorates model fit under most circumstances, though these effects are nuanced, variable, and contingent on many factors. These findings can be leveraged by researchers and practitioners to improve survey methods, obtain more accurate survey results, develop more precise theories, and enable more justifiable data-driven decisions.

We propose a novel Bayesian model framework for discrete ordinal and count data based on conditional transformations of the responses. The conditional transformation function is estimated from the data in conjunction with an a priori chosen reference distribution. For count responses, the resulting transformation model is novel in the sense that it is a Bayesian fully parametric yet distribution-free approach that can additionally account for excess zeros with additive transformation function specifications. For ordinal categoric responses, our cumulative link transformation model allows the inclusion of linear and non-linear covariate effects that can additionally be made category-specific, resulting in (non-)proportional odds or hazards models and more, depending on the choice of the reference distribution. Inference is conducted by a generic modular Markov chain Monte Carlo algorithm where multivariate Gaussian priors enforce specific properties such as smoothness on the functional effects. To illustrate the versatility of Bayesian discrete conditional transformation models, applications to counts of patent citations in the presence of excess zeros and on treating forest health categories in a discrete partial proportional odds model are presented.

Objectives/Scope A stable, single-well deconvolution algorithm has been introduced for well test analysis in the early 2000’s, that allows to obtain information about the reservoir system not always available from individual flow periods, for example the presence of heterogeneities and boundaries. One issue, recognised but largely ignored, is that of uncertainty in well test analysis results and non-uniqueness of the interpretation model. In a previous paper (SPE 164870), we assessed these with a Monte Carlo approach, where multiple deconvolutions were performed over the ranges of expected uncertainties affecting the data (Monte Carlo deconvolution). Methods, Procedures, Process In this paper, we use a non-linear Bayesian regression model based on models of reservoir behaviour in order to make inferences about the interpretation model. This allows us to include uncertainty for the measurements which are usually contaminated with large observational errors. We combine the likelihood with flexible probability distributions for the inputs (priors), and we use Markov Chain Monte Carlo algorithms in order to approximate the probability distribution of the result (posterior). Results, Observations, Conclusions We validate and illustrate the use of the algorithm by applying it to the same synthetic and field data sets as in SPE 164870, using a variety of tools to summarise and visualise the posterior distribution, and to carry out model selection. Novel/Additive Information The approach used in this paper has several advantages over Monte Carlo deconvolution: (1) it gives access to meaningful system parameters associated with the flow behaviour in the reservoir; (2) it makes it possible to incorporate prior knowledge in order to exclude non-physical results; and (3) it allows to quantify parameter uncertainty in a principled way by exploiting the advantages of the Bayesian approach.

This article proposes a joint modeling framework for longitudinal insomnia measurements and a stochastic smoking cessation process in the presence of a latent permanent quitting state (i.e., 'cure'). We use a generalized linear mixed-effects model and a stochastic mixed-effects model for the longitudinal measurements of insomnia symptom and for the smoking cessation process, respectively. We link these two models together via the latent random effects. We develop a Bayesian framework and Markov Chain Monte Carlo algorithm to obtain the parameter estimates. We formulate and compute the likelihood functions involving time-dependent covariates. We explore the within-subject correlation between insomnia and smoking processes. We apply the proposed methodology to simulation studies and the motivating dataset, that is, the Alpha-Tocopherol, Beta-Carotene Lung Cancer Prevention study, a large longitudinal cohort study of smokers from Finland.

Testlet design has been widely adopted in educational and psychological assessment. A testlet is a cluster of items that share a common stimulus(e.g., a reading comprehension passage or a figure), and the possible local dependence among items within a testlet is called testlet-effect. Various models have been developed to take into account such testlet effect. Examples included the Rasch testlet model, two-parameter logistic Bayesian testlet model, and higher-order testlet model. However, these existing models all assume that an item is affected by only one single testlet effect. Therefore, they are essentially unidimensional testlet-effect models. In practice, multiple testlet effects may simultaneously affect item responses in a testlet. For example, in addition to common stimulus, items can be grouped according to their domains, knowledge units, or item format, such that multiple testlet effects are involved. In essence, an item measures multiple latent traits, in addition to the target latent trait(s) that the test was designed to measure. Existing unidimensional testlet-effect models become inapplicable when multiple testlet effects are involved. To account for multiple testlet effect, in this study we develop the so-called(within-item) multidimensional testlet-effect Rasch model. The parameters can be estimated with marginal maximum likelihood estimation methods or Bayesian methods with Markov chain Monte Carlo(MCMC) algorithms. In this study, a popular computer program for Rasch models, ConQuest, was used. A series of simulations were conducted to evaluate parameter recovery of the new model, consequences of model misspecification, and the effectiveness of model-data fit statistics. Results show that the parameters of the new model can be recovered fairly well; and ignoring the multiple testlet effects resulted in a biased estimation of item parameters, and an overestimation of test reliability. Additionally, it did little harm on parameter estimation to fit a more complicated model(i.e., the multidimensional testlet-effect Rasch model) to data with a simple structure. In conclusion, the new model is feasible and flexible.

This paper presents a novel partially linear varying coefficient skew-normal spatial autoregression model for accommodating actual data that exhibit skewed tail behaviour, which may not be well modelled by normally distributed errors. We first utilize Bayesian P-splines to effectively approximate the nonparametric components of the model. Along with the Metropolis importance sampling algorithm for the nonparametric components of the model, we propose an effective Markov Chain Monte Carlo algorithm that integrates Gibbs sampling and the Metropolis-Hastings algorithm to generate posterior samples from the joint posterior distribution, thus facilitating statistical inference. We carry out extensive simulation studies to investigate the finite sample performance of the proposed method. Numerical results show that the proposed method is capable of effectively addressing the characteristics of skewed data and yielding conclusions that align well with the simulations under consideration. Finally, a real-data application is provided for illustrative purposes.