Monte Carlo Simulation Study Research Articles

A defective cure rate quantile regression model for male breast cancer data

In this article, we particularly address the problem of assessing the impact of different prognostic factors, such as clinical stage and age, on the specific survival times of men with breast cancer when cure is a possibility. To this end, we developed a quantile regression model for survival data in the presence of long-term survivors based on the generalized Gompertz distribution in a defective version, which is conveniently reparametrized in terms of the q-th quantile and then linked to covariates via a logarithm link function. This proposal allows us to obtain how each variable affects the survival times in different quantiles. In addition, we are able to study the effects of covariates on the cure rate as well. We consider Markov Chain Monte Carlo methods to develop a Bayesian analysis in the proposed model and we evaluate its performance through Monte Carlo simulation studies. Finally, we illustrate the application of our model in a data set about male breast cancer from Brazil analyzed for the very first time.

A Sequential Learning Procedure for Estimating Coefficients in Linear Regression With Applications to Online Sales Examination

ABSTRACTIn this paper, we consider the problem of estimating coefficients in a linear regression model. We propose a sequential learning procedure to determine the sample size for achieving a given small estimation risk, under the widely used Gauss‐Markov setup with independent normal errors. The procedure is proven to enjoy the second‐order efficiency and risk‐efficiency properties, which are validated through Monte Carlo simulation studies. Using e‐commerce data, we implement the procedure to examine the influential factors of online sales.

Parametric Quantile Autoregressive Conditional Duration Models With Application to Intraday Value‐at‐Risk Forecasting

ABSTRACTThe modeling of high‐frequency data that qualify financial asset transactions has been an area of relevant interest among statisticians and econometricians—above all, the analysis of time series of financial durations. Autoregressive conditional duration (ACD) models have been the main tool for modeling financial transaction data, where duration is usually defined as the time interval between two successive events. These models are usually specified in terms of a time‐varying mean (or median) conditional duration. In this paper, a new extension of ACD models is proposed which is built on the basis of log‐symmetric distributions reparametrized by their quantile. The proposed quantile log‐symmetric conditional duration autoregressive model allows us to model different percentiles instead of the traditionally used conditional mean (or median) duration. We carry out an in‐depth study of theoretical properties and practical issues, such as parameter estimation using maximum likelihood method and diagnostic analysis based on residuals. A detailed Monte Carlo simulation study is also carried out to evaluate the performance of the proposed models and estimation method in retrieving the true parameter values as well as to evaluate a form of residuals. Finally, we derive a semiparametric intraday value‐at‐risk (IVaR) model and then the proposed models are applied to two price duration data sets.

Optimal Number of Replications for Obtaining Stable Dynamic Fit Index Cutoffs

Factor analysis is commonly used in behavioral sciences to measure latent constructs, and researchers routinely consider approximate fit indices to ensure adequate model fit and to provide important validity evidence. Due to a lack of generalizable fit index cutoffs, methodologists suggest simulation-based methods to create customized cutoffs that allow researchers to assess model fit more accurately. However, simulation-based methods are computationally intensive. An open question is: How many simulation replications are needed for these custom cutoffs to stabilize? This Monte Carlo simulation study focuses on one such simulation-based method—dynamic fit index (DFI) cutoffs—to determine the optimal number of replications for obtaining stable cutoffs. Results indicated that the DFI approach generates stable cutoffs with 500 replications (the currently recommended number), but the process can be more efficient with fewer replications, especially in simulations with categorical data. Using fewer replications significantly reduces the computational time for determining cutoff values with minimal impact on the results. For one-factor or three-factor models, results suggested that in most conditions 200 DFI replications were optimal for balancing fit index cutoff stability and computational efficiency.

Latent Growth Model with Categorical Indicators: Comparison of the Different Estimators

Despite its potential usage in social and behavioral sciences, there has been limited research on Latent Growth Models (LGM) with categorical indicators. The categorical nature of binary or ordinal variables violates the multivariate normality assumption of the traditional maximum likelihood (ML) estimator. Alternative estimators can be employed, such as marginal maximum likelihood (MML), categorical weighted least squares (c-WLS), and categorical diagonally weighted least squares (c-DWLS). A Monte Carlo simulation study was conducted to compare the performance of the three estimators in the context of categorical LGM. The results revealed that the MML estimator performed the best for the correctly specified linear growth model, whereas the robust c-DWLS or c-WLS estimator excelled in correctly specified quadratic growth model. The robust c-DWLS and c-WLS estimators were more sensitive to model misspecifications. The findings of the present study provide important implications and practical recommendations for empirical researchers using categorical LGM.

A Monte Carlo study on a 3-dimensional comb polymer translocation through a nanopore driven by an electric field

Abstract A lattice Monte Carlo simulation study of the translocation of comb polymers through a nanopore subjected to an electric field is presented. The translocation dynamics was extensively studied in terms of the applied electric field strength, the pore size, and the comb polymer topology. The variations of the most probable translocation time $\tau_p$ and the mean translocation time \mt\ as a function of the applied electric field strength show distinct features, the latter exhibiting a nonmonotonic dependence on the electric field. We were able to show the existence of a critical field strength $\delta \epsilon_c$ defined by the narrowest distribution of the translocation time, which is closely related to the size of the nanopore. In addition, we have found that the critical field strength also defines a transition point between two regimes of translocation: a smooth translocation for a field strength below $\delta \epsilon_c$ and a chaotic translocation for a field strength above $\delta \epsilon_c$. Moreover, for the smallest pore size ($r_p = 1$), monomers can only cross the nanopore in a single file, while for larger pores different modes of polymer translocation are identified. Finally, the dependence of the mean translocation time on the backbone length is governed by a power law relationship $\left < \tau \right > \sim {N_B}^{\alpha}$, where the scaling exponent $\alpha$ is found to be in the range of 1.3--1.7 for the set of side chain lengths and nanopore sizes investigated. As for the side chain length $N_S$, the mean translocation time is found to follow a linear dependence $\left < \tau \right > \sim {N_S}$.

DFT and Monte Carlo simulation studies of potential corrosion inhibition properties of some basic heterocyclic compounds

ABSTRACT This study utilises a combination of density functional theory (DFT) approach, 6-31G (d, p) basis set, and Monte Carlo (MC) simulations. The goal is to understand the relationship between the structure and properties of heterocyclic inhibitors and how they interact with Fe (110) surfaces. Furan, pyrrole, thiophene, pyridine, pyridazine, pyrimidine, indole, benzofuran, carbazole, quinolone, isoquinoline, and imidazole are the chemicals that were looked at in this study. The DFT calculations provide important insights into various properties of the inhibitors, such as molecular structure, dipole moments, electrostatic potential maps, Reduced Density Gradient (RDG), UV spectroscopy, and thermal characteristics. Carbazole has the smallest energy difference (4.789 eV) and the highest softness (0.209 eV−1), It also has the most chemical activity, Furthermore, the Monte Carlo models demonstrate that these derivatives have favourable adsorption energies on the Fe (110) surface. Among them, carbazole shows significant inhibitory potential. The study confirms that the carbazole compound with the biggest negative adsorption energy (−95.495) actually has the smallest energy difference and fits with the MC simulation for adsorption on Fe (110) when it is not charged. Carbazole has much stronger adsorption than oxazole, showing how the structure of a molecule affects how well an inhibitor works.

Guiding computationally intensive theory development with explainable artificial intelligence: The case of shapley additive explanations

This study advances the field of Computationally Intensive Theory Development (CTD) by examining the capabilities of Explainable Artificial Intelligence (XAI), in particular SHapley Additive exPlanations (SHAP), for theory development, while providing guidelines for this process. We evaluate SHAP’s methodological abilities and develop a structured approach for using SHAP to harness insights from black-box predictive models. For this purpose, we leverage a dual-methodological approach. First, to assess SHAP’s capabilities in uncovering patterns that shape a phenomenon, we conduct a Monte-Carlo simulation study. Second, to illustrate and guide the theory development process with SHAP for CTD, we apply SHAP in a use-case using real-world data. Based on these analyses, we propose a stepwise uniform and replicable approach giving guidance that can benefit rigorous theory development and increase the traceability of the theorizing process. With our structured approach, we contribute to the use of XAI approaches in research and, by uncovering patterns in black-box prediction models, add to the ongoing search for next-generation theorizing methods in the field of Information Systems (IS).

When does adjusting covariate under randomization help? A comparative study on current practices

PurposeWe aim to thoroughly compare past and current methods that leverage baseline covariate information to estimate the average treatment effect (ATE) using data from of randomized clinical trials (RCTs). We especially focus on their performance, efficiency gain, and power.MethodsWe compared 6 different methods using extensive Monte-Carlo simulation studies: the unadjusted estimator, i.e., analysis of variance (ANOVA), the analysis of covariance (ANCOVA), the analysis of heterogeneous covariance (ANHECOVA), the inverse probability weighting (IPW), the augmented inverse probability weighting (AIPW), and the overlap weighting (OW) as well as the augmented overlap weighting (AOW) estimators. The performance of these methods is assessed using the relative bias (RB), the root mean square error (RMSE), the model-based standard error (SE) estimation, the coverage probability (CP), and the statistical power.ResultsEven with a well-executed randomization, adjusting for baseline covariates by an appropriate method can be a good practice. When the outcome model(s) used in a covariate-adjusted method is closer to the correctly specified model(s), the efficiency and power gained can be substantial. We also found that most covariate-adjusted methods can suffer from the high-dimensional curse, i.e., when the number of covariates is relatively high compared to the sample size, they can have poor performance (along with lower efficiency) in estimating ATE. Among the different methods we compared, the OW performs the best overall with smaller RMSEs and smaller model-based SEs, which also result in higher power when the true effect is non-zero. Furthermore, the OW is more robust when dealing with the high-dimensional issue.ConclusionTo effectively use covariate adjustment methods, understanding their nature is important for practical investigators. Our study shows that outcome model misspecification and high-dimension are two main burdens in a covariate adjustment method to gain higher efficiency and power. When these factors are appropriately considered, e.g., performing some variable selections if the data dimension is high before adjusting covariate, these methods are expected to be useful.

Model selection for mixture hidden Markov models: an application to clickstream data

AbstractIn a clickstream analysis setting, Mixture Hidden Markov Models (MHMMs) can be used to examine categorical sequences assuming they evolve according to a mixture of latent Markov processes, each related to a different subpopulation. These models involve identifying both the number of subpopulations and hidden states. This study proposes a model selection criterion based on an integrated completed likelihood approach that accounts for the two latent classes in the model. We implemented a Monte Carlo simulation study to compare selection criteria performance. In scenarios characterised by categorical short length sequences, our proposed measure outperforms the most commonly used model selection criteria in identifying components and states. The paper presents a case study on clickstream data collected from the website of a company operating in the hospitality industry and modelled by an MHMM selected by the proposed score.

Emergence of novel magnetic states in a spherical structure with mixed spins σ=5/2 and S=2: A Monte Carlo simulation study

This paper employs Monte Carlo simulations to comprehensively explore the magnetic properties of a spherical nanostructure composed of mixed σ=5/2 and S=2 spins. By systematically varying the proportion (p %) of σ or S spins within the sphere, we investigate the system magnetic behavior, including magnetization, hysteresis loops, remanence, and coercive field. Our findings offer valuable insights into the mechanisms governing the magnetic behavior of this spherical structure, potentially contributing to advancements in fields ranging from data storage to biomedical devices.

Nonseparable panel models with index structure and correlated random effects

. To facilitate semiparametric estimation of general discrete-choice, censored, sample selection, and other complex panel data models, we study identification and estimation of nonseparable multiple-index models in panel data with correlated random effects and a fixed number of time periods. The parameter vectors of interest are shown to be identified up to multiplicative constants and the average marginal effects are identified under the assumption that the distribution of individual effects depends on the explanatory variables only through their averages across time. Under this assumption, we propose to estimate the unknown parameters by the generalized method of moments based on the average and outer product of the difference of derivatives of the regression function. The rate of convergence and asymptotic distribution is established both for the proposed parameter estimates and the average marginal effects. We conduct Monte Carlo simulation studies to assess finite-sample performance of the proposed estimator. We also use it to model dynamic earnings of women, and using our general identification results, we find a negative effect of the number of children not only on the selection into employment as usual, but also on the average earnings.

Statistical Analysis and Several Estimation Methods of New Alpha Power-Transformed Pareto Model with Applications in Insurance

This article defines a new distribution using a novel alpha power-transformed method extension. The model obtained has three parameters and is quite effective in modeling skewed, complex, symmetric, and asymmetric datasets. The new approach has one additional parameter for the model. Certain distributional and mathematical properties are investigated, notably reliability, quartile, moments, skewness, kurtosis, and order statistics, and several approaches of estimation, notably the maximum likelihood, least square, weighted least square, maximum product spacing, Cramer-Von Mises, and Anderson Darling estimators of the model parameters were obtained. A Monte Carlo simulation study was conducted to evaluate the performance of the proposed techniques of estimation of the model parameters. The actuarial measures are computed for our recommended model. At the end of the paper, two insurance applications are illustrated to check the potential and utility of the suggested distribution. Evaluation using four selection criteria indicates that our recommended model is the most appropriate probability model for modeling insurance datasets.

Monte Carlo simulation study of the effect of thyroid shielding on radiation dose in dental cone beam CT in an adult male phantom.

In this paper, the effect of thyroid collars on radiation dose during dental cone-beam computed tomography (CBCT) was evaluated using Monte Carlo simulations and to calculate the effective dose underestimated for the actual CBCT examination due to accounting only for the head and neck. Three thyroid collar models that covered the surface of the phantom were established according to the International Commission on Radiological Protection (ICRP) adult-male mesh-type reference computational phantoms, and a Particle and Heavy Ion Transport code System was used to calculate the equivalent and effective doses of ICRP phantom when different thyroid shielding protocols were used in NewTom VGi evo CBCT, considering one medium (12×8cm) and one small (8×5cm) fields of view (FOVs), and two centre positions were used for each FOV. In four CBCT scanning scenarios, thyroid shielding reduced the equivalent dose for many tissues. The results indicate that the portion of the thyroid collar that wraps around the neck has the main role in reducing the effective dose during dental CBCT examinations, and the higher the axial level of the top of the shielding, the better the effectiveness of the shielding. In this study, the underestimation of the effective dose due to considering only the head and neck was 3.1%-8.1%, and the underestimation was more pronounced in larger FOVs.

Prediction of refraction error after toric lens implantation with biometric input data uncertainties and power labelling tolerances.

The purpose of this study was to simulate the impact of biometric measure uncertainties, lens equivalent and toric power labelling tolerances and axis alignment errors on the refractive outcome after cataract surgery with toric lens implantation. In this retrospective non-randomised cross sectional Monte-Carlo simulation study we evaluated a dataset containing 7458 LenStar 900 preoperative biometric measurements. The biometric uncertainties from literature, lens power labelling according to ISO 11979, and axis alignment tolerances of a modern toric lens (Hoya Vivinex) were taken to be normally distributed and used in a Monte-Carlo simulation with 100 000 samples per eye. The target variable was the defocus equivalent (DEQ) derived using the Castrop (DEQC) and the Haigis (DEQH) formulae. Mean/median / 90% quantile DEQC was 0.22/0.21/0.36 D and DEQH was 0.20/0.19/0.32 D. Ignoring the variation in lens power labelling and toric axis alignment the respective DEQC was 0.20/0.19/0.32 D and DEQH was 0.18/0.17/0.29 D. DEQC and DEQH increased with shorter eyes, steeper corneas, equivalent lens power and highly with toric lens power. According to our simulation results, uncertainties in biometric measures, lens power labelling tolerances, and axis alignment errors are responsible for a significant part of the refraction prediction error after cataract surgery with toric lens implantation. Additional labelling of the exact equivalent and toric power on the lens package could be a step to improve postoperative results.

Bayesian and non‐Bayesian inference of the process capacity index Spk′$S^{\prime }_{pk}$ under progressive type‐II right censored scheme

AbstractProcess capability indices (PCIs), are widely used to gauge how well a process performs within its requirements. While greater PCIs are indicative of improved process “quality,” they do not necessarily translate into lower rejection rates. Therefore, using a loss‐based PCI to gauge process capability makes more sense. In this paper, the PCI has been considered for normal random variable. The article attempts to study the classical and the Bayesian estimation of for type‐II progressive right censored sample under symmetric as well as asymmetric loss functions, namely squared error loss function, and LINEX loss function, respectively. The Markov chain Monte Carlo simulation technique has been efficiently used here to have the approximate solution for . Through an extensive Monte Carlo simulation study along with two real life examples related to electronic industry, we compare the performances of the classical and the Bayes estimates based on symmetric and asymmetric loss functions and compared among the asymptotic confidence interval and highest posterior density credible intervals, in terms of average width and corresponding coverage probabilities of , respectively.

Bivariate iterated Farlie–Gumbel–Morgenstern stress–strength reliability model for Rayleigh margins: Properties and estimation

In this paper, we propose bivariate iterated Farlie–Gumbel–Morgenstern (FGM) due to [Huang and Kotz (1984). Correlation structure in iterated Farlie-Gumbel-Morgenstern distributions. Biometrika 71(3), 633–636. https://doi.org/10.2307/2336577] with Rayleigh marginals. The dependence stress–strength reliability function is derived with its important reliability characteristics. Estimates of dependence reliability parameters are obtained. We analyse the effects of dependence parameters on the reliability function. We found that the upper bound of the positive correlation coefficient is attaining to 0.41 under a single iteration with Rayleigh marginals. A comprehensive comparison between classical FGM with iterated FGM copulas is graphically examined to assess the over or under estimation of reliability with respect to α and β. We propose a two-phase estimation procedure for estimating the reliability parameters. A Monte-Carlo simulation study is conducted to assess the finite sample behaviour of the proposed reliability estimators. Finally, the proposed estimators are examined and validated with real data sets.

Adiabatic light guide with S-shaped strips.

A light guide is an essential part of many scintillator counters and light collection systems. Our main interest is a light guide for a thin, wide scintillator that has high light transmission while converting the area of the light source to the shape of a photo-detector. We propose a variation of the light guide that avoids a 90° twist of the strips, reduces the length of the light pipe, and reduces the complexity of production. Detailed Monte Carlo simulation studies have been performed for a three-strip S-shaped light-guide system.

Reliability estimation and statistical inference under joint progressively Type-II right-censored sampling for certain lifetime distributions

In this article, the parameter estimation of several commonly used two-parameter lifetime distributions, including the Weibull, inverse Gaussian, and Birnbaum–Saunders distributions, based on joint progressively Type-II right-censored sample is studied. Different numerical methods and algorithms are used to compute the maximum likelihood estimates of the unknown model parameters. These methods include the Newton–Raphson method, the stochastic expectation–maximization (SEM) algorithm, and the dual annealing (DA) algorithm. These estimation methods are compared in terms of accuracy (e.g. the bias and mean squared error), computational time and effort (e.g. the required number of iterations), the ability to obtain the largest value of the likelihood, and convergence issues by means of a Monte Carlo simulation study. Recommendations are made based on the simulated results. A real data set is analyzed for illustrative purposes. These methods are implemented in Python, and the computer programs are available from the authors upon request.

Variable selection of nonparametric spatial autoregressive models via deep learning

With the development of deep learning techniques, the application of neural networks to statistical inference has dramatically increased in popularity. In this paper, we extend the deep neural network-based variable selection method to nonparametric spatial autoregressive models. Our approach incorporates feature selection and parameter learning by introducing Lasso penalties in a residual network structure with spatial effects. We transform the problem into a constrained optimization task, where optimizing an objective function with constraints. Without specifying sparsity, we are also able to obtain a specific set of selected variables. The performance of the method with finite samples is demonstrated through an extensive Monte Carlo simulation study. Finally, we apply the method to California housing price data, further validating its superiority in terms of variable selection and predictive performance.