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Journal articles on the topic 'Flexible regression models'

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Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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1

Gurmu, Shiferaw, and John Elder. "Flexible Bivariate Count Data Regression Models." Journal of Business & Economic Statistics 30, no. 2 (April 2012): 265–74. http://dx.doi.org/10.1080/07350015.2011.638816.

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2

O'Donnell, David, Alastair Rushworth, Adrian W. Bowman, E. Marian Scott, and Mark Hallard. "Flexible regression models over river networks." Journal of the Royal Statistical Society: Series C (Applied Statistics) 63, no. 1 (July 11, 2013): 47–63. http://dx.doi.org/10.1111/rssc.12024.

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3

Nikulin, M., and Hong-Dar Isaac Wu. "Flexible regression models for carcinogenesis studies." Journal of Mathematical Sciences 145, no. 2 (August 2007): 4880–93. http://dx.doi.org/10.1007/s10958-007-0322-z.

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4

Lee, Young K., Enno Mammen, and Byeong U. Park. "Flexible generalized varying coefficient regression models." Annals of Statistics 40, no. 3 (June 2012): 1906–33. http://dx.doi.org/10.1214/12-aos1026.

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5

Durrleman, Sylvain, and Richard Simon. "Flexible regression models with cubic splines." Statistics in Medicine 8, no. 5 (May 1989): 551–61. http://dx.doi.org/10.1002/sim.4780080504.

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6

Bonat, Wagner Hugo, and Célestin C. Kokonendji. "Flexible Tweedie regression models for continuous data." Journal of Statistical Computation and Simulation 87, no. 11 (April 23, 2017): 2138–52. http://dx.doi.org/10.1080/00949655.2017.1318876.

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7

Dahl, Christian M., and Svend Hylleberg. "Flexible regression models and relative forecast performance." International Journal of Forecasting 20, no. 2 (April 2004): 201–17. http://dx.doi.org/10.1016/j.ijforecast.2003.09.002.

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8

Santías, Francisco Reyes, Carmen Cadarso-Suárez, and María Xosé Rodríguez-Álvarez. "Estimating hospital production functions through flexible regression models." Mathematical and Computer Modelling 54, no. 7-8 (October 2011): 1760–64. http://dx.doi.org/10.1016/j.mcm.2010.11.087.

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9

da Silva, Nívea B., Marcos O. Prates, and Flávio B. Gonçalves. "Bayesian linear regression models with flexible error distributions." Journal of Statistical Computation and Simulation 90, no. 14 (July 2, 2020): 2571–91. http://dx.doi.org/10.1080/00949655.2020.1783261.

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10

Shaw, J. E. H. "Numerical Bayesian Analysis of Some Flexible Regression Models." Statistician 36, no. 2/3 (1987): 147. http://dx.doi.org/10.2307/2348507.

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11

Saldaña-Zepeda, Dayna P., Ciro Velasco-Cruz, and Víctor H. Torres-Preciado. "Variable Selection in Switching Dynamic Regression Models." Revista Colombiana de Estadística 45, no. 1 (January 1, 2022): 231–63. http://dx.doi.org/10.15446/rce.v45n1.85385.

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Complex dynamic phenomena in which dynamics is related to events (modes) that cause structural changes over time, are well described by the switching linear dynamical system (SLDS). We extend the SLDS by allowing the measurement noise to be mode-specific, a flexible way to model non stationary data. Additionally, for models that are functions of explanatory variables, we adapt a variable selection method to identify which of them are significant in each mode. Our proposed model is a flexible Bayesian nonparametric model that allows to learn about the number of modes and their location, and within each mode, it identifies the significant variables and estimates the regression coefficients. The model performance is evaluated by simulation and two application examples from a dataset of meteorological time series of Barranquilla, Colombia are presented.

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12

Su, Steve. "Fitting Flexible Parametric Regression Models with GLDreg in R." Journal of Modern Applied Statistical Methods 15, no. 2 (November 1, 2016): 768–87. http://dx.doi.org/10.22237/jmasm/1478004240.

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13

Bonat, Wagner H., Ricardo R. Petterle, John Hinde, and Clarice GB Demétrio. "Flexible quasi-beta regression models for continuous bounded data." Statistical Modelling 19, no. 6 (September 2, 2018): 617–33. http://dx.doi.org/10.1177/1471082x18790847.

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We propose a flexible class of regression models for continuous bounded data based on second-moment assumptions. The mean structure is modelled by means of a link function and a linear predictor, while the mean and variance relationship has the form [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] are the mean, dispersion and power parameters respectively. The models are fitted by using an estimating function approach where the quasi-score and Pearson estimating functions are employed for the estimation of the regression and dispersion parameters respectively. The flexible quasi-beta regression model can automatically adapt to the underlying bounded data distribution by the estimation of the power parameter. Furthermore, the model can easily handle data with exact zeroes and ones in a unified way and has the Bernoulli mean and variance relationship as a limiting case. The computational implementation of the proposed model is fast, relying on a simple Newton scoring algorithm. Simulation studies, using datasets generated from simplex and beta regression models show that the estimating function estimators are unbiased and consistent for the regression coefficients. We illustrate the flexibility of the quasi-beta regression model to deal with bounded data with two examples. We provide an R implementation and the datasets as supplementary materials.

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14

Abd El-Monsef, Mohamed, Elhoussainy Rady, and Ayat Sobhy. "WEIBULL SEMIPARAMETRIC REGRESSION MODELS UNDER RANDOM CENSORSHIP." JOURNAL OF ADVANCES IN MATHEMATICS 11, no. 8 (December 22, 2015): 5577–82. http://dx.doi.org/10.24297/jam.v11i8.1209.

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Semiparametric regression is concerned with the flexible combination of non-linear functional relationships in regression analysis. The main advantage of the semiparametric regression models is that any application benefits from regression analysis can also benefit from the semiparametric regression. In this paper, we derived a consistent estimator of parametric portion and nonparametric portion in Weibull semi-parametric regression models under random censorship.

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15

Branscum, Adam J., Wesley O. Johnson, and Andre T. Baron. "Robust Medical Test Evaluation Using Flexible Bayesian Semiparametric Regression Models." Epidemiology Research International 2013 (December 11, 2013): 1–8. http://dx.doi.org/10.1155/2013/131232.

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The application of Bayesian methods is increasing in modern epidemiology. Although parametric Bayesian analysis has penetrated the population health sciences, flexible nonparametric Bayesian methods have received less attention. A goal in nonparametric Bayesian analysis is to estimate unknown functions (e.g., density or distribution functions) rather than scalar parameters (e.g., means or proportions). For instance, ROC curves are obtained from the distribution functions corresponding to continuous biomarker data taken from healthy and diseased populations. Standard parametric approaches to Bayesian analysis involve distributions with a small number of parameters, where the prior specification is relatively straight forward. In the nonparametric Bayesian case, the prior is placed on an infinite dimensional space of all distributions, which requires special methods. A popular approach to nonparametric Bayesian analysis that involves Polya tree prior distributions is described. We provide example code to illustrate how models that contain Polya tree priors can be fit using SAS software. The methods are used to evaluate the covariate-specific accuracy of the biomarker, soluble epidermal growth factor receptor, for discerning lung cancer cases from controls using a flexible ROC regression modeling framework. The application highlights the usefulness of flexible models over a standard parametric method for estimating ROC curves.

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16

Prasetyo, Rindang Bangun, Heri Kuswanto, Nur Iriawan, and Brodjol Sutijo Suprih Ulama. "Binomial Regression Models with a Flexible Generalized Logit Link Function." Symmetry 12, no. 2 (February 2, 2020): 221. http://dx.doi.org/10.3390/sym12020221.

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In binomial regression, a link function is used to join the linear predictor variables and the expectation of the response variable. This paper proposes a flexible link function from a new class of generalized logistic distribution, namely a flexible generalized logit (glogit) link. This approach considers both symmetric and asymmetric models, including the cases of lighter and heavier tails, as compared to standard logistic. The glogit is created from the inverse cumulative distribution function of the exponentiated-exponential logistic (EEL) distribution. Using a Bayesian framework, we conduct a simulation study to investigate the model performance compared to the most commonly used link functions, e.g., logit, probit, and complementary log–log. Furthermore, we compared the proposed model with several other asymmetric models using two previously published datasets. The results show that the proposed model outperforms the existing ones and provides flexibility fitting the experimental dataset. Another attractive aspect of the model are analytically tractable and can be easily implemented under a Bayesian approach.

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17

Gonçalves, Jussiane Nader, and Wagner Barreto-Souza. "Flexible regression models for counts with high-inflation of zeros." METRON 78, no. 1 (January 29, 2020): 71–95. http://dx.doi.org/10.1007/s40300-020-00163-9.

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18

Hogg, David W., and Soledad Villar. "Fitting Very Flexible Models: Linear Regression With Large Numbers of Parameters." Publications of the Astronomical Society of the Pacific 133, no. 1027 (September 1, 2021): 093001. http://dx.doi.org/10.1088/1538-3873/ac20ac.

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19

Jung, Yu Jin, and Yong Ik Yoon. "Study on abnormal behavior prediction models using flexible multi-level regression." Journal of the Korean Data and Information Science Society 27, no. 1 (January 31, 2016): 1–8. http://dx.doi.org/10.7465/jkdi.2016.27.1.1.

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20

Marschner, I. C., and A. C. Gillett. "Relative risk regression: reliable and flexible methods for log-binomial models." Biostatistics 13, no. 1 (September 13, 2011): 179–92. http://dx.doi.org/10.1093/biostatistics/kxr030.

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21

Muñoz Barús, José Ignacio, Manuel Febrero-Bande, and Carmen Cadarso-Suárez. "Flexible regression models for estimating postmortem interval (PMI) in forensic medicine." Statistics in Medicine 27, no. 24 (October 30, 2008): 5026–38. http://dx.doi.org/10.1002/sim.3319.

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22

Greven, Sonja, and Fabian Scheipl. "A general framework for functional regression modelling." Statistical Modelling 17, no. 1-2 (February 2017): 1–35. http://dx.doi.org/10.1177/1471082x16681317.

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Researchers are increasingly interested in regression models for functional data. This article discusses a comprehensive framework for additive (mixed) models for functional responses and/or functional covariates based on the guiding principle of reframing functional regression in terms of corresponding models for scalar data, allowing the adaptation of a large body of existing methods for these novel tasks. The framework encompasses many existing as well as new models. It includes regression for ‘generalized’ functional data, mean regression, quantile regression as well as generalized additive models for location, shape and scale (GAMLSS) for functional data. It admits many flexible linear, smooth or interaction terms of scalar and functional covariates as well as (functional) random effects and allows flexible choices of bases—particularly splines and functional principal components—and corresponding penalties for each term. It covers functional data observed on common (dense) or curve-specific (sparse) grids. Penalized-likelihood-based and gradient-boosting-based inference for these models are implemented in R packages refund and FDboost , respectively. We also discuss identifiability and computational complexity for the functional regression models covered. A running example on a longitudinal multiple sclerosis imaging study serves to illustrate the flexibility and utility of the proposed model class. Reproducible code for this case study is made available online.

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23

Pitha, J., I. Podrapska, R. Poledne, and Z. Valenta. "Gaining Insight from Flexible Models." Methods of Information in Medicine 45, no. 02 (2006): 186–90. http://dx.doi.org/10.1055/s-0038-1634065.

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Summary Objectives: We present results from a secondary prevention trial of coronary heart disease (CHD) in the Czech male population from northern Bohemia with the history of myocardial infarction (MI) and high prevalence of metabolic syndrome. We compare several approaches to analyzing survival data from our study in terms of respective model assumptions. Methods: While both the Cox and Weibull survival regression models assume proportionality of the hazard functions over time, in many instances this assumption appears incompatible with the data at hand. Gray’s implementation of flexible models using penalized splines allows for a more realistic assessment of the covariate effects which may vary over time. Results: Gray’s model results revealed a steady decline in the age-adjusted intervention effect over time, which remained significant until about 2.7 years of follow-up. This was in contrast with the results obtained from the Cox and Weibull models which suggested an overall risk reduction due to intervention during the total follow-up of 6.7 years. Survival estimates based on the Cox and Gray models are shown for the two treatment groups and selected sample quantiles of the age distribution for illustration. Conclusions: Gray’s time-varying coefficients model facilitated a more realistic assessment of the intervention effect. Using suitable historical controls with MI history the effect of intervention was found to gradully diminish over time.

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24

M. Hashimoto, Elizabeth, Gauss M. Cordeiro, Edwin M. M. Ortega, and G. G. Hamedani. "New Flexible Regression Models Generated by Gamma Random Variables with Censored Data." International Journal of Statistics and Probability 5, no. 3 (April 8, 2016): 9. http://dx.doi.org/10.5539/ijsp.v5n3p9.

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We propose and study a new log-gamma Weibull regression model. We obtain explicit expressions for the raw and incomplete moments, quantile and generating functions and mean deviations of the log-gamma Weibull distribution. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models which includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain the maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking different perturbation schemes. Some global-influence measurements are also investigated. Further, for different parameter settings, sample sizes and censoring percentages, various simulations are performed. In addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be extended to a modified deviance residual in the proposed regression model applied to censored data. We demonstrate that our extended regression model is very useful to the analysis of real data and may give more realistic fits than other special regression models.

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25

Marra, Giampiero, and Rosalba Radice. "A joint regression modeling framework for analyzing bivariate binary data in R." Dependence Modeling 5, no. 1 (December 20, 2017): 268–94. http://dx.doi.org/10.1515/demo-2017-0016.

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Abstract We discuss some of the features of the R add-on package GJRM which implements a flexible joint modeling framework for fitting a number of multivariate response regression models under various sampling schemes. In particular,we focus on the case inwhich the user wishes to fit bivariate binary regression models in the presence of several forms of selection bias. The framework allows for Gaussian and non-Gaussian dependencies through the use of copulae, and for the association and mean parameters to depend on flexible functions of covariates. We describe some of the methodological details underpinning the bivariate binary models implemented in the package and illustrate them by fitting interpretable models of different complexity on three data-sets.

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26

Hubin, Aliaksandr, Geir Storvik, and Florian Frommlet. "Flexible Bayesian Nonlinear Model Configuration." Journal of Artificial Intelligence Research 72 (November 22, 2021): 901–42. http://dx.doi.org/10.1613/jair.1.13047.

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Regression models are used in a wide range of applications providing a powerful scientific tool for researchers from different fields. Linear, or simple parametric, models are often not sufficient to describe complex relationships between input variables and a response. Such relationships can be better described through flexible approaches such as neural networks, but this results in less interpretable models and potential overfitting. Alternatively, specific parametric nonlinear functions can be used, but the specification of such functions is in general complicated. In this paper, we introduce a flexible approach for the construction and selection of highly flexible nonlinear parametric regression models. Nonlinear features are generated hierarchically, similarly to deep learning, but have additional flexibility on the possible types of features to be considered. This flexibility, combined with variable selection, allows us to find a small set of important features and thereby more interpretable models. Within the space of possible functions, a Bayesian approach, introducing priors for functions based on their complexity, is considered. A genetically modi ed mode jumping Markov chain Monte Carlo algorithm is adopted to perform Bayesian inference and estimate posterior probabilities for model averaging. In various applications, we illustrate how our approach is used to obtain meaningful nonlinear models. Additionally, we compare its predictive performance with several machine learning algorithms.

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Koochemeshkian, Pantea, Nuha Zamzami, and Nizar Bouguila. "Flexible Distribution-Based Regression Models for Count Data: Application to Medical Diagnosis." Cybernetics and Systems 51, no. 4 (May 18, 2020): 442–66. http://dx.doi.org/10.1080/01969722.2020.1758464.

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28

Alfò, Marco, and Irene Rocchetti. "A flexible approach to finite mixture regression models for multivariate mixed responses." Statistics & Probability Letters 83, no. 7 (July 2013): 1754–58. http://dx.doi.org/10.1016/j.spl.2013.04.004.

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29

Kim, Sung-Hee, and Nakseok Kim. "Development of performance prediction models in flexible pavement using regression analysis method." KSCE Journal of Civil Engineering 10, no. 2 (March 2006): 91–96. http://dx.doi.org/10.1007/bf02823926.

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30

Lang, Moritz N., Georg J. Mayr, Reto Stauffer, and Achim Zeileis. "Bivariate Gaussian models for wind vectors in a distributional regression framework." Advances in Statistical Climatology, Meteorology and Oceanography 5, no. 2 (July 18, 2019): 115–32. http://dx.doi.org/10.5194/ascmo-5-115-2019.

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Abstract. A new probabilistic post-processing method for wind vectors is presented in a distributional regression framework employing the bivariate Gaussian distribution. In contrast to previous studies, all parameters of the distribution are simultaneously modeled, namely the location and scale parameters for both wind components and also the correlation coefficient between them employing flexible regression splines. To capture a possible mismatch between the predicted and observed wind direction, ensemble forecasts of both wind components are included using flexible two-dimensional smooth functions. This encompasses a smooth rotation of the wind direction conditional on the season and the forecasted ensemble wind direction. The performance of the new method is tested for stations located in plains, in mountain foreland, and within an alpine valley, employing ECMWF ensemble forecasts as explanatory variables for all distribution parameters. The rotation-allowing model shows distinct improvements in terms of predictive skill for all sites compared to a baseline model that post-processes each wind component separately. Moreover, different correlation specifications are tested, and small improvements compared to the model setup with no estimated correlation could be found for stations located in alpine valleys.

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31

Umlauf, Nikolaus, and Thomas Kneib. "A primer on Bayesian distributional regression." Statistical Modelling 18, no. 3-4 (March 19, 2018): 219–47. http://dx.doi.org/10.1177/1471082x18759140.

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Abstract: Bayesian methods have become increasingly popular in the past two decades. With the constant rise of computational power, even very complex models can be estimated on virtually any modern computer. Moreover, interest has shifted from conditional mean models to probabilistic distributional models capturing location, scale, shape and other aspects of a response distribution, where covariate effects can have flexible forms, for example, linear, non-linear, spatial or random effects. This tutorial article discusses how to select models in the Bayesian distributional regression setting, how to monitor convergence of the Markov chains and how to use simulation-based inference also for quantities derived from the original model parametrization. We exemplify the workflow using daily weather data on (a) temperatures on Germany's highest mountain and (b) extreme values of precipitation for the whole of Germany.

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32

Robinson, Andrew P., Stephen E. Lane, and Guillaume Thérien. "Fitting forestry models using generalized additive models: a taper model example." Canadian Journal of Forest Research 41, no. 10 (October 2011): 1909–16. http://dx.doi.org/10.1139/x11-095.

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Nonparametric and semiparametric modelling methods are commonly applied in many fields. However, such methods have not been widely adopted in forestry, other than the most similar neighbour and nearest neighbor methods. Generalized additive modelling is a flexible semiparametric regression method that is useful when model-based prediction is the main goal and the parametric form of the model is unknown and possibly complex. Routines to fit generalized additive models (GAMs) are now readily available in much statistical software, making them an attractive option for forest modelling. Here, the use of GAMs is demonstrated by the construction of a taper model for six tree species in British Columbia, Canada. We compare the results with an existing flexible parametric taper model. We assess the performance of the models using the 0.632+ bootstrap method according to five key attributes: whole-stem volume, merchantable volume, number of logs, small-end diameter of the first log, and volume of the first log. The results show that the GAMs and the flexible taper function yielded similar accuracy for all attributes and all species.

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Simon, Thorsten, Georg J. Mayr, Nikolaus Umlauf, and Achim Zeileis. "NWP-based lightning prediction using flexible count data regression." Advances in Statistical Climatology, Meteorology and Oceanography 5, no. 1 (February 4, 2019): 1–16. http://dx.doi.org/10.5194/ascmo-5-1-2019.

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Abstract. A method to predict lightning by postprocessing numerical weather prediction (NWP) output is developed for the region of the European Eastern Alps. Cloud-to-ground (CG) flashes – detected by the ground-based Austrian Lightning Detection & Information System (ALDIS) network – are counted on the 18×18 km2 grid of the 51-member NWP ensemble of the European Centre for Medium-Range Weather Forecasts (ECMWF). These counts serve as the target quantity in count data regression models for the occurrence of lightning events and flash counts of CG. The probability of lightning occurrence is modelled by a Bernoulli distribution. The flash counts are modelled with a hurdle approach where the Bernoulli distribution is combined with a zero-truncated negative binomial. In the statistical models the parameters of the distributions are described by additive predictors, which are assembled using potentially nonlinear functions of NWP covariates. Measures of location and spread of 100 direct and derived NWP covariates provide a pool of candidates for the nonlinear terms. A combination of stability selection and gradient boosting identifies the nine (three) most influential terms for the parameters of the Bernoulli (zero-truncated negative binomial) distribution, most of which turn out to be associated with either convective available potential energy (CAPE) or convective precipitation. Markov chain Monte Carlo (MCMC) sampling estimates the final model to provide credible inference of effects, scores, and predictions. The selection of terms and MCMC sampling are applied for data of the year 2016, and out-of-sample performance is evaluated for 2017. The occurrence model outperforms a reference climatology – based on 7 years of data – up to a forecast horizon of 5 days. The flash count model is calibrated and also outperforms climatology for exceedance probabilities, quantiles, and full predictive distributions.

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34

Abed, Muataz Safaa. "Development of Regression Models for Predicting Pavement Condition Index from the International Roughness Index." Journal of Engineering 26, no. 12 (December 1, 2020): 81–94. http://dx.doi.org/10.31026/j.eng.2020.12.05.

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Flexible pavements are considered an essential element of transportation infrastructure. So, evaluations of flexible pavement performance are necessary for the proper management of transportation infrastructure. Pavement condition index (PCI) and international roughness index (IRI) are common indices applied to evaluate pavement surface conditions. However, the pavement condition surveys to calculate PCI are costly and time-consuming as compared to IRI. This article focuses on developing regression models that predict PCI from IRI. Eighty-three flexible pavement sections, with section length equal to 250 m, were selected in Al-Diwaniyah, Iraq, to develop PCI-IRI relationships. In terms of the quantity and severity of each observed distress, the pavement condition surveys were conducted by actually walking through all the sections. Using these data, PCI was calculated utilizing Micro PAVER software. Dynatest Road Surface Profiler (RSP) was used to collect IRI data of all the sections. Using the SPSS software, linear and nonlinear regressions have been used for developing two models between PCI and IRI based on the collected data. These models have the coefficients of determination (R2) equal to 0.715 and 0.722 for linear and quadratic models. Finally, the results indicate the linear and quadratic models are acceptable to predict PCI from IRI directly.

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35

Morris, Darcy Steeg, and Kimberly F. Sellers. "A Flexible Mixed Model for Clustered Count Data." Stats 5, no. 1 (January 7, 2022): 52–69. http://dx.doi.org/10.3390/stats5010004.

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Clustered count data are commonly modeled using Poisson regression with random effects to account for the correlation induced by clustering. The Poisson mixed model allows for overdispersion via the nature of the within-cluster correlation, however, departures from equi-dispersion may also exist due to the underlying count process mechanism. We study the cross-sectional COM-Poisson regression model—a generalized regression model for count data in light of data dispersion—together with random effects for analysis of clustered count data. We demonstrate model flexibility of the COM-Poisson random intercept model, including choice of the random effect distribution, via simulated and real data examples. We find that COM-Poisson mixed models provide comparable model fit to well-known mixed models for associated special cases of clustered discrete data, and result in improved model fit for data with intermediate levels of over- or underdispersion in the count mechanism. Accordingly, the proposed models are useful for capturing dispersion not consistent with commonly used statistical models, and also serve as a practical diagnostic tool.

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Zhang, Jing, and Hong Xia Guo. "Statistical Inference and Application for Partially Linear Models." Applied Mechanics and Materials 733 (February 2015): 910–13. http://dx.doi.org/10.4028/www.scientific.net/amm.733.910.

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As partially linear regression model contains parameters part and the nonparametric part, it is better than the linear model. Partially linear regression model is more freedom, flexible, and can seize the characteristics of data. This passage first reduces the dimension of expenditure index data using principal component analysis. Then based on the dimension-reduced data, a partial linear model is established to forecast expenditure on army. The results show a great advantage over those by stepwise linear regression analysis.

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Cremers, Jolien, Tim Mainhard, and Irene Klugkist. "Assessing a Bayesian Embedding Approach to Circular Regression Models." Methodology 14, no. 2 (April 1, 2018): 69–81. http://dx.doi.org/10.1027/1614-2241/a000147.

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Abstract. Circular data is different from linear data and its analysis also requires methods different from conventional methods. In this study a Bayesian embedding approach to estimating circular regression models is investigated, by means of simulation studies, in terms of performance, efficiency, and flexibility. A new Markov chain Monte Carlo (MCMC) sampling method is proposed and contrasted to an existing method. An empirical example of a regression model predicting teachers’ scores on the interpersonal circumplex will be used throughout. Performance and efficiency are better for the newly proposed sampler and reasonable to good in most situations. Furthermore, the method in general is deemed very flexible. Additional research should be done that provides an overview of what circular data looks like in practice, investigates the interpretation of the circular effects and examines how we might conduct a way of hypothesis testing or model checking for the embedding approach.

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Makendran, C., R. Murugasan, and S. Velmurugan. "Performance Prediction Modelling for Flexible Pavement on Low Volume Roads Using Multiple Linear Regression Analysis." Journal of Applied Mathematics 2015 (2015): 1–7. http://dx.doi.org/10.1155/2015/192485.

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Prediction models for low volume village roads in India are developed to evaluate the progression of different types of distress such as roughness, cracking, and potholes. Even though the Government of India is investing huge quantum of money on road construction every year, poor control over the quality of road construction and its subsequent maintenance is leading to the faster road deterioration. In this regard, it is essential that scientific maintenance procedures are to be evolved on the basis of performance of low volume flexible pavements. Considering the above, an attempt has been made in this research endeavor to develop prediction models to understand the progression of roughness, cracking, and potholes in flexible pavements exposed to least or nil routine maintenance. Distress data were collected from the low volume rural roads covering about 173 stretches spread across Tamil Nadu state in India. Based on the above collected data, distress prediction models have been developed using multiple linear regression analysis. Further, the models have been validated using independent field data. It can be concluded that the models developed in this study can serve as useful tools for the practicing engineers maintaining flexible pavements on low volume roads.

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Li, Shuwei, Tao Hu, Tiejun Tong, and Jianguo Sun. "Semiparametric regression analysis of multivariate doubly censored data." Statistical Modelling 20, no. 5 (July 14, 2019): 502–26. http://dx.doi.org/10.1177/1471082x19859949.

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This article discusses regression analysis of multivariate doubly censored data with a wide class of flexible semiparametric transformation frailty models. The proposed models include many commonly used regression models as special cases such as the proportional hazards and proportional odds frailty models. For inference, we propose a nonparametric maximum likelihood estimation method and develop a new expectation–maximization algorithm for its implementation. The proposed estimators of the finite-dimensional parameters are shown to be consistent, asymptotically normal and semiparametrically efficient. We also conduct a simulation study to assess the finite sample performance of the developed estimation method, and the proposed methodology is applied to a set of real data arising from an AIDS study.

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Bermúdez, Lluís, and Dimitris Karlis. "Multivariate INAR(1) Regression Models Based on the Sarmanov Distribution." Mathematics 9, no. 5 (March 1, 2021): 505. http://dx.doi.org/10.3390/math9050505.

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A multivariate INAR(1) regression model based on the Sarmanov distribution is proposed for modelling claim counts from an automobile insurance contract with different types of coverage. The correlation between claims from different coverage types is considered jointly with the serial correlation between the observations of the same policyholder observed over time. Several models based on the multivariate Sarmanov distribution are analyzed. The new models offer some advantages since they have all the advantages of the MINAR(1) regression model but allow for a more flexible dependence structure by using the Sarmanov distribution. Driven by a real panel data set, these models are considered and fitted to the data to discuss their goodness of fit and computational efficiency.

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Rubio-Herrero, Javier, and Yuchen Wang. "A flexible rolling regression framework for the identification of time-varying SIRD models." Computers & Industrial Engineering 167 (May 2022): 108003. http://dx.doi.org/10.1016/j.cie.2022.108003.

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Roquim, Fernanda V., Thiago G. Ramires, Luiz R. Nakamura, Ana J. Righetto, Renato R. Lima, and Rayne A. Gomes. "Building flexible regression models: including the Birnbaum-Saunders distribution in the gamlss package." Semina: Ciências Exatas e Tecnológicas 42, no. 2 (November 3, 2021): 163. http://dx.doi.org/10.5433/1679-0375.2021v42n2p163.

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Generalized additive models for location, scale and shape (GAMLSS) are a very flexible statistical modeling framework, being an important generalization of the well-known generalized linear models and generalized additive models. Their main advantage is that any probability distribution (that does not necessarily belong to the exponential family) can be considered to model the response variable and different regression structures can be fitted in each of its parameters. Currently, there are more than 100 distributions that are already implemented in the gamlss package in R software. Nevertheless, researchers can implement different distributions if they are not yet available, e.g., the Birnbaum-Saunders (BS) distribution, which is widely used in fatigue studies. In this paper we make available all codes regarding the inclusion of the BS distribution in the gamlss package, and then present a simple application related to air quality data for illustration purposes

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Lu, Yang. "Flexible (panel) regression models for bivariate count–continuous data with an insurance application." Journal of the Royal Statistical Society: Series A (Statistics in Society) 182, no. 4 (May 11, 2019): 1503–21. http://dx.doi.org/10.1111/rssa.12470.

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Brockhaus, Sarah, Michael Melcher, Friedrich Leisch, and Sonja Greven. "Boosting flexible functional regression models with a high number of functional historical effects." Statistics and Computing 27, no. 4 (May 18, 2016): 913–26. http://dx.doi.org/10.1007/s11222-016-9662-1.

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Espasandín‐Domínguez, J., C. Cadarso‐Suárez, T. Kneib, G. Marra, N. Klein, R. Radice, O. Lado‐Baleato, A. González‐Quintela, and F. Gude. "Assessing the relationship between markers of glycemic control through flexible copula regression models." Statistics in Medicine 38, no. 27 (October 7, 2019): 5161–81. http://dx.doi.org/10.1002/sim.8358.

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Komárek, Arnošt, and Emmanuel Lesaffre. "The regression analysis of correlated interval-censored data." Statistical Modelling 9, no. 4 (December 2009): 299–319. http://dx.doi.org/10.1177/1471082x0900900403.

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The accelerated failure time (AFT) model is a useful alternative to the proportional hazard model for modelling interval-censored survival times. We illustrate the usefulness of a class of flexible AFT models. Flexibility is achieved by assuming that the distributional parts consist of penalized Gaussian mixtures. The AFT models are introduced and exemplified via research questions originating from a longitudinal dental study conducted in Flanders (North of Belgium). Emphasis is put on the analyzes which are performed using routines written in the R-language. They show the practical usefulness of our approach.

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Bottai, Matteo, and Giovanna Cilluffo. "Nonlinear parametric quantile models." Statistical Methods in Medical Research 29, no. 12 (July 19, 2020): 3757–69. http://dx.doi.org/10.1177/0962280220941159.

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Quantile regression is widely used to estimate conditional quantiles of an outcome variable of interest given covariates. This method can estimate one quantile at a time without imposing any constraints on the quantile process other than the linear combination of covariates and parameters specified by the regression model. While this is a flexible modeling tool, it generally yields erratic estimates of conditional quantiles and regression coefficients. Recently, parametric models for the regression coefficients have been proposed that can help balance bias and sampling variability. So far, however, only models that are linear in the parameters and covariates have been explored. This paper presents the general case of nonlinear parametric quantile models. These can be nonlinear with respect to the parameters, the covariates, or both. Some important features and asymptotic properties of the proposed estimator are described, and its finite-sample behavior is assessed in a simulation study. Nonlinear parametric quantile models are applied to estimate extreme quantiles of longitudinal measures of respiratory mechanics in asthmatic children from an epidemiological study and to evaluate a dose–response relationship in a toxicological laboratory experiment.

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Mullen, Randall, Lucy Marshall, and Brian McGlynn. "A Beta Regression Model for Improved Solar Radiation Predictions." Journal of Applied Meteorology and Climatology 52, no. 8 (August 2013): 1923–38. http://dx.doi.org/10.1175/jamc-d-12-038.1.

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AbstractPredicting global solar radiation is an integral part of much environmental modeling. There are several approaches for predicting global solar radiation at a site where no instrumentation exists. One popular approach uses the difference between daily high and low temperature, typically using a nonlinear equation to express the relationship between change in temperature and estimated global solar radiation. Additional variables are usually included in successive steps creating a hierarchy of analysis. The authors propose an alternative beta regression approach to modeling global solar radiation, allowing for the inclusion of multiple environmental predictor variables and strata into one flexible model. The model is applied to several case studies, and results are compared with recently proposed empirical solar radiation models. Beta regression provides a robust, flexible modeling approach for predicting global solar radiation that allows for the addition and removal of independent variables as appropriate and can be interpreted using standard inferential statistics. In addition, the beta regression model provides estimates of uncertainty that can be incorporated into subsequent models and calculations.

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Ramires, Thiago G., Gauss M. Cordeiro, Michael W. Kattan, Niel Hens, and Edwin MM Ortega. "Predicting the cure rate of breast cancer using a new regression model with four regression structures." Statistical Methods in Medical Research 27, no. 11 (February 23, 2017): 3207–23. http://dx.doi.org/10.1177/0962280217695344.

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Cure fraction models are useful to model lifetime data with long-term survivors. We propose a flexible four-parameter cure rate survival model called the log-sinh Cauchy promotion time model for predicting breast carcinoma survival in women who underwent mastectomy. The model can estimate simultaneously the effects of the explanatory variables on the timing acceleration/deceleration of a given event, the surviving fraction, the heterogeneity, and the possible existence of bimodality in the data. In order to examine the performance of the proposed model, simulations are presented to verify the robust aspects of this flexible class against outlying and influential observations. Furthermore, we determine some diagnostic measures and the one-step approximations of the estimates in the case-deletion model. The new model was implemented in the generalized additive model for location, scale and shape package of the R software, which is presented throughout the paper by way of a brief tutorial on its use. The potential of the new regression model to accurately predict breast carcinoma mortality is illustrated using a real data set.

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Menezes, Rui, Nuno Ferreira, Adriano Mendonça Souza, and Francisca Mendonça Souza. "Smooth Transition Regression models: Theory and Applications in JMulti." Ciência e Natura 42 (December 29, 2020): e18. http://dx.doi.org/10.5902/2179460x40466.

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This tutorial aims to analyze nonlinear models of Smooth Transition Regression with JMulTi and contribute to the understanding of STR specification, from the estimation until the evaluation cycle of these models. It provides pedagogical explanations, combining theoretical concepts and empirical results coherently. Especially in economic relationships, where an asymmetric behaviour with distinct effects is often found on contractions and expansions. As economic series generally present asymmetric/nonlinear behaviour, Smooth Transition Regression (STR) models provide a flexible empirical strategy that allows capturing the impacts of possible types of asymmetry in the data, Souza (2016).An overview of theory and applications in software is described. These nonlinear models describe in-sample movements of the stock returns series better than the corresponding linear model. The data used in this study consist of daily prices index from January 02, 1995 to March 29, 2013, a total of 4761 observations, from Germany (DAX30). The data was collected from the DataStream database considering 5 days a week. The data (price index) is converted to base 100 and the yields are then calculated based on the first differences in the log price series. 10-year interest rates treasury bond regarding the same markets identified has also been collected for the same period.

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