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Authors:Paul H.C. Eilers, Thomas Kneib Pages: 407 - 408 Abstract: Statistical Modelling, Volume 23, Issue 5-6, Page 407-408, October 2023.
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Authors:Ufuk Beyaztas, Han Lin Shang, Abhijit Mandal Abstract: Statistical Modelling, Ahead of Print. A function-on-function regression model with quadratic and interaction effects of the covariates provides a more flexible model. Despite several attempts to estimate the model’s parameters, almost all existing estimation strategies are non-robust against outliers. Outliers in the quadratic and interaction effects may deteriorate the model structure more severely than their effects in the main effect. We propose a robust estimation strategy based on the robust functional principal component decomposition of the function-valued variables and [math]-estimator. The performance of the proposed method relies on the truncation parameters in the robust functional principal component decomposition of the function-valued variables. A robust Bayesian information criterion is used to determine the optimum truncation constants. A forward stepwise variable selection procedure is employed to determine relevant main, quadratic, and interaction effects to address a possible model misspecification. The finite-sample performance of the proposed method is investigated via a series of Monte-Carlo experiments. The proposed method’s asymptotic consistency and influence function are also studied in the supplement, and its empirical performance is further investigated using a U.S. COVID-19 dataset. Citation: Statistical Modelling PubDate: 2023-10-23T10:28:35Z DOI: 10.1177/1471082X231198907
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Authors:Christian H. Weiß Abstract: Statistical Modelling, Ahead of Print. There are several real applications where the categories behind compositional data (CoDa) exhibit a natural order, which, however, is not accounted for by existing CoDa methods. For various application areas, it is demonstrated that appropriately developed methods for ordinal CoDa provide valuable additional insights and are, thus, recommended to complement existing CoDa methods. The potential benefits are demonstrated for the (visual) descriptive analysis of ordinal CoDa, for statistical inference based on CoDa samples, for the monitoring of CoDa processes by means of control charts, and for the analysis and modelling of compositional time series. The novel methods are illustrated by a couple of real-world data examples. Citation: Statistical Modelling PubDate: 2023-10-05T08:51:03Z DOI: 10.1177/1471082X231190971
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Authors:Dimitrios M. Stasinopoulos, Robert A. Rigby, Gillian Z. Heller, Fernanda De Bastiani Abstract: Statistical Modelling, Ahead of Print. P-splines are a versatile statistical modelling tool, dealing with nonlinear relationships between the response and explanatory variable(s). GAMLSS is a distributional regression framework which allows modelling of a response variable using any parametric distribution. The combination of the two methodologies provides one of the most powerful tools in modern regression analysis. This article discusses the application of the two techniques when the response variable is zero-adjusted (or semi-continuous), which combines a point probability at zero with a positive continuous distribution. Citation: Statistical Modelling PubDate: 2023-10-03T04:50:54Z DOI: 10.1177/1471082X231176635
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Authors:Alessia Eletti, Giampiero Marra, Rosalba Radice Abstract: Statistical Modelling, Ahead of Print. Multistate modelling is becoming increasingly popular due to the availability of richer longitudinal health data. When the times at which the events characterising disease progression are known, the modelling of the multistate process is greatly simplified as it can be broken down in a number of traditional survival models. We propose to flexibly model them through the existing general link-based additive framework implemented in the R package GJRM. The associated transition probabilities can then be obtained through a simulation-based approach implemented in the R package mstate, which is appealing due to its generality. The integration between the two is seamless and efficient since we model a transformation of the survival function, rather than the hazard function, as is commonly found. This is achieved through the use of shape constrained P-splines which elegantly embed the monotonicity required for the survival functions within the construction of the survival functions themselves. The proposed framework allows for the inclusion of virtually any type of covariate effects, including time-dependent ones, while imposing no restriction on the multistate process assumed. We exemplify the usage of this framework through a case study on breast cancer patients. Citation: Statistical Modelling PubDate: 2023-09-22T06:05:43Z DOI: 10.1177/1471082X231176120
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Authors:Mario Beraha, Alessandra Guglielmi, Fernando Andrés Quintana, Maria De Iorio, Johan Gunnar Eriksson, Fabian Yap Abstract: Statistical Modelling, Ahead of Print. Overweight and obesity in adults are known to be associated with increased risk of metabolic and cardiovascular diseases. Obesity has now reached epidemic proportions, increasingly affecting children. Therefore, it is important to understand if this condition persists from early life to childhood and if different patterns can be detected to inform intervention policies. Our motivating application is a study of temporal patterns of obesity in children from South Eastern Asia. Our main focus is on clustering obesity patterns after adjusting for the effect of baseline information. Specifically, we consider a joint model for height and weight over time. Measurements are taken every six months from birth. To allow for data-driven clustering of trajectories, we assume a vector autoregressive sampling model with a dependent logit stick-breaking prior. Simulation studies show good performance of the proposed model to capture overall growth patterns, as compared to other alternatives. We also fit the model to the motivating dataset, and discuss the results, in particular highlighting cluster differences. We have found four large clusters, corresponding to children sub-groups, though two of them are similar in terms of both height and weight at each time point. We provide interpretation of these clusters in terms of combinations of predictors. Citation: Statistical Modelling PubDate: 2023-09-21T07:20:01Z DOI: 10.1177/1471082X231185892
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Authors:Peter M. Philipson Abstract: Statistical Modelling, Ahead of Print. A truncated, mean-parameterized Conway-Maxwell-Poisson model is developed to handle under- and overdispersed count data owing to individual heterogeneity. The truncated nature of the data allows for a more direct implementation of the model than is utilized in previous work without too much computational burden. The model is applied to a large dataset of Test match cricket bowlers, where the data are in the form of small counts and range in time from 1877 to the modern day, leading to the inclusion of temporal effects to account for fundamental changes to the sport and society. Rankings of sportsmen and women based on a statistical model are often handicapped by the popularity of inappropriate traditional metrics, which are found to be flawed measures in this instance. Inferences are made using a Bayesian approach by deploying a Markov Chain Monte Carlo algorithm to obtain parameter estimates and to extract the innate ability of individual players. The model offers a good fit and indicates that there is merit in a more sophisticated measure for ranking and assessing Test match bowlers. Citation: Statistical Modelling PubDate: 2023-09-19T11:08:51Z DOI: 10.1177/1471082X231178584
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Authors:María Alejandra Hernández, Dae-Jin Lee, María Xosé Rodríguez-álvarez, María Durbán Abstract: Statistical Modelling, Ahead of Print. The estimation of curve derivatives is of interest in many disciplines. It allows the extraction of important characteristics to gain insight about the underlying process. In the context of longitudinal data, the derivative allows the description of biological features of the individuals or finding change regions of interest. Although there are several approaches to estimate subject-specific curves and their derivatives, there are still open problems due to the complicated nature of these time course processes. In this article, we illustrate the use of P-spline models to estimate derivatives in the context of longitudinal data. We also propose a new penalty acting at the population and the subject-specific levels to address under-smoothing and boundary problems in derivative estimation. The practical performance of the proposal is evaluated through simulations, and comparisons with an alternative method are reported. Finally, an application to longitudinal height measurements of 125 football players in a youth professional academy is presented, where the goal is to analyse their growth and maturity patterns over time. Citation: Statistical Modelling PubDate: 2023-09-18T08:16:42Z DOI: 10.1177/1471082X231178078
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Authors:Philippe Lambert, Oswaldo Gressani Abstract: Statistical Modelling, Ahead of Print. Laplace P-splines (LPS) combine the P-splines smoother and the Laplace approximation in a unifying framework for fast and flexible inference under the Bayesian paradigm. The Gaussian Markov random field prior assumed for penalized parameters and the Bernstein-von Mises theorem typically ensure a razor-sharp accuracy of the Laplace approximation to the posterior distribution of these quantities. This accuracy can be seriously compromised for some unpenalized parameters, especially when the information synthesized by the prior and the likelihood is sparse. Therefore, we propose a refined version of the LPS methodology by splitting the parameter space in two subsets. The first set involves parameters for which the joint posterior distribution is approached from a non-Gaussian perspective with an approximation scheme tailored to capture asymmetric patterns, while the posterior distribution for the penalized parameters in the complementary set undergoes the LPS treatment with Laplace approximations. As such, the dichotomization of the parameter space provides the necessary structure for a separate treatment of model parameters, yielding improved estimation accuracy as compared to a setting where posterior quantities are uniformly handled with Laplace. In addition, the proposed enriched version of LPS remains entirely sampling-free, so that it operates at a computing speed that is far from reach to any existing Markov chain Monte Carlo approach. The methodology is illustrated on the additive proportional odds model with an application on ordinal survey data. Citation: Statistical Modelling PubDate: 2023-09-11T06:32:17Z DOI: 10.1177/1471082X231181173
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Authors:Iain D Currie Abstract: Statistical Modelling, Ahead of Print. Actuaries have long been interested in the forecasting of mortality for the purpose of the pricing and reserving of pensions and annuities. Most models of mortality in age and year of death, and often year of birth, are not identifiable so actuaries worried about what constraints should be used to give sensible estimates of the age and year of death parameters, and, if required, the year of birth parameters. These parameters were then forecast with an ARIMA model to give the required forecasts of mortality. A recent article showed that, while the fitted parameters were not identifiable, both the fitted and forecast mortalities were. This result holds if the age term is smoothed with P-splines. The present article deals with generalized linear models with a rank deficient regression matrix. We have two aims. First, we investigate the effect that different constraints have on the estimated regression coefficients. We show that it is possible to fit the model under different constraints in R without imposing any explicit constraints. R does all the necessary booking-keeping ‘under the bonnet’. The estimated regression coefficients under a particular set of constraints can then be recovered from the invariant fitted values. We have a black box approach to fitting the model subject to any set of constraints. Citation: Statistical Modelling PubDate: 2023-08-22T07:16:54Z DOI: 10.1177/1471082X231181165
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Authors:Ludwig Fahrmeir, Göran Kauermann, Gerhard Tutz, Michael Windmann Abstract: Statistical Modelling, Ahead of Print. Spatial smoothing makes use of spatial information to obtain better estimates in regression models. In particular flexible smoothing with B-splines and penalties, which has been propagated by Eilers and Marx (1996), provides strong tools that can be used to include available spatial information. We consider alternative smoothing methods in spatial additive regression and employ them for analysing rental data in Munich. The first method applies tensor product P-splines to the geolocation of apartments, measured on a continuous scale through the centroid of the quarter where an apartment is. The alternative approach exploits the neighbourhood structure of districts on a discrete scale, where districts consist of a set of neighbouring quarters. The discrete modelling approach yields smooth estimates when using ridge-type penalties but can also enforce spatial clustering of districts with a homogeneous structure when using Lasso-type penalties. Citation: Statistical Modelling PubDate: 2023-08-18T12:23:16Z DOI: 10.1177/1471082X231158465
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Authors:Andreas Mayr, Tobias Wistuba, Jan Speller, Francisco Gude, Benjamin Hofner Abstract: Statistical Modelling, Ahead of Print. The specification of a particular type of effect (e.g., linear or non-linear) of a covariate in a regression model can be either based on graphical assessment, subject matter knowledge or also on data-driven model choice procedures. For the latter variant, we present a boosting approach that is available for a huge number of different model classes. Boosting is an indirect regularization technique that leads to variable selection and can easily incorporate also non-linear or smooth effects. Furthermore, the algorithm can be adapted in a way to automatically select whether to model a continuous variable with a smooth or a linear effect. We enhance this model choice procedure by trying to compensate the inherent bias towards the more complex effect by incorporating a pragmatic and simple deselection technique that was originally implemented for enhanced variable selection. We illustrate our approach in the analysis of T3 thyroid hormone levels from a larger Galician cohort and investigate its performance in a simulation study. Citation: Statistical Modelling PubDate: 2023-08-18T12:07:35Z DOI: 10.1177/1471082X231170045
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Authors:Martin P. Boer Abstract: Statistical Modelling, Ahead of Print. A new approach to represent P-splines as a mixed model is presented. The corresponding matrices are sparse allowing the new approach can find the optimal values of the penalty parameters in a computationally efficient manner. Whereas the new mixed model P-splines formulation is similar to the original P-splines, a key difference is that the fixed effects are modelled explicitly, and extra constraints are added to the random part of the model. An important feature ensuring that the entire computation is fast is a sparse implementation of the Automated Differentiation of the Cholesky algorithm. It is shown by means of two examples that the new approach is fast compared to existing methods. The methodology has been implemented in the R-package LMMsolver available on CRAN (https://CRAN.R-project.org/package=LMMsolver). Citation: Statistical Modelling PubDate: 2023-08-18T07:30:10Z DOI: 10.1177/1471082X231178591
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Authors:Vito M.R. Muggeo, Gianluca Sottile, Giovanna Cilluffo Abstract: Statistical Modelling, Ahead of Print. We present a unified framework able to fit the entire quantile process, namely to estimate simultaneously multiple non-crossing quantile curves. The framework relies on assuming each regression parameter varies smoothly across the percentile direction according to B-splines whose coefficients obey proper restrictions. Multiple linear and penalized smooth terms are allowed and the corresponding tuning parameters are estimated efficiently as part of the model fitting. Monotonicity and concavity constraints on the smoothed relationships are also easily accounted for in the framework. Simulation results provide evidence our proposal exhibits good statistical performance with respect to competitors while guaranteeing the non-crossing property and modest computational load. Analyses on a real dataset related to vocabulary size growth are presented to illustrate the model capability in practice. Citation: Statistical Modelling PubDate: 2023-08-14T12:14:29Z DOI: 10.1177/1471082X231181734
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Authors:Chun Pan, Bo Cai Abstract: Statistical Modelling, Ahead of Print. Clustered partly interval-censored survival data naturally arise from many medical and epidemiological studies. We propose a Bayesian semiparametric approach for fitting a mixed effects proportional hazards (PH) model to clustered partly interval-censored data. The proposed method allows for not only a random intercept as most frailty models do for clustered survival data, but also random effects of covariates. We assume a normal prior for each random intercept/random effect, seeing the instability of a gamma prior for a frailty in this situation. Simulation studies with data generated from both mixed effects PH model and mixed effects accelerated failure times model are conducted, to evaluate the performance of the proposed method and compare it with the three methods currently available in the literature. The application of the proposed approach is illustrated through analyzing the progression-free survival data derived from a phase III metastatic colorectal cancer clinical trial. Citation: Statistical Modelling PubDate: 2023-07-24T08:52:03Z DOI: 10.1177/1471082X231165559
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Authors:Alexander Razen, Wolfgang Brunauer, Nadja Klein, Thomas Kneib, Stefan Lang, Nikolaus Umlauf Abstract: Statistical Modelling, Ahead of Print. Real estate valuation is typically based on hedonic regression models where the expected price of a property is explained in dependence of its attributes. However, investors in the housing market are equally interested in the distribution of real estate market values (including price variation), that is, determining the impact of attributes of a property on the entire conditional distribution. We therefore consider Bayesian structured additive distributional and quantile regression models for real estate valuation. In the first approach, each parameter of a potentially complex parametric response distribution is related to a structured additive predictor. In contrast, the second approach proceeds differently and models arbitrary quantiles of the response distribution directly and nonparametrically. Both models presented are based on a multilevel version of structured additive regression thereby utilizing the typical hierarchical structure of real estate data. We demonstrate the proposed methodology within a detailed case study based on more than 3 000 owner-occupied single family homes in Austria, discuss interpretation of the resulting effect estimates, and compare models based on their predictive ability. Citation: Statistical Modelling PubDate: 2023-04-19T06:42:29Z DOI: 10.1177/1471082X231157205
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Authors:Josu Najera-Zuloaga, Dae-Jin Lee, Cristobal Esteban, Inmaculada Arostegui Abstract: Statistical Modelling, Ahead of Print. Patient-reported outcomes (PROs) are often used as primary outcomes in clinical research studies. PROs are usually measured in ordinal scales and they tend to have excess variability beyond the binomial distribution, a property called overdispersion. Beta-binomial distribution has been previously proposed in this context in order to fit PROs, and beta-binomial regression (BBR) as a good alternative for modelling purposes, including the extension to mixed-effects models in a longitudinal framework. Many PROs have various health dimensions, which are commonly correlated within subjects. However, in clinical analysis, dimensions are separately analysed. In this work, we propose a multidimensional BBR model that incorporates a multidimensional outcome including several PROs in a joint analysis. The proposal has been evaluated and compared to the independent analysis through a simulation study and a real data application with patients with respiratory disease. Results show the advantages that a multidimensional approach offers in terms of parameter significance and interpretation. Additionally, the methods proposed in this work are implemented in the PROreg R-package developed by the authors. Citation: Statistical Modelling PubDate: 2023-04-14T11:13:12Z DOI: 10.1177/1471082X231151311
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Authors:Francisco F. Queiroz, Silvia L. P. Ferrari Abstract: Statistical Modelling, Ahead of Print. The main purpose of this article is to introduce a new class of regression models for bounded continuous data, commonly encountered in applied research. The models, named the power logit regression models, assume that the response variable follows a distribution in a wide, flexible class of distributions with three parameters, namely, the median, a dispersion parameter and a skewness parameter. The article offers a comprehensive set of tools for likelihood inference and diagnostic analysis, and introduces the new R package PLreg. Applications with real and simulated data show the merits of the proposed models, the statistical tools, and the computational package. Citation: Statistical Modelling PubDate: 2023-02-14T06:29:59Z DOI: 10.1177/1471082X221140157
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Authors:Maria Felice Arezzo, Serena Arima, Giuseppina Guagnano Abstract: Statistical Modelling, Ahead of Print. In undeclared work research, the estimation of the magnitude of the phenomenon (i.e., the amount of income and/or the percentage of workers involved) is of major interest. This has been done either using indirect methods or by means of ad hoc surveys such as the Eurobarometer special survey on undeclared work, our motivating study. The extent of undeclared work can be measured by means of two different outcomes: the event of working off-the-book (binary variable) and, when the event occurs, the amount of earnings deriving from the undeclared activity (continuous variable). This setup has been typically modeled via the so called two-part model: a binary choice model for the probability of observing a positive-versus-zero outcome and then, conditional on a positive outcome, a regression model for the positive outcome. We propose an extension of the two-part model that goes in two directions. The first regards the measurement error that, given the very nature of undeclared activities, is most likely to affect both the outcomes of interest. The second is that we generalize the linear regression part of the model to allow individual-level means. We also conduct an extensive simulation study to investigate the performance of the proposed model and compare it with traditional approaches. Citation: Statistical Modelling PubDate: 2023-02-07T11:22:06Z DOI: 10.1177/1471082X221145240
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