Copula Regression Model Research Articles

Forecasting Consumer Price Index with Federal Open Market Committee Sentiment Index

AbstractThe Federal Open Market Committee (FOMC) is a component of the Federal Reserve System responsible for overseeing open market operations. The FOMC meets roughly eight or more times per year to assess the economy of the United States. After each meeting, the FOMC releases a statement to the press outlining its assessment of the US economy and its monetary policy stance. The sentiment of these statements may have an influence on the US economy and financial markets. Using sentiment and correlational analyses, this research examines how the sentiment of these statements affects the US economy and financial markets by analyzing how FOMC statement sentiment is correlated with the Consumer Price Index (CPI), the National Financial Conditions Index (NFCI), and the Adjusted National Financial Conditions Index (ANFCI). We find evidence to suggest that there is a moderate negative correlation between an FOMC statement's sentiment and the US City Average CPI value associated with the month before and the month after the statement's release. We also find that there is no evidence to suggest there exists a correlation between an FOMC statement's sentiment and the NFCI value associated with the week before or the week after the statement's release. However, we do find evidence to suggest that there is a moderate negative correlation between an FOMC statement's sentiment and the ANFCI value associated with the week before and the week after the statement's release. We also found that out of the three models we tested (linear regression, vine copula regression, and Gaussian copula regression), the Gaussian copula regression model performs the best when forecasting the CPI and the ANFCI. Additionally, we find that when forecasting CPI values, the models that include FOMC statement sentiment are more accurate than the models that exclude FOMC statement sentiment.

Bivariate Analysis of Birth Weight and Gestational Age by Bayesian Distributional Regression with Copulas

We analyze perinatal data including biometric and obstetric information as well as data on maternal smoking, among others. Birth weight is the primarily interesting response variable. Gestational age is usually an important covariate and included in polynomial form. However, in opposition to this univariate regression, bivariate modeling of birth weight and gestational age is recommended to distinguish effects on each, on both, and between them. Rather than a parametric bivariate distribution, we apply conditional copula regression, where the marginal distributions of birth weight and gestational age (not necessarily of the same form) and the dependence structure are modeled conditionally on covariates. In the resulting distributional regression model, all parameters of the two marginals and the copula parameter are observation specific. While the Gaussian distribution is suitable for birth weight, the skewed gestational age data are better modeled by the three-parameter Dagum distribution. The Clayton copula performs better than the Gumbel and the symmetric Gaussian copula, indicating lower tail dependence (stronger dependence when both variables are low), although this non-linear dependence between birth weight and gestational age is surprisingly weak and only influenced by Cesarean section. A non-linear trend of birth weight on gestational age is detected by a univariate model that is polynomial with respect to the effect of gestational age. Covariate effects on the expected birth weight are similar in our copula regression model and a univariate regression model, while distributional copula regression reveals further insights, such as effects of covariates on the association between birth weight and gestational age.

Bivariate copula regression models for semi-competing risks.

Time-to-event semi-competing risk endpoints may be correlated when both events occur on the same individual. These events and the association between them may also be influenced by individual characteristics. In this article, we propose copula survival models to estimate hazard ratios of covariates on the non-terminal and terminal events, along with the effects of covariates on the association between the two events. We use the Normal, Clayton, Frank and Gumbel copulas to provide a variety of association structures between the non-terminal and terminal events. We apply the proposed methods to model semi-competing risks of graft failure and death for kidney transplant patients. We find that copula survival models perform better than the Cox proportional hazards model when estimating the non-terminal event hazard ratio of covariates. We also find that the inclusion of covariates in the association parameter of the copula models improves the estimation of the hazard ratios.

Copula based trivariate spatial modeling of childhood illnesses in Western African countries

Acute respiratory infections (ARI), diarrhea, and fever are three common childhood illnesses, especially in sub-Saharan Africa. This study investigates the marginal and pairwise correlated effects of these diseases across Western African countries in a single analytical framework. Using data from nationally representative cross-sectional Demographic and Health Surveys, the study analyzed specific and correlated effects of each pair of childhood morbidity from ARI, diarrhea, and fever using copula regression models in fourteen contiguous Western African countries. Data concerning childhood demographic and socio-economic conditions were used as covariates. In this cross-sectional analysis of 152,125 children aged 0–59 months, the prevalence of ARI was 6.9%, diarrhea, 13.8%, and fever 19.6%. The results showed a positive correlation and geographical variation in the prevalence of the three illnesses across the study region. The estimated correlation and 95% confidence interval between diarrhea and fever is 0.431(0.300,0.539); diarrhea and ARI is 0.270(0.096,0.422); and fever and ARI is 0.502(0.350,0.614). The marginal and correlated spatial random effects reveal within-country spatial dependence. Source of water and access to electricity was significantly associated with any of the three illnesses, while television, birth order, and gender were associated with diarrhea or fever. The place of residence and access to newspapers were associated with fever or ARI. There was an increased likelihood of childhood ARI, diarrhea, and fever, which peaked at about ten months but decreased substantially thereafter. Mother’s age was associated with a reduced likelihood of the three illnesses. The maps generated could be resourceful for area-specific policy-making to speed up mitigation processes.

A flexible copula regression model with Bernoulli and Tweedie margins for estimating the effect of spending on mental health.

We develop a flexible two-equation copula model to address endogeneity of medical expenditures in a distribution regression for health. The expenditure margin uses the compound gamma distribution, a special case of the Tweedie family of distributions, to account for a spike at zero and a highly skewed continuous part. An efficient estimation algorithm offers flexible choices of copulae and link functions, including logit, probit and cloglog for the health margin. Our empirical application revisits data from the Rand Health Insurance Experiment. In the joint model, using random insurance plan assignment as instrument for spending, a $1000 increase is estimated to reduce the probability of a low post-program mental health index by 1.9 percentage points. The effect is not statistically significant. Ignoring endogeneity leads to a spurious positive effect estimate.

A semi-supervised soft sensor method based on vine copula regression and tri-training algorithm for complex chemical processes

Soft sensor technology is an important solution for timely prediction of some difficult-to-measure variables in the chemical process. For the data-driven soft sensor models, the modeling process needs a certain amount of labeled samples. In some actual processes, the number of unlabeled samples is very large, but the labeling process of unlabeled samples is very time-consuming and laborious. When soft sensor modeling is performed in the case of sparse labeled samples, the generalization ability of the model is bound to be poor. To address this problem, a semi-supervised soft sensor method based on vine copula regression and tri-training algorithm (tri-training VCR) is proposed in this paper. Semi-supervised learning is to enhance the performance of supervised learning models by using unlabeled samples. The tri-training algorithm is used to expand the labeled samples through the cooperation of three vine copula regression models with different structures and a new method to judge the confidence degree of pseudo-labeled samples, so as to improve the prediction accuracy of the soft sensor model. A numerical example and an industrial example are used to demonstrate the effectiveness of the proposed method.

Efficient and feasible inference for high-dimensional normal copula regression models

The composite likelihood (CL) is amongst the computational methods used for the estimation of high-dimensional multivariate normal (MVN) copula models with discrete responses. Its computational advantage, as a surrogate likelihood method, is that is based on the independence likelihood for the univariate marginal regression and non-regression parameters and pairwise likelihood for the correlation parameters. Nevertheless, the efficiency of the CL method for estimating the univariate regression and non-regression marginal parameters can be low. For a high-dimensional discrete response, weighted versions of the composite likelihood estimating equations and an iterative approach to determine good weight matrices are proposed. The general methodology is applied to the MVN copula with univariate ordinal regressions as the marginals. Efficiency calculations show that the proposed method is nearly as efficient as the maximum likelihood for fully specified MVN copula models. Illustrations include simulations and real data applications regarding longitudinal (low-dimensional) and time (high-dimensional) series ordinal response data with covariates. Our studies suggest that there is a substantial gain in efficiency via the weighted CL method.

Boosting distributional copula regression.

Capturing complex dependence structures between outcome variables (e.g., study endpoints) is of high relevance in contemporary biomedical data problems and medical research. Distributional copula regression provides a flexible tool to model the joint distribution of multiple outcome variables by disentangling the marginal response distributions and their dependence structure. In a regression setup, each parameter of the copula model, that is,the marginal distribution parameters and the copula dependence parameters, can be related to covariates via structured additive predictors. We propose a framework to fit distributional copula regression via model-based boosting, which is a modern estimation technique that incorporates useful features like an intrinsic variable selection mechanism, parameter shrinkage and the capability to fit regression models in high-dimensional data setting, that is,situations with more covariates than observations. Thus, model-based boosting does not only complement existing Bayesian and maximum-likelihood based estimation frameworks for this model class but rather enables unique intrinsic mechanisms that can be helpful in many applied problems. The performance of our boosting algorithm for copula regression models with continuous margins is evaluated in simulation studies that cover low- and high-dimensional data settings and situations with and without dependence between the responses. Moreover, distributional copula boosting is used to jointly analyze and predict the length and the weight of newborns conditional on sonographic measurements of the fetus before delivery together with other clinicalvariables.

A unified Gaussian copula methodology for spatial regression analysis

Spatially referenced data arise in many fields, including imaging, ecology, public health, and marketing. Although principled smoothing or interpolation is paramount for many practitioners, regression, too, can be an important (or even the only or most important) goal of a spatial analysis. When doing spatial regression it is crucial to accommodate spatial variation in the response variable that cannot be explained by the spatially patterned explanatory variables included in the model. Failure to model both sources of spatial dependence—regression and extra-regression, if you will—can lead to erroneous inference for the regression coefficients. In this article I highlight an under-appreciated spatial regression model, namely, the spatial Gaussian copula regression model (SGCRM), and describe said model’s advantages. Then I develop an intuitive, unified, and computationally efficient approach to inference for the SGCRM. I demonstrate the efficacy of the proposed methodology by way of an extensive simulation study along with analyses of a well-known dataset from disease mapping.

A soft sensor regression model for complex chemical process based on generative adversarial nets and vine copula

BackgroundIn the increasingly complex industrial process, it is extremely important to measure the key variables that directly affect the timely operation of the entire process. However, some key variables are challenging to be measured by traditional methods, so it is meaningful to use relevant variables to establish a soft sensor regression model to predict them. Usually, a large number of labeled samples are needed for modeling accurately. However, in some complex chemical industries, only a small number of labeled samples can be used to build a regression model and the model's description of the process is therefore inaccurate. MethodsThis paper proposes a soft sensor method based on generative adversarial nets and vine copula regression (GAN-VCR) to address this problem. This method uses generative adversarial nets (GAN) to generate a large number of samples with a distribution similar to the labeled samples. For more reasonable sample augment, a sample selection strategy based on the generalized local probability (GLP) index is used to select augmented samples from a large number of generated samples to augment the training samples. Then, the augmented training samples are used to build a vine copula regression model and predict the key variables. Finally, numerical and industrial examples are used to prove the effectiveness and practicability of the method. Significant findingsBased on the developed soft sensor, sample augmentation can be effectively performed and the performance can be improved compared to traditional soft sensor methods, and the product quality in practical can be effectively improved.

The Incorporation of Generalized Linear Models into Bivariate Gaussian Copula and An Application

In non-life insurance mathematics, analyses and premium or reserve calculations are carried out in the presence of dependency between the claim variables in recent years. And, thus over- or underestimation of aggregate loss caused by the assumption of dependency between the claim severity and frequency are prevented. The Gaussian copula function, which is frequently used for dependency modeling, is integrated into the marginal generalized linear models to obtain a mixed copula-based regression model called "copula regression". In this study, a copula regression model is created using a bivariate Gaussian copula, Gamma and Poisson marginal generalized linear models for claim severity and frequency, respectively. An application is performed with a simulated data where there is a dependence between the claim severity and frequency using the R package “CopulaRegression”. The importance of the modeling of dependency between claims is investigated by the comparison of the independent and dependent models and the results of application show that the copula regression model in which dependency is considered has lower relative mean square errors compared the independent marginal generalized linear models.

Copula link-based additive models for bivariate time-to-event outcomes with general censoring scheme

Bivariate survival outcomes arise frequently in applied studies where the occurrence of two events of interest are associated. Often the exact event times are unknown due to censoring which can manifest in various forms. A general and flexible copula regression model that can handle bivariate survival data subject to various censoring mechanisms, which include a mixture of uncensored, left-, right-, and interval-censored data, is proposed. The proposal permits to specify all model parameters as flexible functions of covariate effects, flexibly model the baseline survival functions by means of monotonic P-splines, characterise the marginals via transformations of the survival functions which yield, e.g., the proportional hazards and odds models as special cases, and model the dependence between events using a wide variety of copulae. The algorithm is based on a computationally efficient and stable penalised maximum likelihood estimation approach with integrated automatic multiple smoothing parameter selection. The proposed model is evaluated in a simulation study and illustrated using data from the Age-Related Eye Disease Study. The modelling framework has been incorporated in the newly-revised R package GJRM, hence allowing any user to fit the desired model(s) and produce easy-to-interpret numerical and visual summaries.

Multi-model D-vine copula regression model with vine copula-based dependence description

Soft sensor modeling is a popular method to predict the key variables that are not easy to measure in chemical processes. Since the actual process is often a large-scale, multi-working condition, nonlinear, and non-Gaussian complex system, a single soft sensor model cannot fully extract all the information of the process, and the prediction accuracy is relatively low. To address this problem, a multi-model d-vine copula regression model with vine copula-based dependence description (VCDD-MCR) is proposed in this paper. This method first divides the training samples into multiple subsets with repetitive samples, and uses the vine copula-based dependence description (VCDD) model to characterize the distributions of these subsets. Then, a generalized local probability (GLP) index is used to determine the location of every training sample among these distributions. If a training sample is at the edges of all distributions, a new subset centered on this sample will be created. Furthermore, a d-vine copula regression model is established for each subset to predict the key variable. The proposed method can handle large-scale, nonlinear, non-Gaussian systems well. The effectiveness of the proposed method is demonstrated using a numerical example and an industrial example.

A new class of copula regression models for modelling multivariate heavy-tailed data

A new class of copulas, termed the MGL copula class, is introduced. The new copula originates from extracting the dependence function of the multivariate generalized log-Moyal-gamma distribution whose marginals follow the univariate generalized log-Moyal-gamma (GLMGA) distribution as introduced in Li et al. (2021). The MGL copula can capture nonelliptical, exchangeable, and asymmetric dependencies among marginal coordinates and provides a simple formulation for regression applications. We discuss the probabilistic characteristics of MGL copula and obtain the corresponding extreme-value copula, named the MGL-EV copula. While the survival MGL copula can be also regarded as a special case of the MGB2 copula from Yang et al. (2011), we show that the proposed model is effective in regression modelling of dependence structures. Next to a simulation study, we propose two applications illustrating the usefulness of the proposed model. This method is also implemented in a user-friendly R package: rMGLReg.

A Flexible Copula Regression Model with Bernoulli and Tweedie Margins for Estimating the Effect of Spending on Mental Health

A Flexible Copula Regression Model with Bernoulli and Tweedie Margins for Estimating the Effect of Spending on Mental Health

Limitations and performance of three approaches to Bayesian inference for Gaussian copula regression models of discrete data

Limitations and performance of three approaches to Bayesian inference for Gaussian copula regression models of discrete data

Nonlinear non‐Gaussian and multimode probabilistic weighted copula regression model based deep neural network

AbstractA probabilistic weighted copula (WCR) approach based on a sparse robust auto‐encoder (SRAE) is proposed. For the industrial processes, which have multi‐operation conditions, SRAE model with the five‐layer stacked auto‐encoder is introduced to do feature learning. Then, the extracted feature can be used to classify the multi‐operation conditions. Besides, the advanced high‐level features extracted by the SRAE model can deal with the nonlinear and non‐Gaussian process well. The WCR model applies the vine copula function and Monte Carlo estimation to quickly depict the distribution of the process. By considering the abstract features and the copula weights of local data, the predicting uncertainty can be quickly calculated by the SRAE‐WCR model. The effectiveness of the SRAE‐WCR model is illustrated with an ethylene cracking furnace process and a numerical example.

Estimating the national and regional prevalence of drinking or eating more than usual during childhood diarrhea in Malawi using the bivariate sample selection copula regression.

BackgroundEstimation of prevalence of feeding practices during diarrhea using conventional imputation methods may be biased as these methods apply to observed factors and in this study, feeding practice status was unobserved for those without diarrhea. The study aimed at re-estimating the prevalence of feeding practices using the bivariate sample selection model.MethodsThe study used 2015–2016 Malawi demographic health survey (MDHS) data which had 16,246 children records who had diarrhea or not. A bivariate Joe copula regression model with 90 degrees rotation was fitted to either drinking or eating more, with diarrhea as a sample selection outcome in the bivariate models. The prevalence of drinking more than usual and prevalence of eating more than usual were then estimated based on the fitted bivariate model. These prevalences were then compared to the prevalences estimated using the conventional imputation method.ResultsThere was a substantial increase in the re-estimated national prevalence of drinking more fluids (40.0%, 95% CI [31.7–50.5]) or prevalence of eating more food (20.46%, 95% CI [9.87–38.55]) using the bivariate model as compared to the prevalences estimated by the conventional imputation method, that is, (28.9%, 95% CI [27.0–30.7]) and (13.1%, 95% CI [12.0–15.0]) respectively. The maps of the regional prevalences showed similar results where the prevalences estimated by the bivariate model were relatively higher than those estimated by the standard imputation method. The presence of diarrhea was somehow weakly negatively correlated with either drinking more fluids or eating more food.ConclusionThe estimation of prevalence of drinking more fluids or eating more food during diarrhea should use bivariate modelling to model sample selection variable so as to minimize bias. The observed negative correlation between diarrhea presence and feeding practices implies that mothers should be encouraged to let their children drink more fluids or eat more food during diarrhea episode to avoid dehydration and malnutrition.

Bayesian Variable Selection for Gaussian Copula Regression Models

We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any combination of discrete and/or continuous responses and their association with a set of predictors. We use the parameter expansion for data augmentation strategy to construct a Markov chain Monte Carlo algorithm for the estimation of the parameters and the latent variables of the model. Based on a centered parameterization of the Gaussian latent variables, we design a fixed-dimensional proposal distribution to update jointly the latent binary vectors of important predictors and the corresponding nonzero regression coefficients. For Gaussian responses and for outcomes that can be modeled as a dependent version of a Gaussian response, this proposal leads to a Metropolis-Hastings step that allows an efficient exploration of the predictors’ model space. The proposed strategy is tested on simulated data and applied to real datasets in which the responses consist of low-intensity counts, binary, ordinal and continuous variables.

Copula geoadditive modelling of anaemia and malaria in young children in Kenya, Malawi, Tanzania and Uganda

BackgroundAnaemia and malaria are the leading causes of sub-Saharan African childhood morbidity and mortality. This study aimed to explore the complex relationship between anaemia and malaria in young children across the districts or counties of four contiguous sub-Saharan African countries, namely Kenya, Malawi, Tanzania and Uganda, while accounting for the effects of socio-economic, demographic and environmental factors. Geospatial maps were constructed to visualise the relationship between the two responses across the districts of the countries.MethodsA joint bivariate copula regression model was used, which estimates the correlation between the two responses conditional on the linear, non-linear and spatial effects of the explanatory variables considered. The copula framework allows the dependency structure between the responses to be isolated from their marginal distributions. The association between the two responses was set to vary according to the district of residence across the four countries.ResultsThe study revealed a positive association between anaemia and malaria throughout the districts, the strength of which varied across the districts of the four countries. Due to this heterogeneous association between anaemia and malaria, we further considered the joint probability of each combination of outcome of anaemia and malaria to further reveal more about the relationship between the responses. A considerable number of districts had a high joint probability of a child being anaemic but not having malaria. This might suggest the existence of other significant drivers of childhood anaemia in these districts.ConclusionsThis study presents an alternative technique to joint modelling of anaemia and malaria in young children which assists in understanding more about their relationship compared to techniques of multivariate modelling. The approach used in this study can aid in visualising the relationship through mapping of their correlation and joint probabilities. These maps produced can then help policy makers target the correct set of interventions, or prevent the use of incorrect interventions, particularly for childhood anaemia, the causes of which are multiple and complex.