Cumulative Sum Of Residuals Research Articles

Modeling the contribution of district-level cotton production to aggregate cotton production in Punjab (Pakistan): an empirical evidence using correlated component regression approach

This study aims to determine the relative importance of major cotton-producing districts with reference to their aggregate cotton production in Punjab using the time series data from 1982-2021. The empirical analysis is conducted with a correlated component regression approach, which is comparatively more suitable to multicollinear and high-dimensional data sets like those examined in this study. The standardized regression coefficients' absolute value determines each district's rank and relative importance. The degree of geographic concentration of the district-level impact is examined by the Herfindahl-Hirschman Index (HHI). The empirical analysis is analyzed for two-time windows. The first-time window includes crop years from 1982 to 2001, and the second window covers crop years from 2002 to 2021. The Findings of the study indicate that all the included districts had a positive and statistically significant impact on Punjab provincial aggregate cotton production in both the study periods, with the exception of districts Sargodha and Mianwali, which had a negative impact on Punjab-aggregate-cotton-production from 1982 to 2001. Furthermore, the estimated results of the correlated component regression show a decline in the degree of geographic concentration during 2002-2021, as indicated by a 36-point decrease in the value of standardized coefficient HHI. This indicates that technological advancements and policy factors have contributed to greater geographic variation in the relative importance of each district during 2002-2021 compared to 1982-2001. The cumulative sum of residuals (CUSUM) and cumulative sum of square residuals (CUSUMSQ) for both time periods show that the estimated parameters of the correlated component models are structurally stable.

Effect of Major Determinants on Gross Domestic Saving in India: An Application of ARDL Approach

This study investigated the determinants of gross domestic saving in India. Secondary data were extracted from the World Development Indicator (WDI) and the Economic Survey of India from 1972 to 2020. The Augmented Dickey-Fuller (ADF) and Autoregressive Distributed Lag (ARDL) bounds tests were used for stationary and cointegration analysis, respectively. The Cumulative Sum of Residuals (CUSUM) test was also applied to confirm stability. The results indicated that HSV and PBSV positively and significantly impact GDS, while DPR had a significant negative impact in the short and long run. Further, GDP and inflation were insignificant in the long run. The ECT coefficient was found to be -0.53 per year, which suggested that the short-term disequilibrium transforms into long-term equilibrium at a remarkable rate of 53 per cent per year.

A new lack‐of‐fit test for quantile regression with censored data

AbstractA new lack‐of‐fit test for quantile regression models will be presented for the case where the response variable is right‐censored. The test is based on the cumulative sum of residuals, and it extends the ideas of He and Zhu (2003) to censored quantile regression. It will be shown that the empirical process associated with the test statistic converges to a Gaussian process under the null hypothesis and is consistent. To approximate the critical values of the test, a bootstrap mechanism will be used. A simulation study will be carried out to study the performance of the new test in comparison with other tests available in the literature. Finally, a real data application will be presented to show the good properties of the new lack‐of‐fit test in practice.

Weighted cumulative sum tests for random effect models with binary responses.

Correlated binary responses are very commonly encountered in many disciplines like, for example, medical studies. The development of goodness-of-fit tests is essential for examining the adequacy of the fitted models. The objective of this article is to provide weighted modifications of cumulative sums or moving cumulative sums of residuals for testing goodness-of-fit of random effects logistic regression models. The proposed weights can be interpreted as the residuals of a weighted linear regression of an omitted covariate on the covariates already included in the fixed part of the model. These processes lead to supremum statistics whose null distribution is derived using simulation. Results from a simulation study suggest better performance of the weighted when compared to the unweighted supremum statistics. The proposed tests are illustrated using a real data example.

The Impact of Public Health Policy on Labor Force Participation in Paksitan: A Bound Test Approuch

The main objectives of the current study to examine and forecast the short and long run nexus of public health policy on the labor force participation. Current study select eight indicators for the in depth measurement of public health policy in Pakistan. Moreover, the study relies on time series data which was collected from the World development indicator (WDI) and Pakistan bureau of statistics for the period of forty five years (1972-2016). This helped in providing comprehensive description of the labor force participation. The study used auto regressive distributed lagged (ARDL) and Bound test for the short and long run relationship. In addition, the study also used cumulative sum of residuals (CUSUM) and cumulative sum of squared of residuals (CUSUMSQ) for the stability of finding. Result of the study presents that most of the explanatory indicators have significant short and long run relationship with the labor force participation of the country. Specifically, age dependency, health expenditure, secondary school enrollment, trade openness and gross capital formation are the most prevalent factors influencing the labor force supply of the country. Moreover, finding of the current study is confirmed through stability tests like CUSUM and CUSUMSQ. The study provides in depth information for the policy maker to design policy in favor of peoples in order to maximize the labor force and increase the economic development of the country.

Improved change monitoring using an ensemble of time series algorithms

An ensemble of time series algorithms improves land change monitoring. The methodology combines the Continuous Change Detection and Classification (CCDC; Zhu & Woodcock, 2014) and Cumulative Sum of Residuals (CUSUM) algorithms for break detection and the Chow Test (Chow, 1960) for removing false positives (or breaks in time series not representing land change). The algorithms included are based on fundamentally different approaches to change detection and therefore offer unique advantages. The ensemble, or the combination of the three algorithms, was applied to 3 Landsat scenes in the United States and the results were assessed based on their ability to correctly discern structural breaks from stable time periods. The CUSUM test was shown to detect significant breaks 84.18% of the time and the Chow Test correctly removed breaks in 87.4% of the breaks analyzed. The ensemble produced results with lower frequency of errors of omission and commission (Type-I and Type-II errors) than a single algorithm approach. These results indicate that using a combination of break detection algorithms can be an improvement over typical approaches that utilize only one algorithm.

Parsimonious covariate selection for a multicategory ordered response.

We propose a flexible continuation ratio (CR) model for an ordinal categorical response with potentially ultrahigh dimensional data that characterizes the unique covariate effects at each response level. The CR model is the logit of the conditional discrete hazard function for each response level given covariates. We propose two modeling strategies, one that keeps the same covariate set for each hazard function but allows regression coefficients to arbitrarily change with response level, and one that allows both the set of covariates and their regression coefficients to arbitrarily change with response. Evaluating a covariate set is accomplished by using the nonparametric bootstrap to estimate prediction error and their robust standard errors that do not rely on proper model specification. To help with interpretation of the selected covariate set, we flexibly estimate the conditional cumulative distribution function given the covariates using the separate hazard function models. The goodness-of-fit of our flexible CR model is assessed with graphical and numerical methods based on the cumulative sum of residuals. Simulation results indicate the methods perform well in finite samples. An application to B-cell acute lymphocytic leukemia data is provided.

Regression-Based Stiffness Test for Pallets Based on Sample Period Reduction by Trimming

Abstract This article proposes a regression-based stiffness test for pallets based on sample period reduction by trimming. The deflection data are collected from the stiffness tests for pallets, of which one group is from virgin pallets, produced by a Korean and a European vendor, and the other group is from recycle pallets made by a Korean vendor. The data consist of the test sample in normal as well as high temperature condition. Applying the cumulative sum of residuals (CUSUM) and the likelihood ratio (LR) methods, we identify the exact points of structural breaks, thereby rejecting the time-constancy of regression relationship. Specifically, the regression relationship turns out heavily influenced by the initial period of the tests. We remedy the potential biases stemming from the initial period by trimming the initial period out of the sample. It is shown that forecasting performances are substantially improved by the truncation of the first hour data.

A lack-of-fit test for quantile regression models with high-dimensional covariates

A new lack-of-fit test for quantile regression models, that is suitable even with high-dimensional covariates, is proposed. The test is based on the cumulative sum of residuals with respect to unidimensional linear projections of the covariates. To approximate the critical values of the test, a wild bootstrap mechanism convenient for quantile regression is used. An extensive simulation study was undertaken that shows the good performance of the new test, particularly when the dimension of the covariate is high. The test can also be applied and performs well under heteroscedastic regression models. The test is illustrated with real data about the economic growth of 161 countries.

Checking Fine and Gray subdistribution hazards model with cumulative sums of residuals.

Recently, Fine and Gray (J Am Stat Assoc 94:496-509, 1999) proposed a semi-parametric proportional regression model for the subdistribution hazard function which has been used extensively for analyzing competing risks data. However, failure of model adequacy could lead to severe bias in parameter estimation, and only a limited contribution has been made to check the model assumptions. In this paper, we present a class of analytical methods and graphical approaches for checking the assumptions of Fine and Gray's model. The proposed goodness-of-fit test procedures are based on the cumulative sums of residuals, which validate the model in three aspects: (1) proportionality of hazard ratio, (2) the linear functional form and (3) the link function. For each assumption testing, we provide a p-values and a visualized plot against the null hypothesis using a simulation-based approach. We also consider an omnibus test for overall evaluation against any model misspecification. The proposed tests perform well in simulation studies and are illustrated with two real data examples.

Cumulative Sums of Residuals in GLMM and Its Implementation

Test statistics using cumulative sums of residuals have been widely used in various regression models including generalized linear models(GLM). Recently, Pan and Lin (2005) extended this testing procedure to the generalized linear mixed models(GLMM) having random effects, in which we encounter difficulties in computing the marginal likelihood that is expressed as an integral of random effects distribution. The Gaussian quadrature algorithm is commonly used to approximate the marginal likelihood. Many commercial statistical packages provide an option to apply this type of goodness-of-fit test in GLMs but available programs are very rare for GLMMs. We suggest a computational algorithm to implement the testing procedure in GLMMs by a freely accessible R package, and also illustrate through practical examples.

Graphical diagnostics to check model misspecification for the proportional odds regression model.

The cumulative logit or the proportional odds regression model is commonly used to study covariate effects on ordinal responses. This paper provides some graphical and numerical methods for checking the adequacy of the proportional odds regression model. The methods focus on evaluating functional misspecification for specific covariate effects, but misspecification of the link function can also be dealt with under the same framework. For the logistic regression model with binary responses, Arbogast and Lin (Statist. Med. 2005; 24:229-247) developed similar graphical and numerical methods for assessing the adequacy of the model using the cumulative sums of residuals. The paper generalizes their methods to ordinal responses and illustrates them using an example from the VA Normative Aging Study. Simulation studies comparing the performance of the different diagnostic methods indicate that some of the graphical methods are more powerful in detecting model misspecification than the Hosmer-Lemeshow-type goodness-of-fit statistics for the class of models studied.

Pairwise dependence diagnostics for clustered failure-time data

Frailty and copula models specify a parametric dependence structure for multivariate failure-time data. Estimation of some joint quantities can be highly sensitive to the assumed parametric form, and hence model fit is an important issue. This paper lays out a general diagnostic framework for evaluating and selecting frailty and copula models. The approach is based on the cumulative sum of residuals that are calculated in bivariate time. The residuals reflect the difference between the observed and expected bivariate association structures. The proposed model-checking process is interpretable with a limiting distribution which can be approximated using the bootstrap. Simulations and a data example illustrate the practical application of the method.

Goodness‐of‐Fit Methods for Generalized Linear Mixed Models

We develop graphical and numerical methods for checking the adequacy of generalized linear mixed models (GLMMs). These methods are based on the cumulative sums of residuals over covariates or predicted values of the response variable. Under the assumed model, the asymptotic distributions of these stochastic processes can be approximated by certain zero-mean Gaussian processes, whose realizations can be generated through Monte Carlo simulation. Each observed process can then be compared, both visually and analytically, to a number of realizations simulated from the null distribution. These comparisons enable one to assess objectively whether the observed residual patterns reflect model misspecification or random variation. The proposed methods are particularly useful for checking the functional form of a covariate or the link function. Extensive simulation studies show that the proposed goodness-of-fit tests have proper sizes and are sensitive to model misspecification. Applications to two medical studies lead to improved models.

Model-checking techniques for stratified case-control studies

We present graphical and numerical methods for assessing the adequacy of the logistic regression model for stratified case-control data. The proposed methods are derived from the cumulative sum of residuals over the covariate or linear predictor. Under the assumed model, the cumulative residual process converges weakly to a zero-mean Gaussian process whose distribution can be approximated via Monte Carlo simulation. The observed cumulative residual pattern can then be compared both visually and analytically to a number of simulated realizations from the approximate null distribution. These comparisons enable one to examine the functional form of each covariate, the logistic link function as well as the overall model adequacy. Simulation studies demonstrate that the proposed methods perform well in practical settings. Illustration with an oesophageal cancer study is provided.

Goodness‐of‐fit methods for matched case‐control studies

AbstractThe authors propose graphical and numerical methods for checking the adequacy of the logistic regression model for matched case‐control data. Their approach is based on the cumulative sum of residuals over the covariate or linear predictor. Under the assumed model, the cumulative residual process converges weakly to a centered Gaussian limit whose distribution can be approximated via computer simulation. The observed cumulative residual pattern can then be compared both visually and analytically to a certain number of simulated realizations of the approximate limiting process under the null hypothesis. The proposed techniques allow one to check the functional form of each covariate, the logistic link function as well as the overall model adequacy. The authors assess the performance of the proposed methods through simulation studies and illustrate them using data from a cardiovascular study.

Model-Checking Techniques for Linear Models With Parametric Variance Functions

We present graphical and numerical methods for assessing the adequacy of the log-linear model for variances. The proposed methods are derived from the cumulative sum of residuals over the covariate or linear predictor. Under the assumed model, the cumulative residual process converges weakly to a 0-mean Gaussian process whose distribution can be approximated via Monte Carlo simulation. The observed cumulative residual pattern can then be compared both visually and analytically to a number of simulated realizations from the approximate null distribution. These comparisons enable one to examine the functional form of each covariate, the link function as well as the overall model adequacy of the variance model. Simulation studies demonstrate that the proposed methods perform well in practical settings. Illustrations with three datasets are provided.

Model-checking techniques based on cumulative residuals.

Residuals have long been used for graphical and numerical examinations of the adequacy of regression models. Conventional residual analysis based on the plots of raw residuals or their smoothed curves is highly subjective, whereas most numerical goodness-of-fit tests provide little information about the nature of model misspecification. In this paper, we develop objective and informative model-checking techniques by taking the cumulative sums of residuals over certain coordinates (e.g., covariates or fitted values) or by considering some related aggregates of residuals, such as moving sums and moving averages. For a variety of statistical models and data structures, including generalized linear models with independent or dependent observations, the distributions of these stochastic processes tinder the assumed model can be approximated by the distributions of certain zero-mean Gaussian processes whose realizations can be easily generated by computer simulation. Each observed process can then be compared, both graphically and numerically, with a number of realizations from the Gaussian process. Such comparisons enable one to assess objectively whether a trend seen in a residual plot reflects model misspecification or natural variation. The proposed techniques are particularly useful in checking the functional form of a covariate and the link function. Illustrations with several medical studies are provided.