Bias-corrected Percentile Bootstrap Research Articles

Analysis for partially accelerated dependent competing risks model with masked data based on copula function

In the reliability analysis of competing risks model, it is usually assumed that the components are independent and failure causes are observable. However, this assumption may be unrealistic in some applications. In this article, based on the tampered failure rate (TFR) model, we introduce a constant-stress partially accelerated life test (PALT) model of dependent competing risks with masked data. The dependent structure is described by Gumbel copula function and the life distribution of components is described by the Weibull distribution. The maximum likelihood method is used to estimate the dependent parameter and unknown parameters of the model, so as to derive the estimation of the reliability function (RF). Confidence intervals (CIs) of the model parameters are also obtained via asymptotic normality theory and bias-corrected percentile bootstrap (Boot-BCP) technique. Simulation results show that the dependent model with masked data improves the estimation accuracy of system reliability compared with the independent model. Finally, a real data analysis indicates that the statistical inference model and methods have good performance.

The Relationship Between Empowering Motivational Climate in Physical Education and Social Responsibility of High School Students: Chain Mediating Effect Test.

Objective: This study aimed to contribute to understanding the mechanisms underlying the association between empowering motivational climate in physical education and social responsibility among high school students, and have important implications for interventions aimed at improving social responsibility among high school students.Methods: Through the quota sampling, 802 students (average age = 17 years, SD = 0.97 years) that complied with the requirements were surveyed from Anhui Province in China. Empowering motivational climate in physical education, social responsibility, interpersonal disturbance, and general self-efficacy were assessed using standard scales. For data analysis, Pearson’s correlation analysis, structural equation model test, and bias-corrected percentile Bootstrap method were carried out in turn.Results: (1) Common method biases can be accepted in this study, and the correlation among empowering motivational climate in physical education, social responsibility, interpersonal disturbance, and general self-efficacy are all significant; (2)Empowering motivational climate in physical education, interpersonal disturbance and general self-efficacy can all predict social responsibility significantly; (3) Structural equation modeling indicates good fit: χ2/df = 2.86, RMESA = 0.068, CFI = 0.92, NNFI = 0.91, NFI = 0.90, GFI = 0.93. It indicates that interpersonal disturbance and general self-efficacy can play mediating roles between empowering motivational climate in physical education and social responsibility, respectively. After that, interpersonal disturbance as well as general self-efficacy in turn plays the chain mediating effect in the relationship between empowering motivational climate in physical education and social responsibility. The effect size of the mediating effect of interpersonal disturbance and general self-efficacy in the relationship between empowering motivational climate in physical education and social responsibility is 0.048 and 0.148, respectively, and the effect size of the chain mediating effect is 0.031.Conclusion: Empowering motivational climate in physical education not only has a direct effect on social responsibility among high school students, but also influences social responsibility by the chain mediating effect of interpersonal disturbance and general self-efficacy.

Associations Between Attention Deficit/Hyperactivity Disorder and Internet Gaming Disorder Symptoms Mediated by Depressive Symptoms and Hopelessness Among College Students.

PurposeThe mediating role of depressive symptoms and hopelessness on the relationship between attention deficit/hyperactivity disorder (ADHD) and internet gaming disorder (IGD) symptoms has not yet been elucidated. This study assessed this mediating effect in college students.Participants and MethodsParticipants consisted of 1236 freshmen recruited at a local university. Symptoms of ADHD, IGD, depression and hopelessness were measured using self-report scales. The effect of ADHD on IGD mediated by depression and hopelessness was analyzed by Haye’s PROCESS macro for SPSS (Model 6) using the bias-corrected percentile bootstrap method with 5000 bootstrapped samples.ResultsSymptoms of ADHD, depression and hopelessness were common in college students and were strongly associated with the appearance of IGD symptoms. ADHD symptoms of college students impacted their IGD symptoms directly and indirectly via depressive symptoms and hopelessness. The total effect of ADHD symptoms on IGD symptoms was 0.075 (standard error [SE]: 0.009, 95% confidence interval [CI] 0.057, 0.093), with a direct effect of 0.037 (SE: 0.010, 95% CI 0.018, 0.056, effect ratio: 49.3%), and total indirect effect was 0.038 (SE: 0.005, 95% CI 0.029, 0.050, effect ratio: 50.7%).ConclusionDepressive symptoms and hopelessness can mediate the relationship between ADHD and IGD symptoms among college students. These findings point to the importance of evaluating ADHD, depressive and hopelessness symptoms for the prevention and treatment of adult IGD.

Estimation of the generalized process capability index C pyk based on bias-corrected maximum-likelihood estimators for the generalized inverse Lindley distribution and bootstrap confidence intervals

In this paper, we are interested in estimating the generalized process capability index () proposed by Maiti et al. [On generalizing process capability indices. Qual Technol Quant Manag. 2010;7(3):279–300], when the underlying distribution is the generalized inverse Lindley (GIL) distribution. We estimate parameters of the GIL distribution using maximum likelihood (ML), bias-corrected maximum-likelihood (BCML) and bootstrap bias-corrected maximum-likelihood (BBCML) methodologies. are obtained using proposed estimators. Bootstrap confidence intervals called standard bootstrap (SB), percentile bootstrap (PB) and bias-corrected percentile bootstrap (BCPB) are constructed based on the estimators of . We compare efficiencies of the parameter estimators and the performance of ML, BCML and BBCML based Cpyk via an extensive Monte Carlo simulation study. A simulation study is also described to compare the coverage probabilities (CP) and average lengths (AL) of SB, PB and BCPB confidence intervals for proposed . Finally, two real datasets are analysed for illustrative purposes.

Estimation of the reliability characteristics by using classical and Bayesian methods of estimation for xgamma distribution

In this article, estimation of the reliability characteristics viz., mean time to system failure $$M(t; \alpha )$$ , reliability function $$R(t; \alpha )$$ is considered for xgamma lifetime distribution. First, four different methods of estimation of the reliability characteristics for specified value of time t are addressed from frequentist approaches and compared them in terms of their respective mean squared errors using extensive numerical simulations. Second, we compared three bootstrap confidence intervals (BCIs) including standard bootstrap, percentile bootstrap and bias-corrected percentile bootstrap. Third, Bayesian estimation is considered under three loss functions using gamma prior for the considered model. Fourth, we obtained highest posterior density (HPD) credible intervals of $$M(t; \alpha )$$ and $$R(t; \alpha )$$ . Monte Carlo simulation study has been carried out to compare the performances of the classical BCIs and HPD credible intervals of $$M(t; \alpha )$$ and $$R(t; \alpha )$$ in terms of average widths and coverage probabilities. Finally, a real data set has been analyzed for illustrative purpose.

Confidence intervals of the index $C_{pk}$ for normally distributed quality characteristics using classical and Bayesian methods of estimation

One of the indicators for evaluating the capability of a process potential and performance in an effective way is the process capability index (PCI). It is of great significance to quality control engineers as it quantifies the relation between the actual performance of the process and the pre-set specifications of the product. Most of the traditional PCIs performed well when process follows the normal behaviour. In this article, we consider a process capability index, $C_{pk}$, suggested by Kane (Journal of Quality Technology 18 (1986) 41–52) which can be used for normal random variables. The objective of this article is three fold: First, we address different methods of estimation of the process capability index $C_{pk}$ from frequentist approaches for the normal distribution. We briefly describe different frequentist approaches, namely, maximum likelihood estimators, least squares and weighted least squares estimators, maximum product of spacings estimators, Cramèr–von-Mises estimators, Anderson–Darling estimators and Right-Tail Anderson–Darling estimators and compare them in terms of their mean squared errors using extensive numerical simulations. Second, we compare three parametric bootstrap confidence intervals (BCIs) namely, standard bootstrap, percentile bootstrap and bias-corrected percentile bootstrap. Third, we consider Bayesian estimation under squared error loss function using normal prior for location parameter and inverse gamma for scale parameter for the considered model. Monte Carlo simulation study has been carried out to compare the performances of the classical BCIs and highest posterior density (HPD) credible intervals of $C_{pk}$ in terms of average widths and coverage probabilities. Finally, two real data sets have been analyzed for illustrative purposes.

Stress-Strength Reliability for Exponentiated Inverted Weibull Distribution with Application on Breaking of Jute Fiber and Carbon Fibers.

For the first time and by using an entire sample, we discussed the estimation of the unknown parameters θ1, θ2, and β and the system of stress-strength reliability R=P(Y < X) for exponentiated inverted Weibull (EIW) distributions with an equivalent scale parameter supported eight methods. We will use maximum likelihood method, maximum product of spacing estimation (MPSE), minimum spacing absolute-log distance estimation (MSALDE), least square estimation (LSE), weighted least square estimation (WLSE), method of Cramér-von Mises estimation (CME), and Anderson-Darling estimation (ADE) when X and Y are two independent a scaled exponentiated inverted Weibull (EIW) distribution. Percentile bootstrap and bias-corrected percentile bootstrap confidence intervals are introduced. To pick the better method of estimation, we used the Monte Carlo simulation study for comparing the efficiency of the various estimators suggested using mean square error and interval length criterion. From cases of samples, we discovered that the results of the maximum product of spacing method are more competitive than those of the other methods. A two real‐life data sets are represented demonstrating how the applicability of the methodologies proposed in real phenomena.

S73. RELATIONSHIP OF COGNITIVE ABILITY AND PERSONALITY TRAITS WITH HOSTILE ATTRIBUTION BIAS IN NONCLINICAL SUBJECTS: THEORY OF MIND AS A MEDIATOR

BackgroundHostile attribution bias has been reported to be common from nonclinical population to serious mental illness such as schizophrenia and is known to be closely related to social cognition. The aims of this study was to investigate whether theory of mind (ToM) skills mediate the relationship between cognitive ability and personality traits and attribution bias by using the Korean version of Reading the Minds in the eyes test (K-RMET).MethodsOne hundred ninety-six (101 females) nonclinical youths were recruited. To assess general cognitive ability and ToM skills, participants were asked to complete the Raven’s Standard Progressive Matrices (SPM) and the K-RMET. For personality traits, the Eysenck Personality Questionnaire (psychoticism) and Interpersonal Reactivity Index (perspective taking) were administered. To evaluate the hostile attribution bias, the Ambiguous Intentions Hostility Questionnaire was also administered. Path analysis and the bias‐corrected percentile bootstrap method were performed to estimate the parameters of mediating effects.ResultsBased on Akaike Information Criterion(AIC) the best model characterized 1) two direct pathways from psychoticism and the K-RMET to hostility attribution bias and 2) four indirect pathways, wherein SPM, perspective taking and psychoticism influence hostile attribution bias through the K-RMET. The K-RMET fully mediated the association between SPM (p=.028), perspective taking (p=.027), psychoticism (p=.041) and hostile attribution bias.DiscussionThe main findings suggested that ToM skill such as the RMET plays an important role in explaining the relationship between cognitive ability and personality traits and hostile attribution bias. The development of remediation strategy of theory of mind skills may be needed to balance the enhanced hostility bias which is underlying the paranoia.

Classical Estimation of the Index Spmk and Its Confidence Intervals for Power Lindley Distributed Quality Characteristics

The process capability index (PCI) has been introduced as a tool to aid in the assessment of process performance. Usually, conventional PCIs perform well under normally distributed quality characteristics. However, when these PCIs are employed to evaluate nonnormally distributed process, they often provide inaccurate results. In this article, in order to estimate the PCI Spmk when the process follows power Lindley distribution, first, seven classical methods of estimation, namely, maximum likelihood method of estimation, ordinary and weighted least squares methods of estimation, Cramèr–von Mises method of estimation, maximum product of spacings method of estimation, Anderson–Darling, and right-tail Anderson–Darling methods of estimation, are considered and the performance of these estimation methods based on their mean squared error is compared. Next, three bootstrap confidence intervals (BCIs) of the PCI Spmk, namely, standard bootstrap, percentile bootstrap, and bias-corrected percentile bootstrap, are considered and compared in terms of their average width, coverage probability, and relative coverage. Besides, a new cost-effective PCI, namely, Spmkc is introduced by incorporating tolerance cost function in the index Spmk. To evaluate the performance of the methods of estimation and BCIs, a simulation study is carried out. Simulation results showed that the maximum likelihood method of estimation performs better than their counterparts in terms of mean squared error, while bias-corrected percentile bootstrap provides smaller confidence length (width) and higher relative coverage than standard bootstrap and percentile bootstrap across sample sizes. Finally, two real data examples are provided to investigate the performance of the proposed procedures.

The Impact of Gratitude on Core Self-Evaluations of Rural Junior Middle School Students: A Chain Mediation Analysis

Objective: To explore the mediating effects of self-esteem and academic self-efficacy on gratitude and core self-evaluations in rural junior middle school students. Methods: The Gratitude Scale, Self-esteem Scale, Academic Self-Efficacy Scale and Core Self-Evaluations Scale were used to conduct a questionnaire survey among 923 rural junior middle school students. The bias-corrected percentile Bootstrap method was conducted to test the chain mediating role of self-esteem and academic self-efficacy between rural junior middle school students’ gratitude and core self-evaluations. Results: Correlation analysis showed significantly positive correlations between gratitude, self-esteem, academic self-efficacy and core self-evaluations (r = 0.30 - 0.56, P Conclusion: Gratitude not only directly influences the core self-evaluations of rural junior middle school students, but also through the indirect path of self-esteem and academic self-efficacy, as well as the chain mediating path between these two variables.

Comparison between two generalized process capability indices for Burr XII distribution using bootstrap confidence intervals

Process capability index is an effective indicator for gauging the capability of a process potential and performance. It is used to quantify the relation between the actual performance of the process and the preset specifications of the product. In this article, we utilize bootstrap re-sampling simulation method to construct bootstrap confidence intervals, namely, standard bootstrap, percentile bootstrap, Student’s t bootstrap (STB) and bias-corrected percentile bootstrap to study the difference between two generalized process capability indices $$C_{\text {pTk1}}$$ and $$C_{\text {pTk2}}$$ ($$\delta =C_{\text {pTk1}}-C_{\text {pTk2}}$$) and to select the better of the two processes or manufacturer’s (or supplier’s) through simulation when the underlying distribution is Burr XII distribution. The model parameters are estimated by maximum likelihood method. The proposed four bootstrap confidence intervals can be effectively employed to determine which one of the two processes or manufacturers (or suppliers) has a better process capability. Monte Carlo simulations are performed to compare the performances of the proposed bootstrap confidence intervals for $$\delta $$ in terms of their estimated average widths, coverage probabilities and relative coverages. Simulation results showed that the estimated average width and relative coverages of the STB confidence interval perform better than their counterparts. Finally, real data are presented to illustrate the bootstrap confidence intervals of the difference between two process capability indices.

Inference of accelerated dependent competing risks model for Marshall–Olkin bivariate Weibull distribution with nonconstant parameters

In this paper, we discuss the statistical inference of constant-stress accelerated dependent competing risks model under Type-II hybrid censoring schemes. The dependency structure is modeled by a Marshall–Olkin bivariate Weibull distribution. Both the shape and the scale parameters in the model are assumed to be dependent on the stress levels through a log-linear relationship. The maximum likelihood estimates (MLEs) of the model parameters are derived. Confidence intervals (CIs) of the model parameters are constructed based on the asymptotic normality of MLEs and the bias-corrected percentile bootstrap method. Bayes estimates with the squared error loss function and the highest posterior density (HPD) credible intervals (CIs) are obtained by using an importance sampling method. In addition, the estimates for the accelerated coefficients and the reliability under normal use stress level at mission time are derived. A Monte Carlo simulation study is used to evaluate the performance of the proposed statistical inference methods. A real data example is used to illustrate the methodologies proposed in this paper and to compare the proposed model with the copula model.

Assessing the process capability index $$S_\mathrm{{pmk}}$$ using improved estimators

Process capability indices (PCIs) are widely used to determine whether the production process is working according to given specifications or not. It plays an important role in monitoring and analyzing process quality and productivity. Since PCI is based on sample observations, it is a point estimate of the true PCI. It is well known that confidence interval (CI) provides much more information about the population characteristic of interest than a point estimate. In this paper, new estimator for PCI $$S_\mathrm{{pmk}}$$ has been proposed using improved estimators of population mean and variance. The proposed and classical index is compared with respect to mean squared error (MSE). Numerical results are provided to illustrate the proposed index and to judge the merits of the proposed estimators. Further, asymptotic confidence interval (ACI) and three non-parametric BCIs, namely, standard bootstrap (s-boot), percentile bootstrap (p-boot) and bias-corrected percentile bootstrap (BCp-boot) of the proposed modified PCI $$S_\mathrm{{pmk}}$$ are studied through simulation when the underlying distribution follows Lindley distribution. Method of maximum likelihood is used to estimate the parameter of the model. A Monte Carlo simulation has been used to investigate the estimated coverage probabilities and average widths of the ACI and BCIs for the modified PCI $$S_\mathrm{{pmk}}$$ . Finally, four real data sets are analyzed for illustrative purposes.

Bootstrap confidence intervals of CpTk for two parameter logistic exponential distribution with applications

Process capability index is an important statistical technique that measures the ability of a process and hence it is used in quality control to quantify the relation between the actual performance of the process and the preset specification of the product. In this article bootstrap confidence intervals (BCIs) of generalized process capability index (GPCI) $$C_{pTk}$$ proposed by Maiti et al. (J Qual Technol Quant Manag 7(3):279–300, 2010) are studied through simulation when the underlying distribution is logistic-exponential (LE). The model parameters are estimated by the maximum likelihood method of estimation. Three non-parametric (NPR) as well as parametric (PR) BCIs, namely, percentile bootstrap ( $$\mathcal P$$ -boot), student’s t bootstrap ( $$\mathcal T$$ -boot) and bias-corrected percentile bootstrap ( $$\mathcal BC_p$$ -boot) are considered for obtaining confidence intervals (CIs) of GPCI $$C_{pTk}$$ . Through extensive Monte Carlo simulations, we examine the estimated coverage probabilities and average widths of the BCIs for two parameter LE distribution and in particular for exponential distribution. Simulation results show that the estimated coverage probabilities of the $$\mathcal P$$ -boot CI perform better than their counterparts. Finally, three real data sets are analyzed for illustrative purposes.

Evaluation of Bootstrap Confidence Intervals Using a New Non-Normal Process Capability Index

This paper assesses the bootstrap confidence intervals of a newly proposed process capability index (PCI) for Weibull distribution, using the logarithm of the analyzed data. These methods can be applied when the quality of interest has non-symmetrical distribution. Bootstrap confidence intervals, which consist of standard bootstrap (SB), percentile bootstrap (PB), and bias-corrected percentile bootstrap (BCPB) confidence interval are constructed for the proposed method. A Monte Carlo simulation study is used to determine the efficiency of newly proposed index Cpkw over the existing method by addressing the coverage probabilities and average widths. The outcome shows that the BCPB confidence interval is recommended. The methodology of the proposed index has been explained by using the real data of breaking stress of carbon fibers.

Bootstrap confidence intervals of generalized process capability index Cpyk using different methods of estimation

ABSTRACTOne of the indicators for evaluating the capability of a process is the process capability index. In this article, we consider six frequentest estimation methods, namely, the method of maximum likelihood (ML), the method of least square (LS), the method of weighted least square, method of percentile (PC), the method of maximum product of spacing and method of Cramèr-von-Mises (CM) to estimate the parameters and the generalized process capability index (GPCI) for the logistic exponential (LE) distribution and in particular for exponential distribution. It is well known that confidence interval (CI) provides much more information about the population characteristic of interest than does a point estimate. Hence, next, we consider three bootstrap confidence intervals (BCIs) namely, standard bootstrap (s-boot), percentile bootstrap (p-boot) and bias-corrected percentile bootstrap (-boot) for obtaining CIs of GPCI using the aforementioned methods of estimation. A Monte Carlo simulation has been used to investigate the estimated coverage probabilities and average widths of the BCIs. The performances of the estimators have been compared in terms of their mean squared error using simulated samples. Simulation results showed that the estimated coverage probabilities of the p-boot CI and the s-boot CI get closer to the nominal confidence level than those of the -boot CI for both cases. Finally, three real data sets are analyzed for illustrative purposes.

Improved bootstrap confidence intervals for the process capability index Cpk

The process capability index, Cpk, is a useful tool for assessing the capability of a manufacturing process. There exist three well-known confidence intervals for the process capability index. These intervals are based on the standard bootstrap, the percentile bootstrap and the bias-corrected percentile bootstrap, respectively. We propose three variants of these bootstrap confidence intervals where each of the three intervals are modified in a particular way. Extensive Monte Carlo simulations are carried out and the results indicate that the three proposed bootstrap methods are generally preferred over the corresponding original schemes.

暴力环境接触对大学生网络攻击行为的影响：反刍思维与网络道德的作用 &amp;lt;sup&amp;gt;*&amp;lt;/sup&amp;gt;

<p id="C2">With the development of science, the internet has become an indispensable tool in college students' study and daily life. However, online aggressive behavior has become a much more serious problem for college students in recent few years. It is necessary to find out which factors have significant effects on online aggressive behavior of college students. According to the previous researches, the violent exposure was found to be able to predict aggressive behavior significantly. In addition, some theorists also have confirmed that ruminative responses and aggressive behavior are strongly related. However, as a special form of aggressive behavior, there was little research focused on online aggressive behavior and violent exposure. So the purposes of the present study is to explore the relationship between violent exposure, ruminative responses, internet moral and online aggressive behavior as well as the mechanism the effect of violent exposure on online aggressive behavior of college students.<br/>A total sample of 1000 college students from some universities was selected, with 326 males and 508 females, the average age was 20.74-year-old. All subjects were gathered in the class and finished the questionnaires within about 30 minutes. The questionnaires included the Violent Exposure Questionnaire (VEQ), Online Aggressive Behavior Scale (OABS), Ruminative Responses Scale (RSS), and the Internet Moral Questionnaire (IMQ). Data was collected and analyzed with SPSS 24.0, Amos 21.0 and Mplus 7.4, and the bias-corrected percentile Bootstrap method was used to analyze the role of ruminative responses and internet moral between violent exposure and college students' online aggressive behavior. A single factor analysis was calculated to test the common method variance. Results showed that the study was in-existent common method variance.<br/>The results show that: (1)The relationships between each pair of violent exposure, ruminative responses, internet moral and online aggressive behavior are correlated significantly and positively, the correlation coefficient ranges 0.07 from 0.96 (<italic>p</italic> &lt; 0.01); (2)The structural equation model (SEM) reveals that the data fits the theoretical model well (c ²/<italic>df</italic> = 2.45, CFI = 0.99, TLI = 0.98, SRMR = 0.03, RMSEA = 0.04). (3) Violent exposure has a significant direct effect on online aggressive behavior (<italic>β</italic> = 0.29, <italic>p</italic> &lt; 0.01); Violent exposure has a significant direct effect on ruminative responses (<italic>β</italic> = 0.23, <italic>p </italic>&lt; 0.01); Ruminative responses has a significant direct effect on online aggressive behavior (<italic>β</italic> = 0.17, <italic>p</italic> &lt; 0.01); Internet moral has a significant direct effect on online aggressive behavior (<italic>β</italic> = -0.17, <italic>p</italic> &lt; 0.01); Interaction has a significant direct effect on online aggressive behavior (<italic>β</italic> = -0.17, <italic>p</italic> &lt; 0.01). (4)Violent exposure has a significant indirect effect on online aggressive behavior through ruminative responses, and the confidence interval of 95% is [0.025, 0.061]; (5) Internet moral moderates the relation between violent exposure and online aggressive behavior of college students, that is, there is a significant positive relation between violent exposure and online aggressive behavior under the low internet moral level, however, there is a non-significant relation between violent exposure and online aggressive behavior under the high internet moral level. <br/>It is concluded that in the structural equation model of violent exposure on online aggressive behavior of college students, ruminative responses plays a partial mediating role and internet moral moderates the direct effect. These findings suggest some measures of prevention and treatment for college students’ online aggressive behavior should be taken. Schools and families should set up a good core self-evaluation system in order to help them improve their moral level and eradicate online aggressive behavior.

Inference about the Population Kurtosis with Confidence: Parametric and Bootstrap Approaches

This paper considers some classical and bootstrap methods in constructing confidence intervals for the kurtosis parameter of a distribution. The bootstrap techniques used are: Bias-Corrected Standard Bootstrap, Efron’s Percentile Bootstrap, Hall’s Percentile Bootstrap and Bias-Corrected Percentile Bootstrap. The performance of these estimators is compared through confidence intervals by determining the average width and probabilities of capturing the kurtosis parameter of a distribution. We observed that the parametric method works well in terms of coverage probability when data come from a normal distribution, while the bootstrap intervals struggled in constantly reaching a 95% confidence level. When sample data are from a distribution with negative kurtosis, both parametric and bootstrap confidence intervals performed well, although we noticed that bootstrap methods tend to have shorter intervals. When it comes to positive kurtosis, bootstrap methods perform slightly better than classical methods in the sense of high coverage probability. For illustration purposes, two real life health related data are analyzed.

Caregiver burden in Alzheimer's disease: Moderation effects of social support and mediation effects of positive aspects of caregiving.

Although there are many studies on the relationship between patient-related factors and negative caregiver outcomes, the specifics of this relationship are poorly understood. We aimed to examine whether caregiver social support moderated the relationship between patient factors and negative outcomes for caregivers of community-dwelling older adults with Alzheimer's disease (AD), and whether positive aspects of caregiving mediated this relationship. We conducted a cross-sectional study of patients diagnosed with AD from 2 hospitals and 3 communities in Taiyuan, China, and their caregivers. Latent moderated structural equations and the bias-corrected percentile bootstrap method were used to estimate the parameters of moderating and mediating effects, respectively. Social support significantly moderated the effects of AD patient cognitive function (P<0.001) and depression (P=0.001) on caregiver burden. Positive aspects of caregiving completely mediated the association between patient depression and caregiver burden (P=0.006), caregiver anxiety (P=0.007), and caregiver depression (P=0.034). The findings identify social support as a moderator and positive aspects of caregiving as a mediator of the relationship between patient-related factors and negative caregiver outcomes. The results suggest that health care providers must offer more effective social support for caregivers. In addition, prompt identification of patient and caregiver emotional states could help to improve quality of life.