The often overlooked issue of statistical power: This and other issues regarding assessing importance weighting in quality of life measures

In the area of quality of life research, researchers may ask respondents to rate importance as well as satisfaction of various life domains (such as job and health) and use importance ratings as weights to calculate overall, or global, life satisfaction. The practice of giving more important domains more weight, known as importance weighting, has not been without controversy. Several previous studies assessed importance weighting using the analytical approach of moderated regression. This study discusses major issues related to how importance weighting has been assessed. Specifically, this study highlights that studies on importance weighting without considering statistical power are prone to type II error, i.e., failing to reject the null hypothesis of no significant weighting effect when the null hypothesis is actually false. The sample size required for adequate statistical power to detect importance weighting functions appeared larger than most previous studies could offer.     

Finite mixture of regression models for a stratified sample

Despite the popularity and importance, there is limited work on modelling data which come from complex survey design using finite mixture models. In this work, we explored the use of finite mixture regression models when the samples were drawn using a complex survey design. In particular, we considered modelling data collected based on stratified sampling design. We developed a new design-based inference where we integrated sampling weights in the complete-data log-likelihood function. The expectation–maximisation algorithm was developed accordingly. A simulation study was conducted to compare the new methodology with the usual finite mixture of a regression model. The comparison was done using bias-variance components of mean square error. Additionally, a simulation study was conducted to assess the ability of the Bayesian information criterion to select the optimal number of components under the proposed modelling approach. The methodology was implemented on real data with good results.     

The exponentiated power exponential regression model with different regression structures: application in nursing data

We define the exponentiated power exponential distribution and propose a regression model with different systematic structures based on the new distribution. We show that the new regression model can be applied to dispersion data since it represents a parametric family of models that includes as sub-models some widely-known regression models. It then can be used more effectively in the analysis of real data. We use maximum likelihood estimation and derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. Some global-influence measurements are also investigated and simulation studies are performed to evaluate the accuracy of the estimates. We provide an application of the regression model with four systematic structures to nursing activities score data in the Unit of the Medical Clinic of University of São Paulo (USP) Hospital.     

Cox regression of clustered event times with covariates missing not at random

Motivated by a recent tuberculosis (TB) study, this paper is concerned with covariates missing not at random (MNAR) and models the potential intracluster correlation by a frailty. We consider the regression analysis of right‐censored event times from clustered subjects under a Cox proportional hazards frailty model and present the semiparametric maximum likelihood estimator (SPMLE) of the model parameters. An easy‐to‐implement pseudo‐SPMLE is then proposed to accommodate more realistic situations using readily available supplementary information on the missing covariates. Algorithms are provided to compute the estimators and their consistent variance estimators. We demonstrate that both the SPMLE and the pseudo‐SPMLE are consistent and asymptotically normal by the arguments based on the theory of modern empirical processes. The proposed approach is examined numerically via simulation and illustrated with an analysis of the motivating TB study data.     

Choice of the ridge factor from the correlation matrix determinant

Ridge regression is the alternative method to ordinary least squares, which is mostly applied when a multiple linear regression model presents a worrying degree of collinearity. A relevant topic in ridge regression is the selection of the ridge parameter, and different proposals have been presented in the scientific literature. Since the ridge estimator is biased, its estimation is normally based on the calculation of the mean square error (MSE) without considering (to the best of our knowledge) whether the proposed value for the ridge parameter really mitigates the collinearity. With this goal and different simulations, this paper proposes to estimate the ridge parameter from the determinant of the matrix of correlation of the data, which verifies that the variance inflation factor (VIF) is lower than the traditionally established threshold. The possible relation between the VIF and the determinant of the matrix of correlation is also analysed. Finally, the contribution is illustrated with three real examples.     

Bayesian spatial quantile regression for areal count data,with application on substitute care placements in Texas

Quantile regression (QR) allows one to model the effect of covariates across the entire response distribution, rather than only at the mean, but QR methods have been almost exclusively applied to continuous response variables and without considering spatial effects. Of the few studies that have performed QR on count data, none have included random spatial effects, which is an integral facet of the Bayesian spatial QR model for areal counts that we propose. Additionally, we introduce a simplifying alternative to the response variable transformation currently employed in the QR for counts literature. The efficacy of the proposed model is demonstrated via simulation study and on a real data application from the Texas Department of Family and Protective Services (TDFPS). Our model outperforms a comparable non-spatial model in both instances, as evidenced by the deviance information criterion (DIC) and coverage probabilities. With the TDFPS data, we identify one of four covariates, along with the intercept, as having a nonconstant effect across the response distribution.     

Oracle GMM estimation for misspecified models via thresholding

We propose a thresholding generalized method of moments (GMM) estimator for misspecified time series moment condition models. This estimator has the following oracle property: its asymptotic behavior is the same as of any efficient GMM estimator obtained under the a priori information that the true model were known. We propose data adaptive selection methods for thresholding parameter using multiple testing procedures. We determine the limiting null distributions of classical parameter tests and show the consistency of the corresponding block-bootstrap tests used in conjunction with thresholding GMM inference. We present the results of a simulation study for a misspecified instrumental variable regression model and for a vector autoregressive model with measurement error. We illustrate an application of the proposed methodology to data analysis of a real-world dataset.     

Part-time employment and worker health in the United States

A growing body of research has highlighted the consequences of part-time employment for workers’ health and well-being. However, these studies have yielded inconsistent results and relied on cross-sectional data. In addition, relatively little empirical research has explored whether the effect of working part-time on health varies by gender, particularly in the United States. Using longitudinal data from three waves of the General Social Survey panel (2010–2012–2014), our study examined the association between part-time employment and perceived health among U.S employees, and whether this association varied by gender. The results showed that part-time workers were less likely to report poor self-rated health than full-time workers, especially among males. The pattern of results was consistent across empirical approaches—including generalized estimating equations and random effects models, with an extensive set of covariates. Taken together, these findings suggest that for U.S. employees, working part-time appears to be beneficial or at least not detrimental to perceived health, which warrants further investigation.     

Regression models with ordered multiple categorical predictors

Ordered multiple categorical (MC) variable has been widely considered and studied as response variable, and few studies have carefully considered it as a predictor in linear regression. When doing this, the existence of some pseudo-categories may result in overfitting, and to detect those pseudo-categories by hypothesis test of all dummy variables might have low specificity. In this paper, we propose a transformation method of dummy variables for such ordered MC predictors, after which a model selection method combined with BIC will be elaborated. Theoretical consistency of our model selection method is established under some common assumptions. Both simulation studies and real data analysis of a medical survey indicate that our method provides good performance and is applicable to a wide range of biomedical research.