A bootstrap cross-validation method is studied. It achieves accurate error estimation through a simple procedure with bootstrap resampling and only costs computer CPU time. Simulation studies and applications to microarray data demonstrate that it performs consistently better than its competitors. This method possesses several attractive properties: (1) it is implemented through a simple procedure; (2) it performs well for small samples with sample size, as small as 16; (3) it is not restricted to any particular classification rules and thus applies to many parametric or non-parametric methods.
We consider regression analysis when covariate variables are the underlying regression coefficients of another linear mixed model. A naive approach is to use each subject's repeated measurements, which are assumed to follow a linear mixed model, and obtain subject-specific estimated coefficients to replace the covariate variables. However, directly replacing the unobserved covariates in the primary regression by these estimated coefficients may result in a significantly biased estimator. The aforementioned problem can be evaluated as a generalization of the classical additive error model where repeated measures are considered as replicates. To correct for these biases, we investigate a pseudo-expected estimating equation (EEE) estimator, a regression calibration (RC) estimator, and a refined version of the RC estimator. For linear regression, the first two estimators are identical under certain conditions. However, when the primary regression model is a nonlinear model, the RC estimator is usually biased. We thus consider a refined regression calibration estimator whose performance is close to that of the pseudo-EEE estimator but does not require numerical integration. The RC estimator is also extended to the proportional hazards regression model. In addition to the distribution theory, we evaluate the methods through simulation studies. The methods are applied to analyze a real dataset from a child growth study.
Active commuting to school (ACS) may increase children’s daily physical activity and help them maintain a healthy weight. Previous studies have identified various perceived barriers related to children’s ACS. However, it is not clear whether and how these studies were methodologically sound and theoretically grounded. The purpose of this review was to critically assess the current literature on perceived barriers to children’s ACS and provide recommendations for future studies. Empirically based literature on perceived barriers to ACS was systematically searched from six databases. A methodological quality scale (MQS) and a theory utilization quality scale (TQS) were created based on previously established instruments and tailored for the current review. Among the 39 studies that met the inclusion criteria, 19 (48.7%) reported statistically significant perceived barriers to child’s ACS. The methodological and theory utilization qualities of reviewed studies varied, with MQS scores ranging between 7 and 20 (Mean =12.95, SD =2.95) and TQS scores from 1 to 7 (Mean =3.62, SD =1.74). A detailed appraisal of the literature suggests several empirical, methodological, and theoretical recommendations for future studies on perceived barriers to ACS. Empirically, increasing the diversity of study regions and samples should be a high priority, particularly in Asian and European countries, and among rural residents; more prospective and interventions studies are needed to determine the causal mechanism liking the perceived factors and ACS; future researchers should include policy-related barriers into their inquiries. Methodologically, the conceptualization of ACS should be standardized or at least well rationalized in future studies to ensure the comparability of results; researchers’ awareness need to be increased for improving the methodological rigor of studies, especially in regard to appropriate statistical analysis techniques, control variable estimation, multicollinearity testing, and reliability and validity reporting. Theoretically, future researchers need to first ground their investigations in theoretical foundations; efforts should be devoted to make sure theories are used thoroughly and correctly; important theoretical constructs, in particular, need to be conceptualized and operationalized appropriately to ensure accurate measurement. By reviewing what has been achieved, this review offered insights for more sophisticated ACS studies in the future.
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