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Physical activity measurements derived from self-report surveys are prone to measurement errors. Monitoring devices like accelerometers offer more objective measurements of physical activity, but are impractical for use in large-scale surveys. A model capable of predicting objective measurements of physical activity from self-reports would offer a practical alternative to obtaining measurements directly from monitoring devices. Using data from National Health and Nutrition Examination Survey 2003–2006, we developed and validated models for predicting objective physical activity from self-report variables and other demographic characteristics. The prediction intervals produced by the models were large, suggesting that the ability to predict objective physical activity for individuals from self-reports is limited. [ABSTRACT FROM AUTHOR]

In this and a second article, we propose ‘coregionalization analysis with a drift’ (CRAD), as a method to assess the multi-scale variability of and relationships between ecological variables from a multivariate spatial data set. CRAD is carried out in two phases: (I) a deterministic component representing the large-scale pattern (called ‘drift’) and a random component modeled as a second-order stationary process are estimated for each variable separately; (II) a linear model of coregionalization is fitted to the direct and cross experimental variograms of residuals (i.e., after removing the estimated drifts) to assess relationships at smaller scales, while the estimated drifts are used to study relationships at large scale. In this article, we focus on phase I of CRAD, by addressing the questions of the choice of the drift estimation procedure, which is linked to the estimation of random components, and of the presence of a bias in the direct experimental variogram of residuals. In this phase, both the estimation of the drift and the fitting of a model to the direct experimental variogram of residuals are performed iteratively by estimated generalized least squares (EGLS). We use theoretical calculations and a Monte Carlo study to demonstrate that complex large-scale patterns, such as patchy drifts, are better captured with local drift estimation procedures using low-order polynomials within a moving window, than with global procedures. Furthermore, despite the bias in direct experimental variograms of residuals, good estimates of spatial autocovariance parameters are obtained with the double iterative EGLS procedure in the conditions of application of CRAD. An example with forest soil property and tree species diversity data is presented to discuss the choice of drift estimation procedure in practice. [ABSTRACT FROM AUTHOR]

We consider a linear regression with the error term that obeys an autoregressive model of infinite order and estimate parameters of the models. The parameters of the autoregressive model should be estimated based on estimated residuals obtained by means of the method of ordinary least squares, because the errors are unobservable. The consistency of the coefficients, variance and spectral density of the model obeyed by the error term is shown. Further, we estimate the coefficients of the linear regression by means of the method of estimated generalized least squares. We also show the consistency of the estimator. We consider a linear regression with the error term that obeys an autoregressive model of infinite order and estimate parameters of the models. The parameters of the autoregressive model should be estimated based on estimated residuals obtained by means of the method of ordinary least squares, because the errors are unobservable. The consistency of the coefficients, variance and spectral density of the model obeyed by the error term is shown. Further, we estimate the coefficients of the linear regression by means of the method of estimated generalized least squares. We also show the consistency of the estimator. [ABSTRACT FROM AUTHOR]

To analyze simulation runs which use the same random numbers, the blocking concept of experimental design is not needed. Instead, this paper applies a linear regression model with a nondiagonal covariance matrix. This covariance matrix does not need to have a specific pattern such as constant covariances. A simple example yields surprising results. The paper proposes a new framework for the error analysis. This framework consists of three factors (namely, common random numbers, replication, model validity), each with three levels. [ABSTRACT FROM AUTHOR]