FITTING BOLE-VOLUME EQUATIONS TO SPATIALLY CORRELATED WITHIN-TREE DATA

Equations to predict the volume of an individual tree bole between stump height and the height at which its diameter has tapered to a specified minimum are common in forestry. When fitting such a regression equation, a sample of trees which span the range of sizes needed for eventual application of the equation is selected. Bole diameter is measured at ascending heights on the bole. Each tree, therefore, contributes multiple measurements to the data fitted to the equation. In contrast to past practice, we model these data in a manner which accounts for the likely spatial correlation among measurements within a tree. The resulting mixed-effects nonlinear model is fitted by REML and also by generalized estimating equations (GEE). Results from the two approaches are nearly identical, which suggests that the computationally less demanding GEE may be acceptable as a routine alternative to a fully parameterized approach

An R 2 statistic for fixed effects in the linear mixed model

Statisticians most often use the linear mixed model to analyze Gaussian longitudinal data. The value and familiarity of the R2 statistic in the linear univariate model naturally creates great interest in extending it to the linear mixed model. We define and describe how to compute a model R2 statistic for the linear mixed model by using only a single model. The proposed R2 statistic measures multivariate association between the repeated outcomes and the fixed effects in the linear mixed model. The R2 statistic arises as a 1–1 function of an appropriate F statistic for testing all fixed effects (except typically the intercept) in a full model. The statistic compares the full model to a null model with all fixed effects deleted (except typically the intercept) while retaining exactly the same covariance structure. Furthermore, the R2 statistic leads immediately to a natural definition of a partial R2 statistic. A mixed model in which ethnicity gives a very small p-value as a longitudinal predictor of blood pressure compellingly illustrates the value of the statistic. In sharp contrast to the extreme p-value, a very small R2, a measure of statistical and scientific importance, indicates that ethnicity has an almost negligible association with the repeated blood pressure outcomes for the study

A conspectus on Estimating Function theory and its applicability to recurrent modeling issues in forest biometry.

Much of forestry data is characterized by a longitudinal or repeated measures structure where multiple observations taken on some units of interest are correlated. Such dependencies are often ignored in favor of an apparently simpler analysis at the cost of invalid inferences. The last decade has brought to light many new statistical techniques that enable one to successfully deal with dependent observations. Although apparently distinct at first, the theory of Estimating Functions provides a natural extension of classical estimation that encompasses many ot these new approaches. This contribution introduces Estimating Function Theory as a principle with potential for unification and presents examples covering a variety of modeling issues to demonstrate its applicability

Contemporary statistical models for the plant and soil sciences /

System requirements: Windows 95/98/NT/2000 or Macintosh, Solaris, OS2; Web browser such as Microsoft Internet Explorer or Netscape Navigator.Includes bibliographical references (p. 703-720) and indexes