Approaches for Modeling Vertical Distribution of Maximum Knot Size in Black Spruce: A Comparison of Fixed- and Mixed-Effects Nonlinear Models
Abstract:Both linear and nonlinear hierarchical mixed-effects models have been used in recent years to analyze nested data sets. These types of models are effective for partitioning variance between hierarchical levels and increasing model flexibility. Models of knot size and distribution have been developed for several commercially important conifer species. Modeling knots is particularly amendable to the mixed-models approach as they are inherently nested at multiple levels including the individual whorl, tree, and stand levels. Although mixed models are effective for addressing hierarchical nesting of data, in this study we contend that improvements achieved by inclusion of mixed effects can be effectively negated with the use of an appropriate model form. This contention is presented as a case study on the development of a maximum knot size model for plantation-grown black spruce in Ontario (Picea mariana [Mill.] BSP). With a naive and simple model form, the nonlinear mixed-effects approach was significantly superior to comparable generalized nonlinear models as the root mean square error was 16% lower. In contrast, when a model form that accounted for primary covariates with a robust model form was used, difference in root mean square error between nonlinear mixed-effects and generalized nonlinear models was approximately 6%. In addition, graphic techniques for exploring distributions of random effects are presented and discussed. Mixed models are effective tools, but, as illustrated by this case study, their limitations need to be recognized and use of mixed models should not precede development of sound model forms.
Document Type: Research Article
Publication date: 2009-06-01
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