A comparison of three canopy interception models for a leafless mixed deciduous forest stand in the eastern United States

Canopy interception of incident precipitation is a critical component of the forest water balance during each of the four seasons. Models have been developed to predict precipitation interception from standard meteorological variables because of acknowledged difficulty in extrapolating direct measurements of interception loss from forest to forest. No known study has compared and validated canopy interception models for a leafless deciduous forest stand in the eastern United States. Interception measurements from an experimental plot in a leafless deciduous forest in northeastern Maryland (39°42'N, 75°5'W) for 11 rainstorms in winter and early spring 2004/05 were compared to predictions from three models. The Mulder model maintains a moist canopy between storms. The Gash model requires few input variables and is formulated for a sparse canopy. The WiMo model optimizes the canopy storage capacity for the maximum wind speed during each storm. All models showed marked underestimates and overestimates for individual storms when the measured ratio of interception to gross precipitation was far more or less, respectively, than the specified fraction of canopy cover. The models predicted the percentage of total gross precipitation (PG) intercepted to within the probable standard error (8.1%) of the measured value: the Mulder model overestimated the measured value by 0.1% of PG; the WiMo model underestimated by 0.6% of PG; and the Gash model underestimated by 1.1% of PG. The WiMo model’s advantage over the Gash model indicates that the canopy storage capacity increases logarithmically with the maximum wind speed. This study has demonstrated that dormant-season precipitation interception in a leafless deciduous forest may be satisfactorily predicted by existing canopy interception models.

An overview of mixed-effects statistical models for second language researchers

As in any field of scientific inquiry, advancements in the field of second language acquisition (SLA) rely in part on the interpretation and generalizability of study findings using quantitative data analysis and inferential statistics. While statistical techniques such as ANOVA and t-tests are widely used in second language research, this review article provides a review of a class of newer statistical models that have not yet been widely adopted in the field, but have garnered interest in other fields of language research. The class of statistical models called mixed-effects models are introduced, and the potential benefits of these models for the second language researcher are discussed. A simple example of mixed-effects data analysis using the statistical software package R (R Development Core Team, 2011) is provided as an introduction to the use of these statistical techniques, and to exemplify how such analyses can be reported in research articles. It is concluded that mixed-effects models provide the second language researcher with a powerful tool for the analysis of a variety of types of second language acquisition data.

The utility and application of mixed-effects models in second language research

Second language acquisition researchers often face particular challenges when attempting to generalize study findings to the wider learner population. For example, language learners constitute a heterogeneous group, and it is not always clear how a study’s findings may generalize to other individuals who may differ in terms of language background and proficiency, among many other factors. In this paper, we provide an overview of how mixed-effects models can be used to help overcome these and other issues in the field of second language acquisition. We provide an overview of the benefits of mixed-effects models and a practical example of how mixed-effects analyses can be conducted. Mixed-effects models provide second language researchers with a powerful statistical tool in the analysis of a variety of different types of data.

Mixed-phase cloud physics and Southern Ocean cloud feedback in climate models

Increasing optical depth poleward of 45° is a robust response to warming in global climate models. Much of this cloud optical depth increase has been hypothesized to be due to transitions from ice-dominated to liquid-dominated mixed-phase cloud. In this study, the importance of liquid-ice partitioning for the optical depth feedback is quantified for 19 Coupled Model Intercomparison Project Phase 5 models. All models show a monotonic partitioning of ice and liquid as a function of temperature, but the temperature at which ice and liquid are equally mixed (the glaciation temperature) varies by as much as 40 K across models. Models that have a higher glaciation temperature are found to have a smaller climatological liquid water path (LWP) and condensed water path and experience a larger increase in LWP as the climate warms. The ice-liquid partitioning curve of each model may be used to calculate the response of LWP to warming. It is found that the repartitioning between ice and liquid in a warming climate contributes at least 20% to 80% of the increase in LWP as the climate warms, depending on model. Intermodel differences in the climatological partitioning between ice and liquid are estimated to contribute at least 20% to the intermodel spread in the high-latitude LWP response in the mixed-phase region poleward of 45°S. It is hypothesized that a more thorough evaluation and constraint of global climate model mixed-phase cloud parameterizations and validation of the total condensate and ice-liquid apportionment against observations will yield a substantial reduction in model uncertainty in the high-latitude cloud response to warming.

Influence diagnostics in nonlinear mixed-effects elliptical models

In this work we propose and analyze nonlinear elliptical models for longitudinal data, which represent an alternative to gaussian models in the cases of heavy tails, for instance. The elliptical distributions may help to control the influence of the observations in the parameter estimates by naturally attributing different weights for each case. We consider random effects to introduce the within-group correlation and work with the marginal model without requiring numerical integration. An iterative algorithm to obtain maximum likelihood estimates for the parameters is presented, as well as diagnostic results based on residual distances and local influence [Cook, D., 1986. Assessment of local influence. journal of the Royal Statistical Society - Series B 48 (2), 133-169; Cook D., 1987. Influence assessment. journal of Applied Statistics 14 (2),117-131; Escobar, L.A., Meeker, W.Q., 1992, Assessing influence in regression analysis with censored data, Biometrics 48, 507-528]. As numerical illustration, we apply the obtained results to a kinetics longitudinal data set presented in [Vonesh, E.F., Carter, R.L., 1992. Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17], which was analyzed under the assumption of normality. (C) 2009 Elsevier B.V. All rights reserved.

Improved testing inference in mixed linear models

Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Often, the number of observations is small, and it is thus important to use inference strategies that incorporate small sample corrections. In this paper, we develop modified versions of the likelihood ratio test for fixed effects inference in mixed linear models. In particular, we derive a Bartlett correction to such a test, and also to a test obtained from a modified profile likelihood function. Our results generalize those in [Zucker, D.M., Lieberman, O., Manor, O., 2000. Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. Journal of the Royal Statistical Society B, 62,827-838] by allowing the parameter of interest to be vector-valued. Additionally, our Bartlett corrections allow for random effects nonlinear covariance matrix structure. We report simulation results which show that the proposed tests display superior finite sample behavior relative to the standard likelihood ratio test. An application is also presented and discussed. (C) 2008 Elsevier B.V. All rights reserved.

A note on influence diagnostics in nonlinear mixed-effects elliptical models

This paper provides general matrix formulas for computing the score function, the (expected and observed) Fisher information and the A matrices (required for the assessment of local influence) for a quite general model which includes the one proposed by Russo et al. (2009). Additionally, we also present an expression for the generalized leverage on fixed and random effects. The matrix formulation has notational advantages, since despite the complexity of the postulated model, all general formulas are compact, clear and have nice forms. (C) 2010 Elsevier B.V. All rights reserved.

A class of mixed integrable models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Evaluation of the Hosmer -Lemeshow global goodness -of-fit statistic for mixed variable logistic regression models

The performance of the Hosmer-Lemeshow global goodness-of-fit statistic for logistic regression models was explored in a wide variety of conditions not previously fully investigated. Computer simulations, each consisting of 500 regression models, were run to assess the statistic in 23 different situations. The items which varied among the situations included the number of observations used in each regression, the number of covariates, the degree of dependence among the covariates, the combinations of continuous and discrete variables, and the generation of the values of the dependent variable for model fit or lack of fit.^ The study found that the $\rm\ C$g* statistic was adequate in tests of significance for most situations. However, when testing data which deviate from a logistic model, the statistic has low power to detect such deviation. Although grouping of the estimated probabilities into quantiles from 8 to 30 was studied, the deciles of risk approach was generally sufficient. Subdividing the estimated probabilities into more than 10 quantiles when there are many covariates in the model is not necessary, despite theoretical reasons which suggest otherwise. Because it does not follow a X$\sp2$ distribution, the statistic is not recommended for use in models containing only categorical variables with a limited number of covariate patterns.^ The statistic performed adequately when there were at least 10 observations per quantile. Large numbers of observations per quantile did not lead to incorrect conclusions that the model did not fit the data when it actually did. However, the statistic failed to detect lack of fit when it existed and should be supplemented with further tests for the influence of individual observations. Careful examination of the parameter estimates is also essential since the statistic did not perform as desired when there was moderate to severe collinearity among covariates.^ Two methods studied for handling tied values of the estimated probabilities made only a slight difference in conclusions about model fit. Neither method split observations with identical probabilities into different quantiles. Approaches which create equal size groups by separating ties should be avoided. ^

Improved models for estimating temporal changes in carbon sequestration in above-ground biomass of mixed-species environmental plantings

Plantings of mixed native species (termed 'environmental plantings') are increasingly being established for carbon sequestration whilst providing additional environmental benefits such as biodiversity and water quality. In Australia, they are currently one of the most common forms of reforestation. Investment in establishing and maintaining such plantings relies on having a cost-effective modelling approach to providing unbiased estimates of biomass production and carbon sequestration rates. In Australia, the Full Carbon Accounting Model (FullCAM) is used for both national greenhouse gas accounting and project-scale sequestration activities. Prior to undertaking the work presented here, the FullCAM tree growth curve was not calibrated specifically for environmental plantings and generally under-estimated their biomass. Here we collected and analysed above-ground biomass data from 605 mixed-species environmental plantings, and tested the effects of several planting characteristics on growth rates. Plantings were then categorised based on significant differences in growth rates. Growth of plantings differed between temperate and tropical regions. Tropical plantings were relatively uniform in terms of planting methods and their growth was largely related to stand age, consistent with the un-calibrated growth curve. However, in temperate regions where plantings were more variable, key factors influencing growth were planting width, stand density and species-mix (proportion of individuals that were trees). These categories provided the basis for FullCAM calibration. Although the overall model efficiency was only 39-46%, there was nonetheless no significant bias when the model was applied to the various planting categories. Thus, modelled estimates of biomass accumulation will be reliable on average, but estimates at any particular location will be uncertain, with either under- or over-prediction possible. When compared with the un-calibrated yield curves, predictions using the new calibrations show that early growth is likely to be more rapid and total above-ground biomass may be higher for many plantings at maturity. This study has considerably improved understanding of the patterns of growth in different types of environmental plantings, and in modelling biomass accumulation in young (<25. years old) plantings. However, significant challenges remain to understand longer-term stand dynamics, particularly with temporal changes in stand density and species composition. © 2014.