On the Assessment of Monte Carlo Error in Simulation-Based Statistical Analyses

Koehler, Elizabeth; Brown, Elizabeth R.; Haneuse, Sebastien

doi:10.1198/tast.2009.0030

Cited by 234 publications

(181 citation statements)

References 20 publications

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“…The effects of design and sample size on these estimates were assessed from 400 Monte Carlo replications of the 15 design settings. With this number of replications, the estimated standard error of the mean number of observed species SO in a given design was always less than 0.3 (Koehler et al, 2009).…”

Section: Sampling Designsmentioning

confidence: 95%

Sample-based Estimation of Regional Forest Tree Species Richness

Magnussen¹

2011

ENRR

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Sample-based estimates of species richness for large heterogeneous regions may be affected by interactions between the sampling design and sub-regional heterogeneity in species richness and diversity. To investigate this issue a Monte Carlo simulation study was conducted with actual forest inventory tree species incidence data from two large regions, four estimators of species richness, three sampling designs, two sampling units (fixed area plots and tree nearest to plot center), and five sample sizes. The regions represent forested areas in central and eastern Canada and three states in the USA. Design effects in estimates of regional species richness were generally weak, of little practical import, and limited to settings with the smallest sample sizes. The study shows that accurate regional estimates of richness can be obtained by pooling sub-regional species incidence data. Sampling with fixed area plots was, with few estimator-dependent exceptions, considerably more efficient than sampling with one tree per sample location. A proposed ratio-based procedure for combining sub-regional estimates of richness broadens the options for regional estimation.

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Section: Sampling Designsmentioning

confidence: 95%

Sample-based Estimation of Regional Forest Tree Species Richness

Magnussen¹

2011

ENRR

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“…In a Canadian NFI context with photo-interpreted data, however, this generally attractive aspect of MI may not materialize to its full potential. An expectation of T 1 differences in area-proportions and per unit area stem-volume, predicates a relatively large Monte-Carlo error (Koehler et al 2009), all else equal, which translates to a recommendation of a relatively large number of MI replications (20 in this study) and modest gains in precision. Far fewer replicates are needed for data with small T 1 differences and stronger temporal and contemporaneous correlations, (Kangas 1991, McRoberts 2003.…”

Section: Discussionmentioning

confidence: 99%

“…The number M of replications was determined by considering the Monte Carlo error (Koehler et al 2009) and the fraction of missing information (FMI) 2017, VOL. 93, N o 3 -THE FORESTRY CHRONICLE The Forestry Chronicle Downloaded from pubs.cif-ifc.org by 54.245.13.81 on 05/12/18 ward 2013).…”

Section: Multiple Imputationsmentioning

confidence: 99%

Updating Canada’s National Forest Inventory with multiple imputations of missing contemporary data

Magnussen

StinsonGraham

BoudewynPaul

2017

The Forestry Chronicle

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Canada's National Forest Inventory (NFI) is facing an issue of spatial imbalance in photo interpreted data from 400 ha photo-plots available for estimation of state and change. Multiple imputations (MI) of missing data is therefore considered as a means to mitigate a potential bias arising from spatial imbalance, and-to a lesser degree-improve the precision relative to what can be achieved with the subset of plots having current data. In this study we explored MI with data from three study sites located in the provinces of Quebec, Ontario, and Saskatchewan. Specifically, we looked at state at time T 2 and change between T 1 and T 2 in cover-type area proportions and in per unit area stem volume. At each location we found significant T 1 differences in these attributes between plots with and without T 2 data. A MI procedure with 20 replications of stochastic model-based imputations of missing data was therefore effective as a way to mitigate a bias that would arise if T 2 inference was based exclusively on plots with T 2 data. Possible differences between the T 2 and T 1 photointerpretation, paired with no efficient stratification of disturbed and undisturbed plots, largely eliminated expected gains in precision from the MI boosting of the effective T 2 sample size. Despite recognized limitations, we recommend MI as an effective tool to counteract an emerging spatial imbalance in the NFI.Key words: forest cover-types, area proportions, stem volume, disturbance rates, ratio estimators. RÉSUMÉL'inventaire forestier national du Canada (NFI) est confronté à une problématique de déséquilibre dans les données de placettes photographiques de 400 ha disponibles pour évaluer l' état de la forêt et son changement. On envisage donc d'utiliser l'imputation multiple (MI) des données manquantes afin d'amoindrir le biais occasionné par le déséquilibre spatial et, dans une moindre mesure, améliorer la précision par rapport à ce qu'il est possible d'atteindre avec le sous-ensemble de placettes pour lesquelles nous disposons de données à jour. Dans cette étude, nous avons exploré les possibilités de MI avec les données provenant de trois sites d' étude situés dans les provinces de Québec, de l'Ontario et de la Saskatchewan. De façon plus particulière, nous nous sommes intéressés à l' état à temps T 2 et au changement survenu entre T 1 et T 2 dans les proportions des surfaces par type de couvert et le volume par tige par unité de surface. À chaque endroit nous avons observé des différences significatives pour ces paramètres à T 1 selon qu' on utilisait ou non les données de T 2 . Une procé-dure MI avec 20 répétitions d'imputations des données manquantes basées sur un modèle stochastique s' est avérée efficace pour atténuer le biais qui résulterait si l'inférence à T 2 reposait uniquement sur les placettes disposant des données à T 2 . Toutefois, les différences dans la technique de photo-interprétation à T 1 et à T 2 combinées à l'absence de stratification des placettes perturbées et intactes a masqué la majeure partie du g...

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“…As it is important to report the uncertainty in any estimates from simulation based studies (Koehler et al, 2009), Monte Carlo error (MCE) was calculated using the joint performance method of β and s i outlined in White (2010). A confidence interval for coverage probabilities, bias, type 1 error and power was calculated using the following:…”

Section: Data Generationmentioning

confidence: 99%

Robustness of the linear mixed effects model to error distribution assumptions and the consequences for genome-wide association studies

Warrington¹,

Tilling²,

Howe³

et al. 2014

Statistical Applications in Genetics and Molecular Biology

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Genome-wide association studies have been successful in uncovering novel genetic variants that are associated with disease status or cross-sectional phenotypic traits. Researchers are beginning to investigate how genes play a role in the development of a trait over time. Linear mixed effects models (LMM) are commonly used to model longitudinal data; however, it is unclear if the failure to meet the models distributional assumptions will affect the conclusions when conducting a genome-wide association study. In an extensive simulation study, we compare coverage probabilities, bias, type 1 error rates and statistical power when the error of the LMM is either heteroscedastic or has a non-Gaussian distribution. We conclude that the model is robust to misspecification if the same function of age is included in the fixed and random effects. However, type 1 error of the genetic effect over time is inflated, regardless of the model misspecification, if the polynomial function for age in the fixed and random effects differs. In situations where the model will not converge with a high order polynomial function in the random effects, a reduced function can be used but a robust standard error needs to be calculated to avoid inflation of the type 1 error. As an illustration, a LMM was applied to longitudinal body mass index (BMI) data over childhood in the ALSPAC cohort; the results emphasised the need for the robust standard error to ensure correct inference of associations of longitudinal BMI with chromosome 16 single nucleotide polymorphisms.

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On the Assessment of Monte Carlo Error in Simulation-Based Statistical Analyses

Cited by 234 publications

References 20 publications

Sample-based Estimation of Regional Forest Tree Species Richness

Sample-based Estimation of Regional Forest Tree Species Richness

Updating Canada’s National Forest Inventory with multiple imputations of missing contemporary data

Robustness of the linear mixed effects model to error distribution assumptions and the consequences for genome-wide association studies

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