andrew_gelman_stats andrew_gelman_stats-2012 andrew_gelman_stats-2012-1102 knowledge-graph by maker-knowledge-mining
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Introduction: David LeBauer points me to this article in PLoS One by Andy Hector, Thomas Bell, Yann Hautier, Forest Isbell, Marc Kéry, Peter Reich, Jasper van Ruijven, and Bernhard Schmid. Here’s the abstract: The idea that species diversity can influence ecosystem functioning has been controversial and its importance relative to compositional effects hotly debated. Unfortunately, assessing the relative importance of different explanatory variables in complex linear models is not simple. In this paper we assess the relative importance of species richness and species composition in a multilevel model analysis of net aboveground biomass production in grassland biodiversity experiments by estimating variance components for all explanatory variables. We compare the variance components using a recently introduced graphical Bayesian ANOVA [emphasis added]. We show that while the use of test statistics and the R2 gives contradictory assessments, the variance components analysis reveals that species
sentIndex sentText sentNum sentScore
1 David LeBauer points me to this article in PLoS One by Andy Hector, Thomas Bell, Yann Hautier, Forest Isbell, Marc Kéry, Peter Reich, Jasper van Ruijven, and Bernhard Schmid. [sent-1, score-0.087]
2 Here’s the abstract: The idea that species diversity can influence ecosystem functioning has been controversial and its importance relative to compositional effects hotly debated. [sent-2, score-1.345]
3 Unfortunately, assessing the relative importance of different explanatory variables in complex linear models is not simple. [sent-3, score-0.756]
4 In this paper we assess the relative importance of species richness and species composition in a multilevel model analysis of net aboveground biomass production in grassland biodiversity experiments by estimating variance components for all explanatory variables. [sent-4, score-3.159]
5 We compare the variance components using a recently introduced graphical Bayesian ANOVA [emphasis added]. [sent-5, score-0.887]
6 We show that while the use of test statistics and the R2 gives contradictory assessments, the variance components analysis reveals that species richness and composition are of roughly similar importance for primary productivity in grassland biodiversity experiments. [sent-6, score-2.564]
7 That “recently introduced graphical Bayesian ANOVA” is from my 2005 paper , “Analysis of variance: why it is more important than ever. [sent-7, score-0.283]
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Introduction: David LeBauer points me to this article in PLoS One by Andy Hector, Thomas Bell, Yann Hautier, Forest Isbell, Marc Kéry, Peter Reich, Jasper van Ruijven, and Bernhard Schmid. Here’s the abstract: The idea that species diversity can influence ecosystem functioning has been controversial and its importance relative to compositional effects hotly debated. Unfortunately, assessing the relative importance of different explanatory variables in complex linear models is not simple. In this paper we assess the relative importance of species richness and species composition in a multilevel model analysis of net aboveground biomass production in grassland biodiversity experiments by estimating variance components for all explanatory variables. We compare the variance components using a recently introduced graphical Bayesian ANOVA [emphasis added]. We show that while the use of test statistics and the R2 gives contradictory assessments, the variance components analysis reveals that species
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Introduction: John Lawson writes: I have been experimenting using Bayesian Methods to estimate variance components, and I have noticed that even when I use a noninformative prior, my estimates are never close to the method of moments or REML estimates. In every case I have tried, the sum of the Bayesian estimated variance components is always larger than the sum of the estimates obtained by method of moments or REML. For data sets I have used that arise from a simple one-way random effects model, the Bayesian estimates of the between groups variance component is usually larger than the method of moments or REML estimates. When I use a uniform prior on the between standard deviation (as you recommended in your 2006 paper ) rather than an inverse gamma prior on the between variance component, the between variance component is usually reduced. However, for the dyestuff data in Davies(1949, p74), the opposite appears to be the case. I am a worried that the Bayesian estimators of the varian
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Introduction: Alexander Volfovsky and Peter Hoff write : ANOVA decompositions are a standard method for describing and estimating heterogeneity among the means of a response variable across levels of multiple categorical factors. In such a decomposition, the complete set of main effects and interaction terms can be viewed as a collection of vectors, matrices and arrays that share various index sets defined by the factor levels. For many types of categorical factors, it is plausible that an ANOVA decomposition exhibits some consistency across orders of effects, in that the levels of a factor that have similar main-effect coefficients may also have similar coefficients in higher-order interaction terms. In such a case, estimation of the higher-order interactions should be improved by borrowing information from the main effects and lower-order interactions. To take advantage of such patterns, this article introduces a class of hierarchical prior distributions for collections of interaction arrays t
Introduction: Chris Che-Castaldo writes: I am trying to compute variance components for a hierarchical model where the group level has two binary predictors and their interaction. When I model each of these three predictors as N(0, tau) the model will not converge, perhaps because the number of coefficients in each batch is so small (2 for the main effects and 4 for the interaction). Although I could simply leave all these as predictors as unmodeled fixed effects, the last sentence of section 21.2 on page 462 of Gelman and Hill (2007) suggests this would not be a wise course of action: For example, it is not clear how to define the (finite) standard deviation of variables that are included in interactions. I am curious – is there still no clear cut way to directly compute the finite standard deviation for binary unmodeled variables that are also part of an interaction as well as the interaction itself? My reply: I’d recommend including these in your model (it’s probably easiest to do so
5 0.14747486 810 andrew gelman stats-2011-07-20-Adding more information can make the variance go up (depending on your model)
Introduction: Andy McKenzie writes: In their March 9 “ counterpoint ” in nature biotech to the prospect that we should try to integrate more sources of data in clinical practice (see “ point ” arguing for this), Isaac Kohane and David Margulies claim that, “Finally, how much better is our new knowledge than older knowledge? When is the incremental benefit of a genomic variant(s) or gene expression profile relative to a family history or classic histopathology insufficient and when does it add rather than subtract variance?” Perhaps I am mistaken (thus this email), but it seems that this claim runs contra to the definition of conditional probability. That is, if you have a hierarchical model, and the family history / classical histopathology already suggests a parameter estimate with some variance, how could the new genomic info possibly increase the variance of that parameter estimate? Surely the question is how much variance the new genomic info reduces and whether it therefore justifies t
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Introduction: David LeBauer points me to this article in PLoS One by Andy Hector, Thomas Bell, Yann Hautier, Forest Isbell, Marc Kéry, Peter Reich, Jasper van Ruijven, and Bernhard Schmid. Here’s the abstract: The idea that species diversity can influence ecosystem functioning has been controversial and its importance relative to compositional effects hotly debated. Unfortunately, assessing the relative importance of different explanatory variables in complex linear models is not simple. In this paper we assess the relative importance of species richness and species composition in a multilevel model analysis of net aboveground biomass production in grassland biodiversity experiments by estimating variance components for all explanatory variables. We compare the variance components using a recently introduced graphical Bayesian ANOVA [emphasis added]. We show that while the use of test statistics and the R2 gives contradictory assessments, the variance components analysis reveals that species
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Introduction: Alexander Volfovsky and Peter Hoff write : ANOVA decompositions are a standard method for describing and estimating heterogeneity among the means of a response variable across levels of multiple categorical factors. In such a decomposition, the complete set of main effects and interaction terms can be viewed as a collection of vectors, matrices and arrays that share various index sets defined by the factor levels. For many types of categorical factors, it is plausible that an ANOVA decomposition exhibits some consistency across orders of effects, in that the levels of a factor that have similar main-effect coefficients may also have similar coefficients in higher-order interaction terms. In such a case, estimation of the higher-order interactions should be improved by borrowing information from the main effects and lower-order interactions. To take advantage of such patterns, this article introduces a class of hierarchical prior distributions for collections of interaction arrays t
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Introduction: Karri Seppa writes: My topic is regional variation in the cause-specific survival of breast cancer patients across the 21 hospital districts in Finland, this component being modeled by random effects. I am interested mainly in the district-specific effects, and with a hierarchical model I can get reasonable estimates also for sparsely populated districts. Based on the recommendation given in the book by yourself and Dr. Hill (2007) I tend to think that the finite-population variance would be an appropriate measure to summarize the overall variation across the 21 districts. However, I feel it is somewhat incoherent first to assume a Normal distribution for the district effects, involving a “superpopulation” variance parameter, and then to compute the finite-population variance from the estimated district-specific parameters. I wonder whether the finite-population variance were more appropriate in the context of a model with fixed district effects? My reply: I agree that th
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Introduction: Ramu Sudhagoni writes: I am working on combining three longitudinal studies using Bayesian hierarchical technique. In each study, I have at least 70 subjects follow up on 5 different visit months. My model consists of 10 different covariates including longitudinal and cross-sectional effects. Mixed models are used to fit the three studies individually using Bayesian approach and I noticed that few covariates were significant. When I combined using three level hierarchical approach, all the covariates became non-significant at the population level, and large estimates were found for variance parameters at the population level. I am struggling to understand why I am getting large variances at population level and wider credible intervals. I assumed non-informative normal priors for all my cross sectional and longitudinal effects, and non-informative inverse-gamma priors for variance parameters. I followed the approach explained by Inoue et al. (Title: Combining Longitudinal Studie
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Introduction: Dean Eckles writes: I remember reading on your blog that you were working on some tools to fit multilevel models that also include “fixed” effects — such as continuous predictors — that are also estimated with shrinkage (for example, an L1 or L2 penalty). Any new developments on this front? I often find myself wanting to fit a multilevel model to some data, but also needing to include a number of “fixed” effects, mainly continuous variables. This makes me wary of overfitting to these predictors, so then I’d want to use some kind of shrinkage. As far as I can tell, the main options for doing this now is by going fully Bayesian and using a Gibbs sampler. With MCMCglmm or BUGS/JAGS I could just specify a prior on the fixed effects that corresponds to a desired penalty. However, this is pretty slow, especially with a large data set and because I’d like to select the penalty parameter by cross-validation (which is where this isn’t very Bayesian I guess?). My reply: We allow info
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1 0.92387629 694 andrew gelman stats-2011-05-04-My talk at Hunter College on Thurs
Introduction: Of beauty, sex, and power: Statistical challenges in estimating small effects . Thurs 5 May at 11am at Roosevelt House, at 47-49 East 65th Street (north side of East 65th street, between Park and Madison Avenues).
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Introduction: Your taxes pay for the research funding that supports the work we do here, some of which appears on this blog and almost all of which is public, free, and open-source. So, to all of the taxpayers out there in the audience: thank you.
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Introduction: David LeBauer points me to this article in PLoS One by Andy Hector, Thomas Bell, Yann Hautier, Forest Isbell, Marc Kéry, Peter Reich, Jasper van Ruijven, and Bernhard Schmid. Here’s the abstract: The idea that species diversity can influence ecosystem functioning has been controversial and its importance relative to compositional effects hotly debated. Unfortunately, assessing the relative importance of different explanatory variables in complex linear models is not simple. In this paper we assess the relative importance of species richness and species composition in a multilevel model analysis of net aboveground biomass production in grassland biodiversity experiments by estimating variance components for all explanatory variables. We compare the variance components using a recently introduced graphical Bayesian ANOVA [emphasis added]. We show that while the use of test statistics and the R2 gives contradictory assessments, the variance components analysis reveals that species
4 0.83161807 97 andrew gelman stats-2010-06-18-Economic Disparities and Life Satisfaction in European Regions
Introduction: Grazia Pittau, Roberto Zelli, and I came out with a paper investigating the role of economic variables in predicting regional disparities in reported life satisfaction of European Union citizens. We use multilevel modeling to explicitly account for the hierarchical nature of our data, respondents within regions and countries, and for understanding patterns of variation within and between regions. Here’s what we found: - Personal income matters more in poor regions than in rich regions, a pattern that still holds for regions within the same country. - Being unemployed is negatively associated with life satisfaction even after controlled for income variation. Living in high unemployment regions does not alleviate the unhappiness of being out of work. - After controlling for individual characteristics and modeling interactions, regional differences in life satisfaction still remain. Here’s a quick graph; there’s more in the article:
5 0.82909369 1698 andrew gelman stats-2013-01-30-The spam just gets weirder and weirder
Introduction: In the inbox today, under the header, “Hidden Costs behind Milk & Dairy Consumption (video)”: Hey Professor Gelman, Our site’s production team recently released a short video uncovering the local and global impact that milk has on our lives. After spending some time on your posts, I noticed you talked about dairy products and milk so I thought I’d email you. Are you the correct person to contact in regards to the content on the site? If so, let me know if you’re interested in checking out the video. Thanks, Emily S. Hmmm . . . I guess I do talk a lot about dairy products and milk on this site!
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