andrew_gelman_stats andrew_gelman_stats-2010 andrew_gelman_stats-2010-464 knowledge-graph by maker-knowledge-mining
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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
sentIndex sentText sentNum sentScore
1 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. [sent-1, score-1.264]
2 I am interested mainly in the district-specific effects, and with a hierarchical model I can get reasonable estimates also for sparsely populated districts. [sent-2, score-0.463]
3 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. [sent-4, score-0.682]
4 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. [sent-5, score-0.931]
5 I wonder whether the finite-population variance were more appropriate in the context of a model with fixed district effects? [sent-6, score-0.506]
6 My reply: I agree that these points can be confusing, as can be seen by the 5 different definitions of fixed/random effects that I discuss in the Anova paper. [sent-7, score-0.256]
7 Here’s what I would say: Your goal is to estimate what’s going on in these 21 districts. [sent-9, score-0.18]
8 To the extent there is a “true” superpopulation, it could be thought of as representing variation over time as well as space. [sent-10, score-0.256]
9 But, mathematically, the superpop and the associated normal (or whatever) distribution can be viewed as a tool for getting statistically efficient estimates for the 21 districts that you have. [sent-11, score-1.244]
10 Now that you have simultaneously estimated parameters for these 21 districts, you might also be interested in ensemble properties, for example the maximum, minimum, interquartile range, or even–gasp–standard deviation of these 21 numbers. [sent-12, score-0.723]
11 It’s well known that no point estimate in high-dimensional space can capture ensemble properties–the key paper here is a 1984 article by Tom Louis, which is referred to in one of my books (BDA or ARM). [sent-13, score-0.48]
12 I guess what I’m saying is that you make it clear that your goal is the 21 districts and that the Bayesian inference and superpop is a tool for getting there. [sent-14, score-0.967]
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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: 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: Stuart Buck writes: I have a question about fixed effects vs. random effects . Amongst economists who study teacher value-added, it has become common to see people saying that they estimated teacher fixed effects (via least squares dummy variables, so that there is a parameter for each teacher), but that they then applied empirical Bayes shrinkage so that the teacher effects are brought closer to the mean. (See this paper by Jacob and Lefgren, for example.) Can that really be what they are doing? Why wouldn’t they just run random (modeled) effects in the first place? I feel like there’s something I’m missing. My reply: I don’t know the full story here, but I’m thinking there are two goals, first to get an unbiased estimate of an overall treatment effect (and there the econometricians prefer so-called fixed effects; I disagree with them on this but I know where they’re coming from) and second to estimate individual teacher effects (and there it makes sense to use so-called
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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: I received the following email from someone who wishes to remain anonymous: My colleague and I are trying to understand the best way to approach a problem involving measuring a group of individuals’ abilities across time, and are hoping you can offer some guidance. We are trying to analyze the combined effect of two distinct groups of people (A and B, with no overlap between A and B) who collaborate to produce a binary outcome, using a mixed logistic regression along the lines of the following. Outcome ~ (1 | A) + (1 | B) + Other variables What we’re interested in testing was whether the observed A random effects in period 1 are predictive of the A random effects in the following period 2. Our idea being create two models, each using a different period’s worth of data, to create two sets of A coefficients, then observe the relationship between the two. If the A’s have a persistent ability across periods, the coefficients should be correlated or show a linear-ish relationshi
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Introduction: José Iparraguirre writes: There’s a letter in the latest issue of The Economist (July 31st) signed by Sir Richard Branson (Virgin), Michael Masters (Masters Capital Management) and David Frenk (Better Markets) about an “>OECD report on speculation and the prices of commodities, which includes the following: “The report uses a Granger causality test to measure the relationship between the level of commodities futures contracts held by swap dealers, and the prices of those commodities. Granger tests, however, are of dubious applicability to extremely volatile variables like commodities prices.” The report says: Granger causality is a standard statistical technique for determining whether one time series is useful in forecasting another. It is important to bear in mind that the term causality is used in a statistical sense, and not in a philosophical one of structural causation. More precisely a variable A is said to Granger cause B if knowing the time paths of B and A toge
Introduction: John Transue sent it in with the following thoughtful comment: I’d imagine you’ve already received this, but just in case, here’s a cartoon you’d like. At first blush it seems to go against your advice (more nuanced than what I’m about to say by quoting the paper title) to not worry about multiple comparisons. However, if I understand correctly your argument about multiple comparisons in multilevel models, the situation in this comic might have been avoided if shrinkage toward the grand mean (of all colors) had prevented the greens from clearing the .05 threshold. Is that right?
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