andrew_gelman_stats andrew_gelman_stats-2011 andrew_gelman_stats-2011-850 knowledge-graph by maker-knowledge-mining
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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
sentIndex sentText sentNum sentScore
1 Ramu Sudhagoni writes: I am working on combining three longitudinal studies using Bayesian hierarchical technique. [sent-1, score-1.247]
2 In each study, I have at least 70 subjects follow up on 5 different visit months. [sent-2, score-0.337]
3 My model consists of 10 different covariates including longitudinal and cross-sectional effects. [sent-3, score-1.109]
4 Mixed models are used to fit the three studies individually using Bayesian approach and I noticed that few covariates were significant. [sent-4, score-1.172]
5 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. [sent-5, score-1.886]
6 I am struggling to understand why I am getting large variances at population level and wider credible intervals. [sent-6, score-1.02]
7 I assumed non-informative normal priors for all my cross sectional and longitudinal effects, and non-informative inverse-gamma priors for variance parameters. [sent-7, score-1.528]
8 I followed the approach explained by Inoue et al. [sent-8, score-0.383]
9 My reply: I don’t know but I’d recommend you graph your data and fitted model so you can try to understand where the estimates are coming from. [sent-10, score-0.561]
10 Also, get rid of those inverse-gamma priors, which aren’t noninformative at all! [sent-11, score-0.227]
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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: Philipp Doebler writes: I was quite happy that recently you shared some thoughts of yours and others on meta-analysis. I especially liked the slides by Chris Schmid that you linked from your blog. A large portion of my work deals with meta-analysis and I am also fond of using Bayesian methods (actually two of the projects I am working on are very Bayesian), though I can not say I have opinions with respect to the underlying philosophy. I would say though, that I do share your view that there are good reasons to use informative priors. The reason I am writing to you is that this leads to the following dilemma, which is puzzling me. Say a number of scientists conduct similar studies over the years and all of them did this in a Bayesian fashion. If each of the groups used informative priors based on the research of existing groups the priors could become more and more informative over the years, since more and more is known over the subject. At least in smallish studies these p
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Introduction: Yi-Chun Ou writes: I am using a multilevel model with three levels. I read that you wrote a book about multilevel models, and wonder if you can solve the following question. The data structure is like this: Level one: customer (8444 customers) Level two: companys (90 companies) Level three: industry (17 industries) I use 6 level-three variables (i.e. industry characteristics) to explain the variance of the level-one effect across industries. The question here is whether there is an over-fitting problem since there are only 17 industries. I understand that this must be a problem for non-multilevel models, but is it also a problem for multilevel models? My reply: Yes, this could be a problem. I’d suggest combining some of your variables into a common score, or using only some of the variables, or using strong priors to control the inferences. This is an interesting and important area of statistics research, to do this sort of thing systematically. There’s lots o
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Introduction: Fred Wu writes: I work at National Prescribing Services in Australia. I have a database representing say, antidiabetic drug utilisation for the entire Australia in the past few years. I planned to do a longitudinal analysis across GP Division Network (112 divisions in AUS) using mixed-effects models (or as you called in your book varying intercept and varying slope) on this data. The problem here is: as data actually represent the population who use antidiabetic drugs in AUS, should I use 112 fixed dummy variables to capture the random variations or use varying intercept and varying slope for the model ? Because some one may aruge, like divisions in AUS or states in USA can hardly be considered from a “superpopulation”, then fixed dummies should be used. What I think is the population are those who use the drugs, what will happen when the rest need to use them? In terms of exchangeability, using varying intercept and varying slopes can be justified. Also you provided in y
Introduction: Nelson Villoria writes: I find the multilevel approach very useful for a problem I am dealing with, and I was wondering whether you could point me to some references about poolability tests for multilevel models. I am working with time series of cross sectional data and I want to test whether the data supports cross sectional and/or time pooling. In a standard panel data setting I do this with Chow tests and/or CUSUM. Are these ideas directly transferable to the multilevel setting? My reply: I think you should do partial pooling. Once the question arises, just do it. Other models are just special cases. I don’t see the need for any test. That said, if you do a group-level model, you need to consider including group-level averages of individual predictors (see here ). And if the number of groups is small, there can be real gains from using an informative prior distribution on the hierarchical variance parameters. This is something that Jennifer and I do not discuss in our
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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: Yes, it can be done : Hereby I contact you to clarify the situation that occurred with the publication of the article entitled *** which was published in Volume 11, Issue 3 of *** and I made the mistake of declaring as an author. This chapter is a plagiarism of . . . I wish to express and acknowledge that I am solely responsible for this . . . I recognize the gravity of the offense committed, since there is no justification for so doing. Therefore, and as a sign of shame and regret I feel in this situation, I will publish this letter, in order to set an example for other researchers do not engage in a similar error. No more, and to please accept my apologies, Sincerely, *** P.S. Since we’re on Retraction Watch already, I’ll point you to this unrelated story featuring a hilarious photo of a fraudster, who in this case was a grad student in psychology who faked his data and “has agreed to submit to a three-year supervisory period for any work involving funding from the
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