andrew_gelman_stats andrew_gelman_stats-2014 andrew_gelman_stats-2014-2163 knowledge-graph by maker-knowledge-mining
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Introduction: Adriana Lins de Albuquerque writes: Do you have any suggestions for the best way to represent multinominal logit results graphically? I am using stata. My reply: I don’t know from Stata, but here are my suggestions: 1. If the categories are unordered, break them up into a series of binary choices in a tree structure (for example, non-voter or voter, then voting for left or right, then voting for left party A or B, then voting for right party C or D). Each of these is a binary split and so can be displayed using the usual techniques for logit (as in chapters 3 and 4 of ARM). 2. If the categories are ordered, see Figure 6.4 of ARM for an example (from our analysis of storable votes).
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1 Adriana Lins de Albuquerque writes: Do you have any suggestions for the best way to represent multinominal logit results graphically? [sent-1, score-0.929]
2 My reply: I don’t know from Stata, but here are my suggestions: 1. [sent-3, score-0.037]
3 If the categories are unordered, break them up into a series of binary choices in a tree structure (for example, non-voter or voter, then voting for left or right, then voting for left party A or B, then voting for right party C or D). [sent-4, score-3.049]
4 Each of these is a binary split and so can be displayed using the usual techniques for logit (as in chapters 3 and 4 of ARM). [sent-5, score-1.303]
5 4 of ARM for an example (from our analysis of storable votes). [sent-8, score-0.342]
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same-blog 1 1.0 2163 andrew gelman stats-2014-01-08-How to display multinominal logit results graphically?
Introduction: Adriana Lins de Albuquerque writes: Do you have any suggestions for the best way to represent multinominal logit results graphically? I am using stata. My reply: I don’t know from Stata, but here are my suggestions: 1. If the categories are unordered, break them up into a series of binary choices in a tree structure (for example, non-voter or voter, then voting for left or right, then voting for left party A or B, then voting for right party C or D). Each of these is a binary split and so can be displayed using the usual techniques for logit (as in chapters 3 and 4 of ARM). 2. If the categories are ordered, see Figure 6.4 of ARM for an example (from our analysis of storable votes).
2 0.30946189 782 andrew gelman stats-2011-06-29-Putting together multinomial discrete regressions by combining simple logits
Introduction: When predicting 0/1 data we can use logit (or probit or robit or some other robust model such as invlogit (0.01 + 0.98*X*beta)). Logit is simple enough and we can use bayesglm to regularize and avoid the problem of separation. What if there are more than 2 categories? If they’re ordered (1, 2, 3, etc), we can do ordered logit (and use bayespolr() to avoid separation). If the categories are unordered (vanilla, chocolate, strawberry), there are unordered multinomial logit and probit models out there. But it’s not so easy to fit these multinomial model in a multilevel setting (with coefficients that vary by group), especially if the computation is embedded in an iterative routine such as mi where you have real time constraints at each step. So this got me wondering whether we could kluge it with logits. Here’s the basic idea (in the ordered and unordered forms): - If you have a variable that goes 1, 2, 3, etc., set up a series of logits: 1 vs. 2,3,…; 2 vs. 3,…; and so forth
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Introduction: Jeff writes: How far off is bglmer and can it handle ordered logit or multinom logit? My reply: bglmer is very close. No ordered logit but I was just talking about it with Sophia today. My guess is that the easiest way to fit a hierarchical ordered logit or multinom logit will be to use stan. For right now I’d recommend using glmer/bglmer to fit the ordered logits in order (e.g., 1 vs. 2,3,4, then 2 vs. 3,4, then 3 vs. 4). Or maybe there’s already a hierarchical multinomial logit in mcmcpack or somewhere?
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Introduction: Elissa Brown writes: I’m working on some data using a multinomial model (3 categories for the response & 2 predictors-1 continuous and 1 binary), and I’ve been looking and looking for some sort of nice graphical way to show my model at work. Something like a predicted probabilities plot. I know you can do this for the levels of Y with just one covariate, but is this still a valid way to describe the multinomial model (just doing a pred plot for each covariate)? What’s the deal, is there really no way to graphically represent a successful multinomial model? Also, is it unreasonable to break down your model into a binary response just to get some ROC curves? This seems like cheating. From what I’ve found so far, it seems that people just avoid graphical support when discussing their fitted multinomial models. My reply: It’s hard for me to think about this sort of thing in the abstract with no context. We do have one example in chapter 6 of ARM where we display data and fitted m
5 0.16357714 888 andrew gelman stats-2011-09-03-A psychology researcher asks: Is Anova dead?
Introduction: A research psychologist writes in with a question that’s so long that I’ll put my answer first, then put the question itself below the fold. Here’s my reply: As I wrote in my Anova paper and in my book with Jennifer Hill, I do think that multilevel models can completely replace Anova. At the same time, I think the central idea of Anova should persist in our understanding of these models. To me the central idea of Anova is not F-tests or p-values or sums of squares, but rather the idea of predicting an outcome based on factors with discrete levels, and understanding these factors using variance components. The continuous or categorical response thing doesn’t really matter so much to me. I have no problem using a normal linear model for continuous outcomes (perhaps suitably transformed) and a logistic model for binary outcomes. I don’t want to throw away interactions just because they’re not statistically significant. I’d rather partially pool them toward zero using an inform
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Introduction: Adriana Lins de Albuquerque writes: Do you have any suggestions for the best way to represent multinominal logit results graphically? I am using stata. My reply: I don’t know from Stata, but here are my suggestions: 1. If the categories are unordered, break them up into a series of binary choices in a tree structure (for example, non-voter or voter, then voting for left or right, then voting for left party A or B, then voting for right party C or D). Each of these is a binary split and so can be displayed using the usual techniques for logit (as in chapters 3 and 4 of ARM). 2. If the categories are ordered, see Figure 6.4 of ARM for an example (from our analysis of storable votes).
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Introduction: Jeff writes: How far off is bglmer and can it handle ordered logit or multinom logit? My reply: bglmer is very close. No ordered logit but I was just talking about it with Sophia today. My guess is that the easiest way to fit a hierarchical ordered logit or multinom logit will be to use stan. For right now I’d recommend using glmer/bglmer to fit the ordered logits in order (e.g., 1 vs. 2,3,4, then 2 vs. 3,4, then 3 vs. 4). Or maybe there’s already a hierarchical multinomial logit in mcmcpack or somewhere?
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Introduction: In the context of a discussion of Democratic party strategies, Matthew Yglesias writes : Given where things stood in January 2009, large House losses were essentially inevitable. The Democratic majority elected in 2008 was totally unsustainable and was doomed by basic regression to the mean. I’d like to push back on this, if for no other reason than that I didn’t foresee all this back in January 2009. Regression to the mean is a fine idea, but what’s the “mean” that you’re regressing to? Here’s a graph I made a couple years ago , showing the time series of Democratic vote share in congressional and presidential elections: Take a look at the House vote in 2006 and 2008. Is this a blip, just begging to be slammed down in 2010 by a regression to the mean? Or does it represent a return to form, back to the 55% level of support that the Democrats had for most of the previous fifty years? It’s not so obvious what to think–at least, not simply from looking at the graph.
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Introduction: In a review of psychologist Jonathan Haidt’s recent book, “The Righteous Mind,” William Saletan writes : You’re smart. You’re liberal. You’re well informed. You think conservatives are narrow-minded. You can’t understand why working-class Americans vote Republican. You figure they’re being duped. You’re wrong. . . . Haidt diverges from other psychologists who have analyzed the left’s electoral failures. The usual argument of these psycho-pundits is that conservative politicians manipulate voters’ neural roots — playing on our craving for authority, for example — to trick people into voting against their interests. But Haidt treats electoral success as a kind of evolutionary fitness test. He figures that if voters like Republican messages, there’s something in Republican messages worth liking. He chides psychologists who try to “explain away” conservatism, treating it as a pathology. Conservatism thrives because it fits how people think, and that’s what validates it. Workers who
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Introduction: Within any education category, richer people vote more Republican. In contrast, the pattern of education and voting is nonlinear. High school graduates are more Republican than non-HS grads, but after that, the groups with more education tend to vote more Democratic. At the very highest education level tabulated in the survey, voters with post-graduate degrees lean toward the Democrats. Except for the rich post-graduates; they are split 50-50 between the parties. What does this say about America’s elites? If you define elites as high-income non-Hispanic whites, the elites vote strongly Republican. If you define elites as college-educated high-income whites, they vote moderately Republican. There is no plausible way based on these data in which elites can be considered a Democratic voting bloc. To create a group of strongly Democratic-leaning elite whites using these graphs, you would need to consider only postgraduates (no simple college grads included, even if they have achieved s
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Introduction: Adriana Lins de Albuquerque writes: Do you have any suggestions for the best way to represent multinominal logit results graphically? I am using stata. My reply: I don’t know from Stata, but here are my suggestions: 1. If the categories are unordered, break them up into a series of binary choices in a tree structure (for example, non-voter or voter, then voting for left or right, then voting for left party A or B, then voting for right party C or D). Each of these is a binary split and so can be displayed using the usual techniques for logit (as in chapters 3 and 4 of ARM). 2. If the categories are ordered, see Figure 6.4 of ARM for an example (from our analysis of storable votes).
2 0.84804881 1078 andrew gelman stats-2011-12-22-Tables as graphs: The Ramanujan principle
Introduction: Tables are commonly read as crude graphs: what you notice in a table of numbers is (a) the minus signs, and thus which values are positive and which are negative, and (b) the length of each number, that is, its order of magnitude. The most famous example of such a read might be when the mathematician Srinivasa Ramanujan supposedly conjectured the asymptotic form of the partition function based on a look at a table of the first several partition numbers: he was essentially looking at a graph on the logarithmic scale. I discuss some modern-day statistical examples in this article for Significance magazine . I had a lot of fun creating the “calculator font” for the above graph in R and then writing the article. I hope you enjoy it too! P.S. Also check out this short note by Marcin Kozak and Wojtek Krzanowski on effective presentation of data. P.P.S. I wrote this blog entry a month ago and had it in storage. Then my issue of Significance came in the mail—with my
3 0.84634584 313 andrew gelman stats-2010-10-03-A question for psychometricians
Introduction: Don Coffin writes: A colleague of mine and I are doing a presentation for new faculty on a number of topics related to teaching. Our charge is to identify interesting issues and to find research-based information for them about how to approach things. So, what I wondered is, do you know of any published research dealing with the sort of issues about structuring a course and final exam in the ways you talk about in this blog post ? Some poking around in the usual places hasn’t turned anything up yet. I don’t really know the psychometrics literature but I imagine that some good stuff has been written on principles of test design. There are probably some good papers from back in the 1920s. Can anyone supply some references?
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Introduction: The official announcement: The Excellence in Statistical Reporting Award for 2010 is presented to Felix Salmon for his body of work, which exemplifies the highest standards of scientific reporting. His insightful use of statistics as a tool to understanding the world of business and economics, areas that are critical in today’s economy, sets a new standard in statistical investigative reporting. Here are some examples: Tiger Woods Nigerian spammers How the government fudges job statistics This one is important to me. The idea is that “statistical reporting” is not just traditional science reporting (journalist talks with scientists and tries to understand the consensus) or science popularization or silly feature stories about the lottery. Salmon is doing investigative reporting using statistical thinking. Also, from a political angle, Salmon’s smart and quantitatively sophisticated work (as well as that of others such as Nate Silver) is an important counterweigh
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