andrew_gelman_stats andrew_gelman_stats-2014 andrew_gelman_stats-2014-2296 knowledge-graph by maker-knowledge-mining
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Introduction: Someone who doesn’t want his name shared (for the perhaps reasonable reason that he’ll “one day not be confused, and would rather my confusion not live on online forever”) writes: I’m exploring HLMs and stan, using your book with Jennifer Hill as my field guide to this new territory. I think I have a generally clear grasp on the material, but wanted to be sure I haven’t gone astray. The problem in working on involves a multi-nation survey of students, and I’m especially interested in understanding the effects of country, religion, and sex, and the interactions among those factors (using IRT to estimate individual-level ability, then estimating individual, school, and country effects). Following the basic approach laid out in chapter 13 for such interactions between levels, I think I need to create a matrix of indicator variables for religion and sex. Elsewhere in the book, you recommend against indicator variables in favor of a single index variable. Am I right in thinking t
sentIndex sentText sentNum sentScore
1 Someone who doesn’t want his name shared (for the perhaps reasonable reason that he’ll “one day not be confused, and would rather my confusion not live on online forever”) writes: I’m exploring HLMs and stan, using your book with Jennifer Hill as my field guide to this new territory. [sent-1, score-0.253]
2 I think I have a generally clear grasp on the material, but wanted to be sure I haven’t gone astray. [sent-2, score-0.078]
3 Following the basic approach laid out in chapter 13 for such interactions between levels, I think I need to create a matrix of indicator variables for religion and sex. [sent-4, score-1.544]
4 Elsewhere in the book, you recommend against indicator variables in favor of a single index variable. [sent-5, score-0.625]
5 Am I right in thinking that this is purely a matter of convenience, and that the matrix formulation of chapter 13 requires indicator variables, but that the matrix of indicators or the vector of indices yield otherwise identical results? [sent-6, score-2.064]
6 I replied: Yes, models can be formulated equivalently in terms of index or indicator variables. [sent-8, score-0.635]
7 If a discrete variable can take on a bunch of different possible values (for example, 50 states), it makes sense to use a multilevel model rather than to include indicators as predictors with unmodeled coefficients. [sent-9, score-0.657]
8 If the variable takes on only two or three values, you can still do a multilevel model but really it would be better at that point to use informative priors for any variance parameters. [sent-10, score-0.227]
9 That’s a tactic we do not discuss in our book but which is easy to implement in Stan, and I’m hoping to do more of it in the future. [sent-11, score-0.212]
10 To which my correspondent wrote: The main difference that occurs to me as I work through implementing this is that the matrix of indicator variables loses information about what the underlying variable was. [sent-12, score-1.374]
11 So, for instance, if the matrix mixes an indicator for sex and n indicators for religion and m indicators for schools, we’d have Sigma_beta be an m+n+1 x m+n+1 matrix, when we really want a 3×3 matrix. [sent-13, score-1.854]
12 I could set up the basic structure of Sigma_beta, separately estimate the diagonal elements with a series of multilevel loops by sex, religion, and school, and eschew the matrix formulation in the individual model. [sent-14, score-1.381]
13 So instead of y~N(X_iB_j[i],sigma^2_y) it would be (roughly, I’m doing this on my phone): y_i~N(beta_sex[i]+beta_sex_country[country[i]]+beta_religion[i]+beta_religion_country[i,country[i]]+beta_school[i]+beta_school_country[i,country[i]],sigma^2_y) And the group-level formulation unchanged. [sent-15, score-0.198]
14 Sigma_beta becomes a 3×3 matrix rather than an m+n+1 matrix, which seems both more reasonable and more computationally tractable. [sent-16, score-0.627]
15 My reply: Now I’m getting tangled in your notation. [sent-17, score-0.071]
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