Ecological Inference: New Methodological Strategies by Gary King, Ori Rosen, Martin A. Tanner

By Gary King, Ori Rosen, Martin A. Tanner

This selection of essays brings jointly a various crew of students to survey the most recent ideas for fixing ecological inference difficulties in a variety of fields. The final half-decade has witnessed an explosion of analysis in ecological inference--the means of attempting to infer person habit from mixture information. even supposing uncertainties and data misplaced in aggregation make ecological inference probably the most complicated kinds of examine to depend upon, those inferences are required in lots of educational fields, in addition to by way of legislatures and the Courts in redistricting, by means of company in advertising study, and by way of governments in coverage research.

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The model also allows area-level covariates to be added at the second stage. Wakefield (2004) proposed as an alternative to the beta model a second stage in which the logits of the registration probabilities arose from a bivariate normal distribution; this model was introduced, for the analysis of a series of 2 × 2 tables when the internal cells were observed by Skene and Wakefield (1990). e. p j i = exp(θ j i )/{1 + exp(θ j i )}, j = 0, 1. 5. Nesting of models. In the baseline model the parameters of f (·) are fixed, while in the hierarchical model the common parameters are estimated from the totality of the data.

In fact, data on a small subset of the minority group only can provide accurate inference. The Bayesian hierarchical models described here offer the flexibility to formally accommodate substantive information and/or additional data. 13. 001) priors on the precisions. The first 500,000 iterations are treated as a burn-in and are not plotted; the remaining iterations, up to 3,000,000, are plotted. d. d. ( p1 ), and every 1,000th sample is plotted. The dependence in the chain is apparent, showing that large numbers of samples are required for accurate inference.

6) where l i = max(0, Yi − N1i ), ui = min(N0i , Yi ). 1. McCullagh and Nelder (1989) consider this likelihood under the assumption that p0i = p0 and p1i = p1 ; see also Achen and Shively (1995: 46). 8) where µi = µi ( p0i , p1i ) = Ni × q i = Ni { p0i xi + p1i (1 − xi )} and Vi = Vi ( p0i , p1i ) = Ni { p0i (1 − p0i )xi + p1i (1 − p1i )(1 − xi )}. 8 with µi = a + bxi and σi2 = Ni σ 2 . Similar equivalences hold for the quadratic models. 8, though (since the weights depend on p0 , p1 ) an iterative procedure would be required to obtain estimates of a and b.

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