Mallick, B. K. & Gelfand, A. E. (1994). Generalized linear models with unknown link functions. Biometrika, 81, 237-245.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of W and the amount of influence the data can have on its posterior. Up to this point, it has been tacitly assumed that OE, and hence, a(OE) is a known constant value. However, OE can also be introduced as a parameter into the generalized linear model as a method for modeling overdispersion (Mallick and Gelfand, 1994), although we do not pursue this topic here. As mentioned in the introduction, the Bayesian generalized linear model is traditionally fit using rejection based Gibbs sampling methods such as in Zeger and Karim (1991) Gilks and Wild (1992) or Dellaportas and Smith (1993) However, normal ....

Mallick, B. K. and Gelfand, A. E. (1994). Generalized linear models with unknown link functions. Biometrika 81 237-245.

....the link is in the symmetric family of normal or t distributions. Czado (1993a, 1993b) develops Bayesian inference for model (2) Gelfand and Kuo (1991) show nonparametric posterior computations for the bioassay model, i.e. a binary regression model involving only a single regresser. Recently, Mallick and Gelfand (1994) have studied Bayesian inference in a mixture model allowing more general parametric flexibility in the link function. Their work applies to the larger class of generalized linear models. 2.2 Our proposal We propose to model the binary regression data by (1) where F is an arbitrary distribution ....

....and a vector of multiplicities to improve mixing of the algorithm in Escobar (1994) In our implementation, the separate updates of wild card variables and selection indices produces essentially the same effect. Further work is needed to compare our methodology to the mixture models proposed by Mallick and Gelfand (1994), Erkanli and Stangl (1993) and others. Binary regression 18 APPENDIX A: PROOFS Proposition 1 By construction, F (0) 1 0) Theta(1 Gammap) 2 (1 0) Thetap=2 = 1=2. Similarly, F ( Gammad) 1 Gammap) 2 and F ( 1 p) 2, for any realized . Proposition 2 Since F is summary of four ....

Mallick, B. and A. E. Gelfand (1994), "Generalized linear models with unknown link functions", Biometrika. To appear.

....monotone function, with the property that g(0) 0. For a general function g(x) modeling in such a circumstance has been considered previously by many authors, e.g. using regression splines. These methods do not guarantee monotonicity of the dose response. We thus use instead the approach of Mallick and Gelfand (1994), which has three steps: a) monotonically transform the range of the function to the unit interval; b) note that then modeling g is equivalent to modeling an unknown distribution function; and (c) model this distribution function as a mixture of Beta distribution functions. Thus, for some ....

....might think of r, 1 ; r ) and the (c ; d ) as unknown. In practice, we have found that assuming r is unknown gains little compared to say r = 6. Given r, it is mathematically easier to assume that the component Beta densities are speci ed but that the weights are unknown. Following Mallick and Gelfand (1994), we take c = d = r 1 , providing a collection of densities which blanket the unit interval. Hence, speci cation of g is equivalent to speci cation of the s. In addition to the constraints that 0 and r =1 = 1; 9) and the condition g(0) 0 implies that k 1 1 k 1 = ....

Mallick, B. K. & Gelfand, A. E. (1994). Generalized linear models with unknown link functions. Biometrika, 81, 237-245.

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Mallick, B. and Gelfand, A.E. (1994). "Generalized linear models with unknown link functions". Biometrika, 81, 237-245.

No context found.

Mallick, B.K. and Gelfand, A.E. (1994). Generalized Linear Models with Unknown Link Function. Biometrika, 81, 237-245.

No context found.

Mallick, B. K., and Gelfand, A. E. (1994). Generalized linear models with unknown link functions. Biometrika, 81, 237-246.

....AE denotes the expected value of the negative of the portion of vegetative mass viewed as invested capital for reproduction. Eventually we will model using the covariates mentioned above. Then g necessarily satisfies two conditions it is strictly monotone and meets the constraint g(0) 0. Mallick and Gelfand (1994) introduce the idea of modeling monotonic functions by monotonically transforming their range to [0,1] Then modeling say g is equivalent to modeling an unknown distribution function. Transforming the domain to [0,1] as well, they propose to use discrete mixtures of Beta c.d.f. s. Here they argue ....

....from that with much larger r: Indeed, r larger than the sample size does not ensure perfect fit due to the monotonicity restriction. Given r; it is mathematically easier to assume that the component Beta densities are specified but that the weights are unknown. In particular, following Mallick and Gelfand (1994) we take c = d = r 1 Gamma providing a collection of densities (equally spaced in the mean) which blanket (0,1) Hence, specification of g is equivalent to specification of w: In addition to the constraints that w 0 and Sigmaw = 1; the condition g(0) 0 implies, using (5) that ....

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Mallick, B.K. and Gelfand, A.E. (1994). Generalized linear models with unknown link functions.

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Mallick, B.K. and Gelfand, A.E. (1994). Generalized linear models with unknown link functions. Biometrika, 81, 237-245.

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