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# 统计代写|广义线性模型代写Generalized linear model代考|Deviance residuals

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## 统计代写|广义线性模型代写Generalized linear model代考|Deviance residuals

The deviance plays a key role in our derivation of GLM and in the inference of our results. The deviance residual is the increment to the overall deviance for each observation. These residuals are common and are often standardized, studentized, or both. The residuals are based on the $\chi^2$ distribution.

$$r_i^D=\operatorname{sign}\left(y_i-\widehat{\mu}_i\right) \sqrt{\widehat{d}_i^2}$$
Computation formulas of $d_i^2$ for individual families are given in table A.11.
In general, the deviance residual (standardized or not) is preferred to the Pearson residual for model checking because its distributional properties are closer to the residuals arising in linear regression models.

The deviance residual may be adjusted (corrected) to make the convergence to the limiting normal distribution faster. The adjustment removes an $O\left(n^{-1 / 2}\right)$ term.
$$r_i^{D_a}=r_i^D+\frac{1}{6} \rho_3(\theta)$$
Here $\rho_3(\theta)$ is defined for individual families in table A. 11 .

## 统计代写|广义线性模型代写Generalized linear model代考|Likelihood residuals

Likelihood residuals are a combination of standardized Pearson residuals , $r_i^{P^{\prime}}$, and standardized deviance residuals, $r_i^{D^{\prime}}$.
$$r_i^L=\operatorname{sign}\left(y_i-\widehat{\mu}_i\right)\left{h_i\left(r_i^{P^{\prime}}\right)^2+\left(1-h_i\right)\left(r_i^{D^{\prime}}\right)^2\right}^{1 / 2}$$

These are the scores used in calculating the sandwich estimate of variance. The scores are related to the score function (estimating equation), which is optimized.
$$r_i^S=\frac{y_i-\widehat{\mu}_i}{v\left(\widehat{\mu}_i\right)}\left(\frac{\partial \eta}{\partial \mu}\right)_i^{-1}$$

## 统计代写|广义线性模型代写Generalized linear model代考|Deviance residuals

$$r_i^D=\operatorname{sign}\left(y_i-\widehat{\mu}_i\right) \sqrt{\widehat{d}_i^2}$$

$$r_i^{D_a}=r_i^D+\frac{1}{6} \rho_3(\theta)$$

## 统计代写|广义线性模型代写Generalized linear model代考|Likelihood residuals

$$r_i^L=\operatorname{sign}\left(y_i-\widehat{\mu}_i\right)\left{h_i\left(r_i^{P^{\prime}}\right)^2+\left(1-h_i\right)\left(r_i^{D^{\prime}}\right)^2\right}^{1 / 2}$$

$$r_i^S=\frac{y_i-\widehat{\mu}_i}{v\left(\widehat{\mu}_i\right)}\left(\frac{\partial \eta}{\partial \mu}\right)_i^{-1}$$

## Matlab代写

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