# 统计代写|广义线性模型代写generalized linear model代考|BIOS6940

## 统计代写|广义线性模型代写generalized linear model代考|Two-by-Two Tables

The data shown in Table $6.1$ were collected as part of a quality improvement study at a semiconductor factory. A sample of wafers was drawn and cross-classified according to whether a particle was found on the die that produced the wafer and whether the wafer was good or bad. More details on the study may be found in Hall (1994). The data might have arisen under several possible sampling schemes:

1. We observed the manufacturing process for a certain period of time and observed 450 wafers. The data were then cross-classified. We could use a Poisson model.
2. We decided to sample 450 wafers. The data were then cross-classified. We could use a multinomial model.
3. We selected 400 wafers without particles and 50 wafers with particles and then recorded the good or bad outcome. We could use a binomial model.
4. We selected 400 wafers without particles and 50 wafers with particles that also included, by design, 334 good wafers and 116 bad ones. We could use a hypergeometric model.

The first three sampling schemes are all plausible. The fourth scheme seems less likely in this example, but we include it for completeness. Such a scheme is more attractive when one level of each variable is relatively rare and we choose to oversample both levels to ensure some representation.

The main question of interest concerning these data is whether the presence of particles on the wafer affects the quality outcome. We shall see that all four sampling schemes lead to exactly the same conclusion. First, let’s set up the data in a convenient form for analysis.

## 统计代写|广义线性模型代写generalized linear model代考|Correspondence Analysis

The analysis of the hair-eye color data in the previous section revealed how hair and eye color are dependent. But this does not tell us how they are dependent. To study this, we can use a kind of residual analysis for contingency tables called correspondence analysis.

Compute the Pearson residuals $r_P$ and write them in the matrix form $R_{i j}$, where $i=1, \ldots, r$ and $j=1, \ldots, c$, according to the structure of the data. Perform the singular value decomposition:
$$R_{r \times c}=U_{r \times w} D_{w \times w} V_{w \times c}^T$$
where $r$ is the number of rows, $c$ is the number of columns and $w=\min (r, c) . U$ and $V$ are called the right and left singular vectors, respectively. $D$ is a diagonal matrix with sorted elements $d_i$, called singular values. Another way of writing this is:
$$R_{i j}=\sum_{k=1}^w U_{i k} d_k V_{j k}$$
As with eigendecompositions, it is not uncommon for the first few singular values to be much larger than the rest. Suppose that the first two dominate so that:
$$R_{i j} \approx U_{i 1} d_1 V_{j 1}+U_{i 2} d_2 V_{j 2}$$ We usually absorb the $d$ s into $U$ and $V$ for plotting purposes so that we can assess the relative contribution of the components.

# 广义线性模型代考

## 统计代写|广义线性模型代写generalized linear model代考|Two-by-Two Tables

1. 我们观察了一段时间的制造过程，观察了450片晶圆。然后对数据进行交叉分类。我们可以使用泊松模型。
2. 我们决定对 450 个晶圆进行取样。然后对数据进行交叉分类。我们可以使用多项式模型。
3. 我们选择了 400 个没有颗粒的晶圆和 50 个有颗粒的晶圆，然后记录好或坏的结果。我们可以使用二项式模型。
4. 我们选择了 400 个没有颗粒的晶圆和 50 个有颗粒的晶圆，根据设计，其中还包括 334 个好晶圆和 116 个坏晶圆。我们可以使用超几何模型。

## 统计代写|广义线性模型代写generalized linear model代考|Correspondence Analysis

$$R_{r \times c}=U_{r \times w} D_{w \times w} V_{w \times c}^T$$

$$R_{i j}=\sum_{k=1}^w U_{i k} d_k V_{j k}$$

$$R_{i j} \approx U_{i 1} d_1 V_{j 1}+U_{i 2} d_2 V_{j 2}$$

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