不同的模型有不同的链接函数。要计算预测值,请对模型的链接函数求逆。逆函数位于下表中。
模型 | 链接函数 | 预测公式 |
---|---|---|
二项 | Logit(L) | ![]() |
二项 | Normit | ![]() |
二项 | Gompit | ![]() |
Poisson | 自然对数 | ![]() |
Poisson | 平方根 | ![]() |
Poisson | 致命ID | ![]() |
项 | 说明 |
---|---|
exp(·) | 指数函数 |
Φ(·) | 正态分布的累积分布函数 |
X' | 要预测的点的向量转置 |
![]() | 估计的系数的向量 |
其中 仅从训练数据,只有当有一个测试数据集进行验证时。
项 | 说明 |
---|---|
![]() | 1, for the binomial and Poisson models |
xi | the vector of a design point |
![]() | the transpose of xi |
X | the design matrix |
W | the weight matrix |
![]() | the first derivative of the link function evaluated at ![]() |
![]() | the predicted mean response |
![]() | the predicted probability for the design point in a binary logistic model |
![]() | the inverse cumulative distribution function of the standard normal distribution for the predicted probability in a binary logistic model |
![]() | the probability density function of the standard normal distribution |
置信限使用 Wald 近似法。以下是 100(1 | α双侧置信区间
类型 | 链接 | 拟合值的标准误 |
---|---|---|
二值 Logistic | Logit | ![]() |
二值 Logistic | Normit | ![]() |
二值 Logistic | Gompit | ![]() |
Poisson | 对数 | ![]() |
Poisson | 平方根 | ![]() |
Poisson | 标识 | ![]() |
其中 仅从训练数据,只有当有一个测试数据集进行验证时。
项 | 说明 |
---|---|
![]() | the inverse of the link function evaluated at x |
![]() | ![]() |
![]() | the transpose of the vector of the predictors |
![]() | the vector of estimated coefficients |
![]() | the value of the inverse cumulative distribution function for the normal distribution evaluated at ![]() |
α | the significance level |
![]() | ![]() |
X | the design matrix |
W | the weight matrix |
![]() | 1, for binomial and Poisson models |
![]() | the predicted probability for the design point in a binary logistic model |
![]() | the inverse cumulative distribution function of the standard normal distribution for the predicted probability in a binary logistic model |
![]() | the cumulative distribution function of the standard normal distribution |