Identifiability constraints are necessary for parameter estimation when fitting models with nonlinear covariate associations. The choice of constraint affects standard errors of the estimated curve. Centring constraints are often applied by default because they are thought to yield lowest standard errors out of any constraint, but this claim has not been investigated. We show that whether centring constraints are optimal depends on the response distribution and parameterization, and that for natural exponential family responses under the canonical parametrization, centring constraints are optimal only for Gaussian response.

中文翻译：

---

广义加性模型中的可识别性约束

当拟合具有非线性协变量关联的模型时，可识别性约束对于参数估计是必要的。约束的选择会影响估计曲线的标准误差。通常默认情况下应用居中约束，因为它们被认为在任何约束中产生最低的标准误差，但这种说法尚未得到调查。我们表明，中心约束是否最优取决于响应分布和参数化，并且对于规范参数化下的自然指数族响应，中心约束仅对于高斯响应是最优的。