In this paper, we study a functional regression setting where the random response curve is unobserved, and only its dichotomized version observed at a sequence of correlated binary data is available. We propose a practical computational framework for maximum likelihood analysis via the parameter expansion technique. Compared to existing methods, our proposal relies on the use of a complete data likelihood, with the advantage of being able to handle non-equally spaced and missing observations effectively. The proposed method is used in the Function-on-Scalar regression setting, with the latent response variable being a Gaussian random element taking values in a separable Hilbert space. Smooth estimations of functional regression coefficients and principal components are provided by introducing an adaptive MCEM algorithm that circumvents selecting the smoothing parameters. Finally, the performance of our novel method is demonstrated by various simulation studies and on a real case study. The proposed method is implemented in the R package dfrr.
翻译:在本文中,我们研究一个功能回归设置,随机反应曲线未观测,只有其二分位化版本在相关二进制数据序列中观测到。我们提出了一个实用的计算框架,以便通过参数扩展技术进行最大可能性分析。与现有方法相比,我们的建议依赖于使用完整的数据可能性,其优势是能够有效地处理不均匀的空间和缺失的观测。拟议方法在“功能-对称回归”设置中使用,潜在响应变量是高斯随机元素,在可分离的希尔伯特空间中采集值。功能回归系数和主要组成部分的平滑估算是通过引入适应性 MMCEM 算法来提供,绕过光滑参数的选择。最后,我们的新方法的性能通过各种模拟研究和真正的案例研究得到证明。拟议方法在R 包 dfrr 中实施。