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We propose a dynamic multiplicative factor model for process data arising from complex problem-solving items, an emerging type of data in large-scale educational assessment. The proposed model can be viewed as an extension of the classical frailty models developed in survival analysis for multivariate recurrent event times, but with two important distinctions: (i) the factor (frailty) is of primary interest; (ii) covariates are internal and embedded in the factor. It allows…

依赖且异质的重尾数据中的广义泰勒定律AI 解读

Taylor's law, also known as fluctuation scaling in physics and the power-law variance function in statistics, is an empirical pattern widely observed across fields including ecology, physics, finance, and epidemiology. It states that the variance of a sample scales as a power function of the mean of the sample. We study generalizations of Taylor's law in the context of heavy-tailed distributions with infinite mean and variance. We establish the probabilistic limit and…