In this paper, we present a method for factor analysis of discrete data. This is accomplished by fitting a dependent Poisson model with a factor structure. To be able to analyze ordinal data, we also consider a truncated Poisson distribution. We try to find the model with the lowest AIC by employing a forward selection procedure. The probability to find the correct model is investigated in a simulation study. Moreover, we heuristically derive the corresponding asymptotic probabilities. An empirical study is also included.

中文翻译：

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使用相关泊松模型的离散因子分析

在本文中，我们提出了一种对离散数据进行因子分析的方法。这可以通过将因泊松模型与因子结构拟合来实现。为了能够分析顺序数据，我们还考虑了截断的泊松分布。我们尝试通过采用前向选择程序来找到具有最低AIC的模型。在仿真研究中调查了找到正确模型的可能性。此外，我们试探性地得出相应的渐近概率。实证研究也包括在内。