Social science researchers are generally accustomed to treating ordinal variables as though they are continuous. In this paper, we consider how identification constraints in ordinal factor analysis can mimic the treatment of ordinal variables as continuous. We describe model constraints that lead to latent variable predictions equaling the average of ordinal variables. This result leads us to propose minimal identification constraints, which we call "integer constraints," that center the latent variables around the scale of the observed, integer-coded ordinal variables. The integer constraints lead to intuitive model parameterizations because researchers are already accustomed to thinking about ordinal variables as though they are continuous. We provide a proof that our proposed integer constraints are indeed minimal identification constraints, as well as an illustration of how integer constraints work with real data. We also provide simulation results indicating that integer constraints are similar to other identification constraints in terms of estimation convergence and admissibility.

翻译：社会科学研究者通常习惯于将序次变量视为连续变量处理。本文探讨了序次因子分析中的识别约束如何能够模拟将序次变量作为连续变量处理的方式。我们描述了导致潜变量预测值等于序次变量平均值的模型约束。这一结果促使我们提出最小识别约束，即"整数约束"，该约束使潜变量围绕观测到的整数编码序次变量的尺度中心化。整数约束带来了直观的模型参数化方式，因为研究者已经习惯于将序次变量视为连续变量进行思考。我们提供了证明，表明所提出的整数约束确实是最小识别约束，并通过实际数据展示了整数约束的运作机制。同时，我们提供的模拟结果表明，在估计收敛性和可接受性方面，整数约束与其他识别约束具有相似性。