Estimating latent structure models with categorical variables: One-step versus three-step estimators
Estimating latent structure models with categorical variables: One-step versus three-step estimators
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DOI：
10.1093/pan/mph001
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发表时间：
2004-12-01
影响因子：
5.4
通讯作者：
Hagenaars, J
中科院分区：
文献类型：
--
作者：
Bolck, A;Croon, M;Hagenaars, J
我们研究了一种估计分类数据潜在结构模型参数的三步法的性质，并提出了一种对常见偏差来源的简单修正。这样的模型有测量部分(本质上是潜在类模型)和结构(因果)部分(本质上是一套Logit方程)。在三步法中，首先定义一个独立的测量模型并估计其参数。然后，根据测量模型的参数估计和指标上的个体观察得分模式，计算关于潜在变量的个体预测分数。最后，这些预测分数被用于因果部分，并被视为观察变量。我们表明，这种对预测潜在分数的天真使用是不可取的，因为它导致了对模型结构部分变量之间关联强度的系统性低估，然而，简单的修正程序可以消除这种系统性偏差。用模拟数据和实际数据说明了这种方法。一种利用多重补偿来解释预测的潜变量是随机变量的方法，会对模型结构部分的参数产生标准误差。
We study the properties of a three-step approach to estimating the parameters of a latent structure model for categorical data and propose a simple correction for a common source of bias. Such models have a measurement part (essentially the latent class model) and a structural (causal) part (essentially a system of logit equations). In the three-step approach, a stand-alone measurement model is first defined and its parameters are estimated. Individual predicted scores on the latent variables are then computed from the parameter estimates of the measurement model and the individual observed scoring patterns on the indicators. Finally, these predicted scores are used in the causal part and treated as observed variables. We show that such a naive use of predicted latent scores cannot be recommended since it leads to a systematic underestimation of the strength of the association among the variables in the structural part of the models, However, a simple correction procedure can eliminate this systematic bias. This approach is illustrated on simulated and real data, A method that uses multiple imputation to account for the fact that the predicted latent variables are random variables can produce standard errors for the parameters in the structural part of the model.