Log Multiplicative Association Models for Multivariate Categorical Data with Latent Continuous Variable Interpretations

研究者将一些最近开发的分类数据模型与教育和心理测量中使用的各种现有模型联系起来。观察到的变量之间的关系通常假定是由于少数未观察到的或潜在的变量。通常，观察到的变量是离散的，或者是离散测量的（例如，在多项选择题或调查项目中选择的回答选项，职业，宗教，最高学位）。研究者确定了一些最近开发的分类数据模型和现有的潜在变量模型之间的等价性。这些联系对这些不同模型在社会和行为科学研究中的应用和整合的影响，特别是心理测量学，将被检查。研究者将进行的第二项研究是开发允许研究者将（连续和/或离散测量）协变量纳入模型的模型。这一创新将允许在个人层面上分析分类变量之间的关联，从而允许对产生离散测量变量之间观察到的关系的潜在过程或机制的理论和假设进行测试。这项工作产生的发展和创新将扩大社会和行为科学研究人员在研究观察变量和理论化潜在变量之间关系时可用的统计工具。

The investigator makes connections between some recently developed models for categorical data and various existing models used in educational and psychological measurement. The observed relationships between variables is often postulated to be due to a small number of unobserved or latent variables. Frequently, the observed variables are discrete or are measured discretely (e.g., the response option selected on a multiple choice question or survey item, occupation, religion, highest degree earned). The investigator identifies equivalences between some more recently developed models for categorical data and existing latent variable models. The implications of these connections for the application and integration of these different models in social and behavioral science research, especially psychometric, will be examined. A second line of research that the investigator will undertake is in developing models that allow a researcher to incorporate (continuous and/or discretely measured) covariates into the models. This innovation will allow the association between categorical variables to be analyzed at the level of the individual, which permits tests of theories and hypotheses about underlying processes or mechanisms that give rise to observed relationships between discretely measured variables. The developments and innovations resulting from this work will expand the statistical tools available to social and behavioral science researchers in their investigations of the relationships between observed variables and theorized latent variables.