Multidimensional factor models with moderations on all model parameters have so far been limited to single-factor and two-factor models. This does not align well with existing psychological measures, which are commonly intended to assess 3-5 dimensions of a latent construct. In this paper, I introduce a multidimensional MNLFA model that permits the moderation of item intercepts, loadings, residual variances, factor means, variances, and correlations across three or more latent factors. I describe efforts to implement the model using Bayesian methods through Stan and penalized maximum likelihood approaches to stabilize estimation and detect partial measurement non-invariance while preserving model interpretability. Closed-form analytic gradients of the likelihood, eliminating the need for costly numerical or MCMC-based approximations. We conclude by discussing the theoretical implications of penalization for measurement invariance, computational considerations, and future directions for extending the framework to categorical indicators, longitudinal data, and applied research contexts.

翻译：到目前为止，对所有模型参数进行调节的多维因子模型仅限于单因子和双因子模型，这与现有心理测量工具（通常旨在评估潜在构念的3-5个维度）不太吻合。本文提出了一种多维MNLFA模型，该模型允许对三个及以上潜变量的项目截距、因子载荷、残差方差、因子均值、方差及相关系数进行调节。我们描述了通过Stan使用贝叶斯方法实现该模型，以及采用惩罚最大似然方法以稳定估计、检测部分测量非等值性并保持模型可解释性的相关努力。我们推导了似然函数的闭式解析梯度，从而避免了成本高昂的数值或基于MCMC的近似。最后，我们讨论了惩罚对测量等值性的理论意义、计算考量，以及将该框架扩展至分类指标、纵向数据和应用研究情境的未来方向。