Title: Rank-deficiencies in a reduced information latent variable model Show Chinese title

Title: 秩亏缺陷在降维潜在变量模型中

Abstract: Latent variable models are well-known to suffer from rank deficiencies, causing problems with convergence and stability. Such problems are compounded in the "reduced-group split-ballot multitrait-multimethod model", which omits a set of moments from the estimation through a planned missing data design. This paper demonstrates the existence of rank deficiencies in this model and give the explicit null space. It also demonstrates that sample size and distance from the rank-deficient point interact in their effects on convergence, causing convergence to improve or worsen depending on both factors simultaneously. Furthermore, it notes that the latent variable correlations in the uncorrelated methods SB-MTMM model remain unaffected by the rank deficiency. I conclude that methodological experiments should be careful to manipulate both distance to known rank-deficiencies and sample size, and report all results, not only the apparently converged ones. Practitioners may consider that, even in the presence of nonconvergence or so-called "inadmissible" estimates, a subset of parameter estimates may still be consistent and stable. Show Chinese abstract

Abstract: 潜在变量模型众所周知会受到秩亏问题的影响，这会导致收敛性和稳定性的问题。 这些问题在“减少组别分票多特质-多方法模型”中更加严重，该模型通过计划性缺失数据设计从估计中省略了一组矩。 本文证明了该模型中存在秩亏问题，并给出了明确的零空间。 它还表明样本量和接近秩亏点的距离相互作用，影响收敛性，导致收敛性同时取决于这两个因素而改善或恶化。 此外，它指出未相关方法SB-MTMM模型中的潜在变量相关性不受秩亏的影响。 我得出结论，方法学实验应谨慎操纵已知秩亏的距离和样本量，并报告所有结果，而不仅仅是看似收敛的结果。 实践者可以考虑即使在非收敛或所谓的“不可接受”估计的情况下，参数估计的一部分仍然可能是前后一致且稳定的。