Mathematical Sciences: Large-Sample Approximations for Analysis of Qualitative Data

分析中使用的大样本近似 将审查定性数据。 应考虑的问题 涉及大量参数和大量 意见。 对数线性模型，条件对数线性模型， 潜在类模型、规范模型和关联模型是 有待探索 应考虑大样本近似值 对于最大似然估计的分布，Pearson和 似然比卡方统计，以及 预测。 在进行分析时， 基础模型是正确的 在大规模调查和人口普查中， 通常在非常大的样品上进行。 在这些分析中， 用于近似观测的模型通常涉及 大量的未知量，必须从 为了应用该模型。 拟议 研究，近似开发的可变性 从未知量的估计中预计， 用于构建预测因子的模型值的度量 未来的观察。 与通常的统计相比， 分析，开发的方法适用，即使提出的模型 与数据并不完全一致。 它示出 近似模型在统计工作中可能相当有价值， 当他们没有完全描述数据时。

Large-sample approximations used in the analysis of qualitative data are to be examined. Problems to be considered involve both large numbers of parameters and large numbers of observations. Log-linear models, conditional log-linear models, latent-class models, canonical models, and association models are to be explored. Large-sample approximations are to be considered for distributions of maximum-likelihood estimates, Pearson and likelihood-ratio chi-square statistics, and measures of predictions. Analyses are to be developed without the assumption that the underlying model is correct. In large-scale surveys and censuses, statistical analyses are commonly performed on very large samples. In such analyses, models used to approximate the observations often involve very large numbers of unknown quantities which must be estimated from the sample in order to apply the model. In the proposed research, approximations are developed for the variability expected from the estimates of unknown quantities and for measures of the value of the model for construction of predictors of future observations. In contrast to usual statistical analyses, the methods developed apply even if the proposed model is not entirely consistent with the data. It is shown that approximate models can be quite valuable in statistical work even when they do not fully describe the data.