Hohensinn Christine, Kubinger Klaus D, Reif Manuel
Division of Psychological Assessment and Applied Psychometrics, Faculty of Psychology, University of Vienna, Liebiggasse 5, 1010 Vienna, Austria,
J Appl Meas. 2014;15(3):252-66.
Recently the linear logistic test model (LLTM) by Fischer (1973) is increasingly used. In applications of LLTM, a likelihood-ratio test comparing the likelihood of the LLTM to the likelihood of the Rasch model is the most often applied model test. The present simulation study evaluates the empirical Type I risk, test power, and approximation to the expected distribution in the context of the LLTM. Furthermore, as possible influence factors on the distribution of the likelihood-ratio test statistic, the misspecification of the superior model, the closeness to singularity of the design matrix, and different sorts of misspecification of the design matrix are implemented. In summary, results of the simulations indicate that the likelihood-ratio test statistic holds the fixed Type I risk under typical conditions. Nevertheless, it is especially important to ensure the fit of the superior model, the Rasch model, and to consider the closeness to singularity of the design matrix.
最近，费舍尔（1973年）提出的线性逻辑测试模型（LLTM）的应用越来越广泛。在LLTM的应用中，将LLTM的似然性与拉施模型的似然性进行比较的似然比检验是最常应用的模型检验。本模拟研究在LLTM的背景下评估了经验性I型风险、检验功效以及对期望分布的近似程度。此外，作为似然比检验统计量分布的可能影响因素，还考虑了上级模型的错误指定、设计矩阵接近奇异性的程度以及设计矩阵的不同类型错误指定。总之，模拟结果表明，在典型条件下，似然比检验统计量具有固定的I型风险。然而，确保上级模型（拉施模型）的拟合以及考虑设计矩阵接近奇异性的程度尤为重要。
