To compare fit statistics for the Rasch model based on estimates of unconditional or conditional response probabilities. Using person estimates to calculate fit statistics can lead to problems because the person estimates are biased. Conditional response probabilities given the total person score could be used instead. Data sets are simulated which fit the Rasch model. Type I error rates are calculated and the distributions of the fit statistics are compared with the assumed normal or chi-square distribution. Parametric bootstrap is used to further study the distributions of the fit statistics. Type I error rates for unconditional chi-square statistics are larger than expected even for moderate sample sizes. The conditional chi-square statistics maintain the significance level. Unconditional outfit and infit statistics have asymmetric distributions with means slighly below 1. Conditional outfit and infit statistics have reduced Type I error rates. Conditional residuals should be used. If only unconditional residuals are available parametric bootstrapping is recommended to calculate valid p-values. Bootstrapping is also necessary for conditional outfit statistics. For conditional infit statistics the adjusted rule-of-thumb critical values look useful.

中文翻译：

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用于Rasch分析的项目拟合统计量：我们可以信任它们吗？

根据无条件或有条件响应概率的估计值比较Rasch模型的拟合统计量。由于人员估计有偏差，因此使用人员估计来计算拟合统计量可能会导致问题。给定总人得分的条件响应概率可以代替使用。模拟适合Rasch模型的数据集。计算I类错误率，并将拟合统计量的分布与假定的正态或卡方分布进行比较。参数引导程序用于进一步研究拟合统计量的分布。即使对于中等样本量，无条件卡方统计量的I类错误率也比预期的要大。条件卡方统计保持显着性水平。无条件的服装和不符合统计信息具有不对称分布，均值略低于1。条件的服装和不符合统计信息降低了I类错误率。应使用条件残差。如果只有无条件残差可用，建议使用参数自举法来计算有效的p值。对于条件服装统计，自举也是必要的。对于条件失常统计，调整后的经验法则临界值看起来很有用。