中文摘要：

研究介绍了等级数据测量模型的建构（LRV,潜在反应变量模型）和参数估计（WLSMV）方法,以及在此基础上测量不变性的检验（DIFFTEST）方法。采用蒙特卡洛模拟研究方法,考察样本量、组间样本量对比情况、阈值差异程度、量表长度等因素,对DIFFTEST方法检验效果的影响,同时考察了WLSMV估计方法对参数估计的精度。研究发现WLSMV估计方法对真值参数的复原效果很好;DIFFTEST的一类错误概率达到可接受水平;在大样本情况下、组间样本量基本相等、阈值差异程度较大时,DIFFTEST检验力较好。在控制测量不变性遭受破坏的项目个数情况下,随着测验长度增加,DIFFTEST的检验力下降。

英文摘要：

Measurement equivalence/invariance（ME/I） is obtained when the relations between observed test scores and the latent trait measured by the test are identical across subpopulations.In particular,individuals with equal standings on the latent trait,but sampled from different subpopulations,should have the same expected observed score.In social sciences,researchers collect and analyze ordinal data frequently,such as data obtained from Likert Scale.While researchers often treat ordinal data as continuous,the ordinal measurement is discrete in nature.Then the x~2 statistic and standard errors of parameter estimation tend to exhibit bias.As a result,the results of the nested model test for exploring ME/I based on the normal theory should be affected.This simulation study uses simulated data with known properties to assess the effect of parameters recovery,difference between estimated value and known population parameters value,and empirical power in various total sample sizes,the ratio of the reference group to the focal group size,the difference of parameters between two groups,and test length. The present study introduced a new method of model construction（latent response variable model,LRV） and parameters estimation （robust weighted least squares estimator with a diagonal weight matrix,WLSMV） for ordinal categorical data,with the method of exploring ME/I based on this method（DIFFTEST）.Two levels of test length were examined：a short test（10 items） and a moderate test（20 items）.To control the number of items whose ME/I were violated,the ME/I of 5 items in these two conditions were simulated to be violated.Three levels of overall sample size（500,1000,and 2000）,as well as two different sample size ratios of reference group to focal group members（5/5 and 8/2） were considered.Another condition of interest in this study was the difference of threshold between the two groups.Four levels of thresholds difference were examined in this study：0,.2,.4,.6.which reflected the violation degree,fro