Abstract: Cognition is the core of intelligence, also an indispensable ability of children to develop and mature. Preschool period is an important time for the development of children’s cognition. As they mature, their understanding of the world get deeper and wider, and the cognition ability also grow rapidly. The most suitable method to analyzing cognitive development trend is longitudinal study, which can shows the development track of children. When researchers analyzing longitudinal data, changes in variables are the emphasis of research. But the longitudinal data can only be interpreted if important psychometric features of the measured variables are assumed invariant across time. The definition of measurement invariance is that the psychometric features of an instrument remain stable in different situation or time point. However, in previous studies, few researchers considerred or test the measurement invariance of the instrument. This will lower the validity of instrument as the result may be biased or even misled. The methods to test the measurement invariance include traditional confirmatory factor analysis (CFA) and newly developed item response theory (IRT). Previous researchers always used CFA to analyze measurement invariance. However comparing to newly developed item response theory (IRT), the CFA method has some limitations as the linear assumption of the relationship between observable variables and latent variables, and IRT non-linear assumption is more suitable for reality and psychology issues. Also, CFA method can only test whether the factor variance and covariance remain stable or not in different situation. But the IRT method can provide the measurement invariance information in item level, which is more useful for future revising of instrument. Thus, we choose IRT method to systematically analyze the measurement invariance of Children’s Cognitive Development Test. In this study, we choose 882 48-mouth-old children from the country, testing in first year and second year. After model comparison and considering the instrument construct, we choose 2-tier multidimensional item response model for further investigation of measurement invariance. The testing of measurement invariance includes two parts: integral testing and item-level testing. The result indicates that the instrument is partially invariance, but the high correlation between the primary factors indicating the construct of the instrument remains stable over time. Item-level test result shows that the discrimination parameter and difficulty parameters of item “direction” do not satisfy invariance condition, which could be considered to deleted or revised. The possible reason is that children’s conception of direction developed rapidly from 4-5, and previous studies shows most 4-year old children hardly distinguish “left” and “right”. Therefore, the item is difficult for 4-year old children since the ability of direction grows rapidly, the corresponding task may be too easy for 5-year old children. Moreover, the difficult parameters of the other four items do not satisfy the measurement invariance condition. This phenomenon is caused by the testlet design of this measurement, children accomplish different level of cognitive tasks in two time points. The float of difficult parameters can be tolerated, but the difficult of these items need to be revised in order to be more suitable for corresponding age of children. Additionally, model estimation results indicate children’s cognitive proficiency grow rapidly and significantly from 4 to 5.

Key words: Item response theory, multidimensional item response theory, longitudinal data, children cognition, measurement invariance, two-tier model

摘要： 本研究以4岁~5岁儿童认知能力测验为例，在IRT框架下探讨了如何进行追踪数据的测量不变性分析。分析模型采用项目间多维项目反应理论模型(between-item MIRT model)和项目内（within-item MIRT model）多维two-tier model，被试为来自全国的882名48个月的儿童，工具为自编4岁~5岁儿童认知能力测验。经测验水平 分析和项目水平分析，结果表明：(1)本文对追踪数据的测量不变性分析方法合理有效; (2)该测验在两个时间点上满足部分测量不变性要求，测验的潜在结构稳定; (3)“方位题”的区分度和难度参数都发生变化，另有4题难度参数出现浮动; (4)儿童在4岁~5岁期间认知能力总体呈快速发展趋势，能力增长显著。

关键词: 项目反应理论, 多维项目反应理论, 追踪数据, 测量不变性, 儿童认知, two-tier模型