用Delta法估计多维测验合成信度的置信区间

大量研究表明，一般情况下用合成信度可以较好地估计测验信度。对于合成信度及其置信区间的估计方法，在单维测验的情形已有不少研究。但罕有研究讨论多维测验合成信度的区间估计方法。本文用Delta法推导出计算多维测验合成信度的标准误公式，进而计算置信区间，并用一个例子说明如何编程估计多维测验合成信度及其置信区间。

Estimating the Confidence Interval of Composite Reliability of a Multidimensional Test Using Delta Method

Reliability is very important in evaluating the quality of a test. Based on confirmatory factor analysis, composite reliability is a well index to estimate the test reliability for general applications. As is well known, point estimate contains limited information about a population parameter and could not give how far it could be from the population parameter. The confidence interval of the parameter could provide more information. In evaluating the quality of a test, the confidence interval of composite reliability has received more attention in recent years. There are three approaches to estimate the confidence interval of composite reliability of a unidimensional test: Bootstrap method, Delta method and directly using the standard error of a software output (e.g., LISREL). Bootstrap method provides an empirical result of the standard error and is the most credible, but it needs data simulation technique and its computation process is rather complex. Delta method computes the standard error of composite reliability by approximate calculation, and it is simpler than Bootstrap method. LISREL software can directly give the standard error, and it is the simplest among the three methods. By simulation study, it has been found that the interval estimates that obtained by Delta method and Bootstrap method were almost the same, whereas the results obtained by LISREL software and by Bootstrap method were large different (Ye & Wen, 2011). They recommended Delta method when estimating the confidence interval of composite reliability of a unidimensional test, because Delta method is simpler than Bootstrap method. There was few research to study how to compute the confidence interval of composite reliability of a multidimensional test. We deduced a formula by using Delta method for computing the standard error of composite reliability of a multidimensional test. Based on the standard error, the confidence interval can be obtained easily. We used an example of a multidimensional test to illustrate how to calculate composite reliability and its confidence interval by using the proposed Delta method. We also illustrated how to get the same result with Mplus software that automatically calculates the stand error with Delta method and presents the confidence interval.