Abstract

Multiple-group confirmatory factor analysis (CFA) has been widely used to analyze measurement equivalence using factor models. Traditionally, in order to conclude that measurement equivalence exists, it is necessary to have evidence that the factor structure and measurement parameters, such as factor loadings are completely identical, with no differences across target groups or measurement occasions. However, when the number of groups is large, these conditions can become overly stringent or impractical. Approximate measurement invariance is a relaxed form of measurement invariance and proposed to practically examine measurement invariance between many groups. Alignment is a widely used procedure for analyzing approximate measurement invariance and has been used to compare measurement models with continuous indicator between many countries. On the other hand, the analysis of measurement invariance of test scores across ages reflecting developmental changes in psychological attributes has been mainly conducted by comparing two or three small age groups using multiple-group CFA. However, in the analysis of measurement invariance across ages, approximate measurement invariance can be applied to ages that are divided into a large number of age groups. The current study discusses the idea, necessity, and analytical model of approximate measurement invariance and illustrates the analysis of the approximate measurement invariance of psychological tests over time using the alignment method. In particular, we discussed the conceptual similarities and differences between measurement invariance and approximate measurement invariance for factor models with categorical data, and introduced the analytical process of measurement invariance and approximate measurement invariance for 26 age groups of K-MMSE test scores, a test for assessing cognitive function, using multiple-group CFA and the alignment method. Based on the results of the analysis, the implications of approximate measurement invariance versus traditional measurement invariance were explained, and discussions related to analysis of approximate measurement invariance with categorical data were summarized.