Abstract
Scale development is an important step in empirical research. This chapter describes the common procedures to follow in scale development with essential factor analytical methods. The concept of measurement invariance, the importance of its testing prior to group comparisons, and testing procedures are discussed. Single-group, multi-group, and hierarchical confirmatory factor analytical methods and associated decision making are described. Procedural steps in scale development and measurement invariance testing are illustrated at length using a real dataset in stereotype threat and principals' leadership style in the United States.
TopIntroduction
Data collection is an important aspect of empirical research. The quality of data collection tools, scales or measuring instruments, is paramount in this process. Psychometric properties of these instruments, reliability and validity, are essential quality indicators. It is a common practice for educational and social researchers to develop their own instruments. To maximize the likelihood to create an instrument with sound psychometric properties, this chapter attempts to offer some procedural guidelines from the instrument development and validation literature. Illustrative examples are incorporated to shed light on the explanations. Exploratory factor analysis will be introduced first for its role in instrument development and the emphasis will be on the use of confirmatory factor analysis. Their functions, related concepts and procedures will be described and analytical steps will be introduced and illustrated.
Key Terms in this Chapter
Latent Variable: In SEM it corresponds to factors or hypothetical constructs which are not directly observable.
Hierarchical Confirmatory Factor Analysis: It is a statistical technique to identify the underlying factors as the cause of first-order factors, not the item indicators.
Multi-Group Confirmatory Factor Analysis: It is a statistical technique used to test measurement invariance. It is confirmatory by nature and theory based.
Second-Order Multi-Group Confirmatory Factor Analysis: The procedures of conducting second-order multi-group confirmatory factor analysis is similar yet not identical to those in conducting multi-group confirmatory factor analysis. They are of higher levels in measurement invariance testing.
Latent Variables: It is used interchangeable with factors, constructs, unobserved variables. It is the underlying variables that cause the intercorrelations among observed variables.
Measurement Invariance: Or measurement equivalence, it concerns whether scores from the operationalization of a construct have the same meaning under different conditions.
Measurement: It is used interchangeably with instrument, scale, and test sometimes. It refers to the questionnaire or inventory that researchers use to collect data.
Confirmatory Factor Analysis: It tests the theoretical model against data to see how closely the hypothesized model fits and represents the data. The model fit is evaluated based on goodness-of-fit indices, factor loadings, residuals, modification indices, etc.