Geographically Weighted Cronbach's Alpha (GWalpha): An Exploratory Local Measure of Reliability for Scale Construction

Scales, as survey instruments, are crucial for investigating people's attitudes and behaviors in social science research. Cronbach's alpha is the most frequently used measure of internal consistency reliability for multi-item survey scales. Affected by the spatial context of respondents' locations, the reliability of responses to a scale may vary geographically, whereas classical Cronbach's Alpha assumes that reliability is stationary across all samples being estimated. In this article, a local version of Cronbach's alpha, Geographically Weighted Cronbach's Alpha (GWalpha), is developed to explore how the reliability of a measure varies spatially. Issues concerning the bandwidth, inference, and interpretation are also discussed. We demonstrate the utility of GWalpha on a synthetic dataset with known parameters and an empirical dataset. Results suggest that GWalpha can effectively reveal and measure how spatial context influences survey reliability, which has been largely overlooked in the existing literature.