Modeling measurement as a sequential process: Autoregressive confirmatory factor analysis (AR-CFA)

Abstract

To model data from multi-item scales, many researchers default to a confirmatory factor analysis (CFA) approach that restricts cross-loadings and residual correlations to zero. This often leads to problems of measurement-model misfit while also ignoring theoretically relevant alternatives. Existing research mostly offers solutions by relaxing assumptions about cross-loadings and allowing residual correlations. However, such approaches are critiqued as being weak on theory and/or indicative of problematic measurement scales. We offer a theoretically-grounded alternative to modeling survey data called an autoregressive confirmatory factor analysis (AR-CFA), which is motivated by recognizing that responding to survey items is a sequential process that may create temporal dependencies among scale items. We compare an AR-CFA to other common approaches using a sample of 8,569 people measured along five common personality factors, showing how the AR-CFA can improve model fit and offer evidence of increased construct validity. We then introduce methods for testing AR-CFA hypotheses, including cross-level moderation effects using latent interactions among stable factors and time-varying residuals. We recommend considering the AR-CFA as a useful complement to other existing approaches and treat AR-CFA limitations.