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.
Highlights
When people respond to multi-item scales, item responses may depend on one another due to the order in which items are presented
Our autoregressive confirmatory factor analysis (AR-CFA) can be used on larger scales, the shorter mini-IPIP facilitates more concise tables and Mplus code while exemplifying typical dilemmas regarding measurement model fit using an IC-CFA, which is common for Big Five scales
For Bayesian analyses, we provide typical fit criteria including posterior-predictive probabilities (PPP; values around 0.5 are optimal and below 0.05 is problematic) and their associated χ2 95% CIs, as well as a deviance information criterion (DIC; lower values are better; Muthén and Asparouhov, 2012; Asparouhov et al, 2015)
Summary
When people respond to multi-item scales, item responses may depend on one another due to the order in which items are presented (as suggested by Schwarz and Clore, 1983; Schwarz, 1999, 2011). Longitudinal and panel data literatures treat autoregressive effects at length (Arellano, 2003; Baltagi, 2013; Hamaker et al, 2015), most survey research overlooks the sequential nature of multi-item scales (Knowles, 1988; Knowles et al, 1992; Knowles and Byers, 1996). To tackle this problem, we offer a new way to model multi-item scales which present items in the same order to all respondents: an autoregressive confirmatory factor analysis (AR-CFA). We conclude by emphasizing the value of theory-based measurement models, limits of our approach, and future research directions
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