From Data to Causes II: Comparing Approaches to Panel Data Analysis

Abstract

This article compares a general cross-lagged model (GCLM) to other panel data methods based on their coherence with a causal logic and pragmatic concerns regarding modeled dynamics and hypothesis testing. We examine three “static” models that do not incorporate temporal dynamics: random- and fixed-effects models that estimate contemporaneous relationships; and latent curve models. We then describe “dynamic” models that incorporate temporal dynamics in the form of lagged effects: cross-lagged models estimated in a structural equation model (SEM) or multilevel model (MLM) framework; Arellano-Bond dynamic panel data methods; and autoregressive latent trajectory models. We describe the implications of overlooking temporal dynamics in static models and show how even popular cross-lagged models fail to control for stable factors over time. We also show that Arellano-Bond and autoregressive latent trajectory models have various shortcomings. By contrasting these approaches, we clarify the benefits and drawbacks of common methods for modeling panel data, including the GCLM approach we propose. We conclude with a discussion of issues regarding causal inference, including difficulties in separating different types of time-invariant and time-varying effects over time.

On the Differences between General Cross-Lagged Panel Model and Random-Intercept Cross-Lagged Panel Model: Interpretation of Cross-Lagged Parameters and Model Choice

“…With this point in mind, in this section we first show how the GCLM (i.e., Equation 8) can be expressed within the unified framework. Then we discuss the interpretative differences of cross-lagged parameters between the GCLM and the RI-CLPM, which was overlooked in Zyphur et al (2020aZyphur et al ( , 2020b. We also warn of the potential difficulty of its interpretation in the GCLM.…”

“…As before, β x and β y are (first-order) autoregressive parameters, and γ x and γ y are (first-order) cross-lagged parameters. The terms B xi and B yi are (unit-specific) common factors, which Zyphur et al (2020aZyphur et al ( , 2020b called unit effects or stable (trait) factors. The means of these factors are set to zero.…”

“…The means of these factors are set to zero. In addition, although not explicitly stated in Zyphur et al (2020aZyphur et al ( , 2020b, these factors are assumed to be uncorrelated with the initial states (x i1 and y i1 ), though this assumption can be relaxed. λ xt and λ yt are weights or occasion-specific factors loadings, expressing changes in the effects of common factors over time.…”

“…Among such methodologies, the general cross-lagged panel model (GCLM; Zyphur et al, 2020aZyphur et al, , 2020b) is a recent variant of the CLPM. This model was not covered in the discussion of .…”

“…The GCLM as a SEM-based approach assumes (time-varying) unit effects as well as moving average (MA) and crosslagged moving average (CLMA) terms, aiming to increase the range of dynamic processes that can be modeled. Zyphur et al (2020b) discuss the relation between the GCLM and other longitudinal models such as the latent growth model (LGM; Meredith & Tisak, 1984, 1990 and the autoregressive latent trajectory (ALT) model (Bollen & Curran, 2004, 2006Curran & Bollen, 2001). Many researchers have shown interest in applying the GCLM, including more than 10 citations on Google Scholar as of August 2020 (e.g., Bollmann, Rouzinov, Berchtold, & Rossier, 2019;Oswald, 2019;Zhang et al, 2019).…”