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The standard recommendation for multi-level models that include a time-varying covariate (TVCs) is to fix the effect of TVC, as allowing the effect of the TVC to vary randomly may prevent convergence if there is insufficient data. However, the assumption that the effect of the TVC is fixed may not hold in reality. A simulation study shows that while treating the effect of the TVC as random performs poorly when using constrained variance estimation, when using unconstrained variance estimation – allowing variance estimates to be negative – treating the effect as random performs better than treating it as fixed when the effect is random in reality.