Evaluating Contextual Models for Intensive Longitudinal Data in the Presence of Noise

Nowadays research into affect frequently employs intensive longitudinal data to assess fluctuations in daily emotional experiences. The resulting data are often analyzed with moderated autoregressive models to capture the influences of contextual events on the emotion dynamics. The presence of noise (e.g., measurement error) in the measures of the contextual events, however, is commonly ignored in these models. Disregarding noise in these covariates when it is present may result in biased parameter estimates and wrong conclusions drawn about the underlying emotion dynamics. In a simulation study we evaluate the estimation accuracy, assessed in terms of bias and variance, of different moderated autoregressive models in the presence of noise in the covariate. We show that estimation accuracy decreases when the amount of noise in the covariate increases. We also show that this bias is magnified by a larger effect of the covariate, a slower switching frequency of the covariate, a discrete rather than a continuous covariate, and constant rather than occasional noise in the covariate. We also show that the bias that results from a noisy covariate does not decrease when the number of observations increases. We end with a few recommendations for applying moderated autoregressive models based on our simulation.