Abstract

In this paper I consider the consequences of analyzing time series data, collected by the
Experience Sampling Method (ESM), with a first-order autoregressive AR(1) model. In ESM research
the time points of measurement occasions are sampled by uniform sampling from successive blocks of
time. This results in time intervals between measurement occasions that
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vary in lengths, both within and
between individuals. For autoregressive models it is assumed that time intervals between measurement
occasions are equidistant. Analyzing ESM data with the AR(1) model, thus theoretically leads to a
mismatch.
In simulation studies I compare Uniform sampling data with data where time intervals between
measurements are equidistant. I do this first for N=1 and then for N >1. Results for N=1 show that
uniform sampling data leads to less biased estimates of the autoregressive coefficient ϕ than equidistant
sampling data, for positive values of ϕ and common lengths of time series.
Results are less clear for N>1. I used three different centering methods for the multilevel AR(1) model
to analyze the data. Equidistant sampling data, analyzed with the uncentered multilevel AR(1) model,
result in the least biased estimates of the average autoregressive parameter. But Uniform sampling data
analyzed with the centered model, result in estimates that are almost as good in terms of bias. Coverage
rates though, are far lower for Uniform sampling data.
These results for the average autoregressive coefficient are replicated when a 2nd level predictor is
added to the multilevel AR(1) model. The estimates of the effect of the 2nd level predictor on each
individual’s autoregressive coefficient ϕ are least biased for Equidistant sampling data analyzed with the
centered multilevel AR(1) model. Uniform data analyzed by the centered model result in estimates that
are almost as good in terms of bias, coverage rate and empirical power.
Is there a mismatch between ESM data (collected by Uniform sampling) and the autoregressive AR(1)
model? There is no unequivocal answer to this question, because this answer largely depends on lengths
of time series used and the population values of the parameters. For applied researchers guidelines are
given.
Contrary to previous research, this study shows that for ESM data, analyzed with the multilevel AR(1)
model, it is better to center the predictor within person, for positive values of the average autoregressive
coefficient. When this parameter is expected to be ≤ 0, not centering the predictor is preferred. No
apriori advice can be given with regard to centering, when the multilevel AR(1) model is used to analyze
ESM data. This is a consequence of the heterogeneity of lengths of time intervals between measurement
occasions in ESM data.
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