ARC Laboratory Sharing

There are three stochastic processes commonly used in time series data and they are autoregressive (AR), moving average (MA) and autoregressive moving average (ARMA) processes. In practice, perhaps the most commonly specified that no autocorrelation is present in the within-participant covariance matrix (VC; ignoring serial correlation: variance components). Another most general covariance structure is the so-called unstructured model (UN) which freely estimate the t(t+1)/2 parameters, where t is the number of observations across time. For a series of repeated measurements, the first level of a multilevel linear model is for describing the growth of individual outcomes as a function of time. The second level is to represent differences in the initial status and rate of change among individuals. Because it is not uncommon to meet these conditions in growth curve modeling applications, it seems reasonable to analyze the potential biasing effects of overlooking or mismodeling such stochastic processes when they are present. Thus, this study examined the performance of a two-level linear growth model when an ARMA(1,1) process is present in the data and the data modeled as VC, AR(1), ARMA(1,1), and UN.

Some conclusion were drawn, first, the estimates of the fixed effects were unbiased. Second, when the analysis model was correctly specified or underspecified, the Type I error rates for the tests of the fixed effects, in general, closely approximated the nominal Type I error rate. Third, the point estimate of the variance components can be biased when serial correlation is not modeled correctly. However, the variance component estimates were biased across many conditions despite correct model specification.

Comments & Questions:

1. In Equation (2b), π_0i=β₀₀+β₀₀x_1i+u_oi needs to revised asπ_0i=β₀₀+β ₀₁ x_1i+u_oi

2. The effect sizes index (η²) is obtained from the sum of squares of effect and error, but these quantities can’t find in the tables. I mean that if this index can be replaced by other indices which can be calculated directly according to the quantities from the tables.