Model fit and measurement outcome in attachment measurements: a simulation study

Serial attachment level measurements were simulated based on 2 hypothetical models of true change: 1) a burst model, where attachment changes rapidly over the duration of one measurement interval, but is unchanging before and after, and 2) a linear model, where attachment changes at a constant rate over time. Normally distributed measurement error was added to the modeled attachment level change to produce the series of measurement simulations. It was then determined for each series whether a burst model or a linear model best fit the simulated measurement series for a range of overall attachment level changes. For series generated by a burst model, the burst model fit better than a linear model a significant proportion of the time at all attachment level changes. However, for series generated by a linear model, the burst model provided the best fit for attachment level changes that were less than 4 times the standard deviation of the measurement error. Estimates of change based on a linear model slightly overestimated change when the true underlying model was a burst model. Estimates of change based on a burst model slightly underestimated change when the true model was a burst model, but substantially underestimated change when the underlying model was a linear model. Model fit when assessed by the least squares criterion may not be a reliable guide to model validity.