The Autoregressive Model of Change David A. Kenny

2 Model The present is determined by the past X 1  X 2  X 3  X 4 A mediational model: the relationship between two time points is explained by intermediate time points. –The relationship between X 1 and X 4 is explained either X 2 or X 3 and so r 14.3 and r 14.2 equal zero.

3 Correlational Structure: Simplex X 1 1 X 2 r 1 1 X 3 r 1 r 2 r 2 1 X 4 r 1 r 2 r 3 r 2 r 3 r 3 1 X 1 X 2 X 3 X 4 Generally the longer the lag, the weaker the correlation. Called a “simplex” correlational structure.

4 Estimation The first-order autoregressive model can be estimated with as few as two waves of data. Model over-identified with three or more waves.

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6 Allowance for Measurement Error A much more realistic model, is a first-order autoregressive model with measurement error. Observed score equals true score plus error. The true score has an autoregressive structure.

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8 Identification Partially identified with a least three waves. Error variances and reliabilities of each wave identified except for the first and last wave. Autoregressive paths identified for each wave except for wave 1 to wave 2. Standardized paths identified except for 1 to 2 and form the next to last to the last wave. Possible identifying assumption: equal error variances.

9 Multiple Indicators Need at least three indicators per latent variable. Correlate errors of the same indicator at each time. Need only two waves of data to be identified.

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11 Second-Order Autoregressive A path from T1 to T3 (and T2 and T4). STARTS as a better conceptual alternative.