Lag Sequential Analysis

Revised Lag Sequential Analysis

Paul D. Allison and Jeffrey K. Liker pointed out that the binomial Z was not an appropriate statistic for almost all the applications in communication and psychology, and they proposed an alternative Z that has supplanted Sackett’s Z in these fields.

Donald D. Morley further pointed out that the use of either Z as a measure of the extent of the effect of one behavior on subsequent behaviors is problematic because its size is greatly dependent upon the number of behaviors in the sequence. This is particularly problematic if one compares the Zs from different series (dyads or groups), because different dyads may generate different amounts of interaction (turns at talk) within the same amount of time. Furthermore, though the Zs were often treated as inferential, this is problematic because of the problem of correlated errors in time series or repeated measures data. Morley proposed converting the Allison and Liker Z to a phi coefficient, which is a product moment coefficient and is more easily interpreted as an effect size for each series or dyad. To conduct systematic analyses on groups of dyads, the phi coefficients can be converted to Fisher Zs, and these can be used as scores for the effects of various lags in tests of difference or regression equations or meta-analytic tests.

Another criticism of the traditional approach to lag sequential analysis is that there were no controls for autocorrelation or the effects of intervening lags when assessing the conditional sequencing of behaviors at higher order lags. Allison and Liker proposed a logit linear model that would test a sequential pattern similar to a Markov chain model. Morley suggested that, since the phi is really a product moment correlation, a researcher could construct a partial phi in the same way as a partial correlation. This would make the phi coefficients at various lags analogous to the autocorrelation function and the partial phi coefficients analogous to the partial autocorrelation functions in traditional time-series analyses. When this is done, interaction data can be shown to usually be structured into shorter sequences than it appeared when only the unpartialed Zs are considered. A husband’s negative behavior may call forth a negative behavior from his wife, to which the husband responds with another negative behavior and then the wife responds again with negativity. The lag 2 Z (and phi) may show that the husband’s original negative behavior predicts a subsequent negative behavior by him at lag 2 when he responds to his wife’s negative behavior. However, the partial phi may show that his lag 2 negativity is mainly the result of his tendency to reciprocate his wife’s negativity, with the effect of his initial negativity being indirect and mediated entirely through his tendency to reciprocate. Likewise, though the lagged Zs (and phi coefficients) may show that the husband’s negative behavior is predictive of the wife’s negative behavior for two, three, or more responses latter, the partial phi coefficients may show that each negative response after the initial lag 1 response is explained by the tendency to respond to the husband’s immediately preceding behavior, which continues to be negative because of his reciprocation of her negative response to his initial negative behavior. Of course, it is possible for a behavior to have lasting influence on subsequent behaviors such that the partial phi coefficients show the residual influence of an initial behavior over and above the effect of the immediately preceding action.

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