Handbook of Quantitative Criminology by Alex R. Piquero & David Weisburd

Author:Alex R. Piquero & David Weisburd
Language: eng
Format: epub, pdf
Publisher: Springer New York, New York, NY

(19.14)

Earlier in this chapter, a main effect for appeared in (19.7), and in that case, it served to restrict the estimate of the event’s effect to within-individual change by making that estimate independent from individual differences in average response level. Equation (19.14) adds the interaction of this variable with age as a way to make the estimated effect of the event independent from individual differences in the rate of age related change.8

To gain perspective on the causal model implicit in the data analysis approach presented in this chapter, it is useful to consider the multiple sources of information that contribute to the baseline of expected change. People who experience the event contribute to the overall baseline age trend through their waves of data before the event occurs. Individuals observed for at least two waves prior to the event provide information about the rate of age related change prior to the event (Bryk and Weisberg 1977). Using this information as the baseline of expected change entails projecting the trend beyond the available data. In the absence of other supporting information, such projections are always risky, and they are especially risky when projecting far into the future and when the trend is curvilinear, as age trends so often are.

People who do not experience the event provide a second source of information about expected age trends. Information from this group has the advantage that it extends throughout the period of study, including time during which others experience the event. Thus, it is free from the problem of projection beyond the data. The corresponding disadvantage of relying on this group as a baseline for change is that their age trend may differ from that of people who do experience the event.

The plausibility of viewing estimates from these models as causal effects will be considerably stronger if these two sources of information are in agreement about the expected pattern of change. Equation (19.14) provides a convenient vehicle for assessing whether they converge. For individuals who will experience the event, change over time before the event occurs is , while for other individuals, change over time is β3Age ti . Thus, β4 captures the difference in age trend, and if its value is zero, then the baseline pattern of change does not depend on whether and for how long the event is experienced.9

What if β4 is not close to zero, thus indicating differences in baseline age trends for people who do and do not experience the result? A causal interpretation of the effect of the event may still be plausible if allowing the baseline age trend to depend on the mean of the event variable does not alter the estimate of the effect (i.e., β1 is little changed upon adding to the model). This pattern would suggest that, though baseline age trends are related to experiencing the event, they do not differ in a way that would account for the relationship between the event and the outcome variable.

The case for interpreting the estimated relationship as a causal impact of the event is weaker if adding this interaction alters the estimate.

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