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The Effects of Sanction Intensity on Criminal Conduct - JDAI Helpdesk

The Effects of Sanction Intensity on Criminal Conduct - JDAI Helpdesk

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incarcerated must also be removed from the risk set – their risk <str<strong>on</strong>g>of</str<strong>on</strong>g> failure <strong>on</strong> those days is<br />

zero. This would be straightforward if we knew the exact dates <str<strong>on</strong>g>of</str<strong>on</strong>g> entry and exit from jail<br />

as well as the exact <str<strong>on</strong>g>of</str<strong>on</strong>g>fense dates, but our dataset <strong>on</strong>ly includes m<strong>on</strong>thly jail status<br />

indicators. When the jail variable is measured at less frequent time intervals than the<br />

failure event, a possible soluti<strong>on</strong> is to treat jail as a time-varying covariate (TVC) and<br />

interpolate jail data for each day. For example, if the m<strong>on</strong>thly jail indicator for January<br />

2008 shows that the <str<strong>on</strong>g>of</str<strong>on</strong>g>fender was in jail during that m<strong>on</strong>th, we code each day from<br />

January 1 to January 31 as a day in jail. Cox regressi<strong>on</strong> allows for this approach using<br />

‘episode splitting,’ which involves creating a separate observati<strong>on</strong> for each pers<strong>on</strong>-day up<br />

to the day <str<strong>on</strong>g>of</str<strong>on</strong>g> failure or censoring. It is also possible to work around the potential problem<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g> overlapping jail and failure dates created by the interpolati<strong>on</strong> (e.g., when the original<br />

dataset indicates that the <str<strong>on</strong>g>of</str<strong>on</strong>g>fender was in jail in February 2008, but he <str<strong>on</strong>g>of</str<strong>on</strong>g>fends <strong>on</strong><br />

February 23) by simply dropping the m<strong>on</strong>th <str<strong>on</strong>g>of</str<strong>on</strong>g> jail time in which the <str<strong>on</strong>g>of</str<strong>on</strong>g>fense took place.<br />

Thus, the <str<strong>on</strong>g>of</str<strong>on</strong>g>fender in this example is coded as being out <str<strong>on</strong>g>of</str<strong>on</strong>g> jail during February.<br />

An obstacle to using the episode-splitting approach in the present applicati<strong>on</strong> is<br />

that the method is usually used in cases in which it is possible to observe either level <str<strong>on</strong>g>of</str<strong>on</strong>g><br />

the TVC <strong>on</strong> the failure date. For example, if our TVC were employment status, the<br />

<str<strong>on</strong>g>of</str<strong>on</strong>g>fender could be either employed or unemployed <strong>on</strong> the <str<strong>on</strong>g>of</str<strong>on</strong>g>fense date. However, we<br />

forced the <str<strong>on</strong>g>of</str<strong>on</strong>g>fender to be out <str<strong>on</strong>g>of</str<strong>on</strong>g> jail <strong>on</strong> the failure day because it did not make sense<br />

theoretically to allow for the overlap. Thus, our jail indicator variable is always coded 0<br />

when our failure variable is coded 1. This results in perfect collinearity between the<br />

covariate and the failure event, which prevents us from estimating parameters for the jail<br />

variable using the Cox model. We could still have dropped jail days out <str<strong>on</strong>g>of</str<strong>on</strong>g> the risk set<br />

84

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