The Effects of Sanction Intensity on Criminal Conduct - JDAI Helpdesk

17 OR = .98, p ≤ .08. A likelihood ratio test comparing the models with and without the squared terms also
indicated that the inclusion <strong>of</strong> the squared term did not improve model fit: LR χ 2 (1 d.f.) = 3.16, p ≤ .08.
18 Probationers from the West were significantly older than those in the Northeast, and significantly more
likely to be nonwhite and <strong>of</strong> lower SES. We examined several combinations <strong>of</strong> interaction terms between
region and these <strong>of</strong>fender characteristics, and found that West region <strong>of</strong>fenders at the $20,000-$29,999 SES
level were significantly less likely to re<strong>of</strong>fend (b = –1.84, p ≤ .023). When this interaction is controlled, the
probability <strong>of</strong> recidivism is higher in the West than the Northeast, but the association is non-significant (OR
= 2.91, p ≤ .172).
19 <strong>The</strong> likelihood ratio test comparing the negative binomial and Poisson models was highly significant,
suggesting that the negative binomial model fits the data better (LR χ 2 (1 d.f.) = 6913.3, p < .001). <strong>The</strong>
likelihood ratio test comparing zero-inflated negative binomial versus zero-inflated Poisson also supports
the use <strong>of</strong> the former model (LR χ 2 (1 d.f.) = 1930.81, p < .0001). <strong>The</strong> Vuong test statistic comparing the
zero-inflated and standard negative binomial models is positive and highly significant (z = 7.04, p < .0001),
again suggesting that the zero-inflated negative binomial model is the most appropriate.
20 <strong>The</strong> key assumption <strong>of</strong> Cox regression is that the hazard function for each individual follows the same
form, although we do not impose any shape for the form. We used scaled Schoenfeld residuals to examine
proportionality. <strong>The</strong> detailed results <strong>of</strong> this test are presented in Appendix G. Non-significant coefficients
indicate that the proportional hazards assumption is satisfied. For this model, our assumption appears to be
justified. One <strong>of</strong> the control variables for jail time appeared to be nonproportional, but this is not a
substantial cause for concern.
21 We again tested a squared jail time term in this model, which was not statistically significant and did not
improve model fit (OR = .99, p ≤ .630; LR χ 2 (1 d.f.) = .23, p ≤ .634.
22 Likelihood ratio test for Poisson vs. negative binomial: LR χ 2 (1 d.f.) = 2946.78, p < .001. Likelihood
ratio test for zero-inflated Poisson vs. zero-inflated negative binomial: LR χ 2 (1 d.f.) = 304.47, p < .0001.
Vuong test for zero-inflated vs. standard negative binomial: z = 5.68, p < .0001.
23 Covariates in Figures 2.6 and 2.8 are held at the same values as they were for Figure 2.4.
24 Likelihood ratio test comparing models with and without squared term: LR χ 2 (1 d.f.) = 6.62, p ≤ .010.
25 Likelihood ratio test for Poisson vs. negative binomial: LR χ 2 (1 d.f.) = 1041.73, p < .001. Likelihood
ratio test for zero-inflated Poisson vs. zero-inflated negative binomial: LR χ 2 (1 d.f.) = 90.93, p < .0001.
Vuong test for zero-inflated vs. standard negative binomial: z = 5.62, p < .0001.
26 See Appendix G for test <strong>of</strong> the assumptions <strong>of</strong> proportional hazards. We proceeded with the
proportional hazards model despite some evidence for nonproportionality in one <strong>of</strong> the monthly jail
indicator variables.
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