A series of binary logistic regressions were utilized to examine plea decisions within the juvenile courts of South Carolina. The relationship between the predictors may be specified using the following equation:
Logit(Y) = ln(odds) = b0 + b1x1 + b2x2
Where odds refer to the odds of Y (outcome) = 1 with several hypothetical predictor variables following on the other side of the equation. Binary logistic regression
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makes several assumptions. First, given the dichotomous nature of the dependent variable, binary logistic regression predicts the probability that one observation will appear in one category (plea bargain) versus the other (adjudication) (Menard, 2002). This, additionally, is useful in determining which measures are stronger or weaker predictors of a dependent variable, wherein one may exponentiate the resulting log-odds to easily interpret odds ratios (DeMaris, 1992; Kahane, 2008). Second, logistic regression assumes that for every independent variable, one must have at least 10 data points
(Kahane, 2008). Given there are over 1,000 cases in this data and 17 independent variables, this key assumption is not violated.
Prior to utilizing logistic regression, the use of hierarchical logistic regression models were considered and estimated. Given the nested structure of the data, multilevel modeling appears to be appropriate (Raudenbush & Bryk, 1999). However, there are three primary reasons why binary logistic regression was used over hierarchical logistical regression models.
First, the logistic models are primarily interested in individual-level
characteristics rather than equal attention paid to both individual-level and county-level predictors. As Austin, Tu, & Alter (2003) note, if this is a researchers’ objective, one may "safely ignore the hierarchical structure of the data." (p. 33). Second, in HLM, there are three types of interaction effects: between two level-1 predictors, between two level-2 (or 3) predicators, and cross-level interactions between level-1 and level-2. As Preacher, Curran, & Bauer (2006) note, the third HLM interaction tends to be the most common: the reason behind this being that interactions at level-1 run the risk of producing a poorly defined regression line at level-2. Given the theoretical component of focal concerns
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(e.g., blameworthiness), there are some interaction effects at the individual level that would this I would be remiss to ignore (e.g., race x no priors). Third, the results of the hierarchical logistic regression models did not vary significantly from the single level logistic models (see Appendix C for an example), and the ICC values produced suggest that: a.) most of the variance was found at level-1 and b.) to the second point, the reliability of the model may be questionable. As a result, traditional logistic regression models were used.
In this analysis, the plea decision was analyzed in three distinct models: 1.) with no interaction terms (Table 4.2 – Model I), 2.) with defendant based variables interacted with race (Table 4.3 – Model II), and 3.) with courtroom based variables interacted with race (Table 4.4 – Model III). Note that in these models, percentage likelihood was calculated using the “listcoef, percent” command in STATA following the computation of the logistic equations. The results are discussed below.
Beginning with Model I (no interaction terms), a number of important findings emerged. With regards to race, African American defendants were less likely (b = -.288, p < .05) to be offered a plea concession compared to their white counterparts. When examining offense types, those who were charged with criminal sexual conduct (b = - 1.126, p < .001) or robbery (b = -.893, p < .01) offenses were less likely to receive a plea concession. First time offenders were significantly much more likely to receive a plea concession (b = 1.026, p < .001); notably, first time offenders were 179% more likely to receive a plea concession, compared to those with one or more prior offenses.
Conversely, chronic offenders were significantly less likely to receive a plea concession (b = -.562, p < .05).
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Outside of defendant based variables, some variables relevant to the judge played a significant role in this model. When there was minority judges on the bench, defendants were significantly less likely to be offered a plea concession (b = -.451, p < .05). When there was a female presence on the bench (female judges), however, defendants were more likely to be offered a plea concession. Results of this model indicate a female bench presence (female judges) increased the likelihood of a concession by 107% (b = .730, p < .01).
Table 4.2: Logistic Regression: Plea Decision With no Interaction Terms.
Model I Variable b SE Exp(B) Plea Decision Race -.288 .143 .750* Sex -.161 .206 .435 Age .021 .083 .800 CSC -.1.126 .287 .324*** Major Assault -.245 .199 .783 Robbery -.893 .385 .410** Burglary -.235 .201 .488 No Priors 1.026 .167 2.790*** Chronic Offender -.562 .194 .570* Accomplices .248 .232 1.281
Minority Bench Presence -.451 .220 .637*
Female Bench Presence .730 .239 2.074**
Violent Crime Rate .002 .004 1.002
Concentrated Disadvantage .335 .133 1.398**
Percent Single Mothers -.094 .078 .910
Court Size .344 .267 .515
White-to-Black Income Ratio -.339 .288 .712
Constant .135
Nagelkerke R2 .139
Cox and Snell R2 .198
† p < .10. * p < .05. ** p < .01. *** p < .001
Among the county-level predictors, concentrated disadvantage was significant in this model and it was associated with the increased likelihood of being granted a plea
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concession. The concentrated disadvantage coefficient of .335 indicates that a unit
change in concentrated disadvantage would increase the expected number of granted plea concessions by 40%. The other county-level variables included in this model did not achieve significance. Overall, this model explained between .139 (Nagelkerke R2) and .198 (Cox and Snell R2) percent of the variance in whether or not plea concessions were granted.
Model II (Table 4.3) provides introduces race as an interaction term. To begin, all three of the interaction terms (race and concentrated disadvantage, race and no priors, race and percent single mothers) were significant. The interaction of race and
concentrated disadvantage significantly impacted whether a plea concession would be granted. In other words, a unit change in concentrated disadvantage for African American defendants increased the likelihood of a plea concession by 138%, holding all else
constant. The interaction of race and no priors was also significant in that plea concessions were more likely to be granted to African American defendants with no priors. However, the interaction of race and percentage of single mothers revealed a negative association with regards to plea concessions. For each unit change in the percent of single mothers, African American defendants were 9.3% times less likely to be granted a plea concession, a somewhat unexpected finding, given the results of the first model.
Among the offense-based variables, the findings were consistent with Model I, with the notable exception being that burglary now emerged as significant in this second model. Minority representation was again a significant predictor of a prosecution rather than a plea concession (b = -.656, p < .01).
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Table 4.3: Logistic Regression: Plea Decision With Defendant Interaction Terms.
Model II
Variable b SE Exp(B)
Plea Decision
Race x Concentrated Disadvantage .327 .153 1.387*
Sex -.262 .204 .770 Age -.200 .162 .819 CSC -.919 .277 .399** Major Assault .265 .198 .767 Robbery -.698 .197 .498*** Burglary -.908 .381 .403** Race x No Priors .689 .204 1.991** Chronic Offender -.208 .115 .425 Accomplices .315 .228 1.370
Minority Bench Presence -.656 .201 .568**
Female Bench Presence .665 .239 1.944**
Violent Crime Rate .003 .003 1.003
Race x Percent Single Mothers -.074 .021 .929***
Court Size -.271 .136 .763
White-to-Black Income Ratio .268 .280 1.307
Constant -.417
Nagelkerke R2 .174
Cox and Snell R2 .220
† p < .10. * p < .05. ** p < .01. *** p < .001
Female representation on the bench (female judges) was significantly associated with plea concessions (b = .665, p < .01). The likelihood of being granted a plea
concession increased by 94% when there was a female bench presence. No additional predictors achieved significance. This model, with interactions, explained approximately .174 (Nagelkerke R2) and .220 (Cox and Snell R2) percent of the variance.
Model III (Table 4.4) presents the results of the binary logistic regression with interaction terms for race and court context (race x female judges, race x minority judges, race x court size). Beginning with offender-level characteristics, males were significantly less likely to receive a plea concession in this model (b = -.723, p < .05). Consistent with
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the first two models, first time offenders were significantly more likely to be granted a plea concession. Findings of the model revealed that first time offenders were 181% more likely to be granted a plea concession, compared to those defendants with one or more prior offenses. Similarly, chronic offenders were less likely to be granted a plea concession (b = -.512, p < .05).
Table 4.4: Logistic Regression: Plea Decision With Courtroom Interaction Terms.
Model III Variable b SE Exp(B) Plea Decision Sex -.723 .322 .485* Age -.187 .207 .829 CSC -1.145 .288 .318*** Major Assault -.300 .201 .741 Robbery -.890 .387 .412** Burglary -.677 .201 .508** No Priors 1.034 .168 2.812*** Chronic Offender -.512 .223 .599* Accomplices .242 .232 1.274
Race x Minority Bench Presence -.361 .262 .697
Race x Female Bench Presence .787 .315 2.197*
Violent Crime Rate .002 .004 1.002
Concentrated Disadvantage .291 .115 1.398†
Percent Single Mothers .365 .138 1.440**
Race x Court Size -.029 .246 .971†
White-to-Black Income Ratio. -.396 .282 .673
Constant -.417
Nagelkerke R2 .185
Cox and Snell R2 .227
† p < .10. * p < .05. ** p < .01. *** p < .001
Criminal sexual conduct (b = =.1.145, p < .001), robbery (b = -.890, p < .01), and burglary (b = -.677, p < .01) were all significantly related to prosecution rather than a plea concession, while major assault was insignificant in either direction. Outside of these
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findings, there was only one significant interaction term (race x female bench presence). A female bench presence was significantly associated with plea concessions. In fact, the interaction of race with female bench presence improved the likelihood of a plea
concession by 120%. No other interaction terms were significant in either direction. Finally, the “percent single mothers” variable was significant in this model. Importantly, the analysis showed that percent single mothers increased the likelihood of receiving a plea concession (b = .365, p < .01) by 44%. Overall, Model III explained approximately .185 (Nagelkerke R2) and .227 (Cox and Snell R2) of the variance.
Compared to the other models, it explained more of the variance than Model I, but less of the variance compared to Model II.