Policymakers, practitioners, and academics have long brought attention to unjustified variations in criminal justice outcomes. M Cassia Spohn, C
Nevertheless, there is much still to be learned. Serious gaps exist in the empirical legal studies literature regarding certain sentencing practices. The modal approaches to sentencing research is to focus on the in/out decision (i.e., whether the penalty requires any time of imprisonment) and sentence length. Travis W. Franklin et al.,
This Article contributes to the literature by producing an empirical study focusing on sentences that constitute upward departures from sentencing guidelines. In particular, federal sentencing is a guidelines-based system, with upward departures issued at the discretion of district judges. Decisions to depart upward are uniquely remarkable because they obviously lead to lengthier prison terms, may represent gaps in the guidelines, and may signify disparities—potentially discrimination—in sentencing decisions. The federal system is worthy of analysis as it often acts as a role model for criminal justice practices, it operates the largest prison system in the country in terms of the number of inmates held, and it represents sentencing decisions across the country.
To date, no research appears to have discretely concentrated on upward departure decisions in federal sentencing. The results presented herein are meant to address this void. This study takes advantage of multilevel modeling as the empirical methodology, which constitutes a more sophisticated model of statistical analysis than is used in most criminal justice research. Most studies rely upon single-level regression models. Jose Pina-Sánchez & Robin Linacre, Rob Tillyer & Richard Hartley,
The Article proceeds as follows. Section II outlines the federal sentencing guidelines system. It then turns to upward departures specifically to contextualize the many reasons they represent extraordinary decision points worthy of scrutiny. Section III reviews contested issues concerning whether disparities are ever warranted and specifically addresses the challenge of regional disparities. Two theoretical views on disparities are relevant. The focal concerns perspective demonstrates that individual penalties tend to be based on perceptions of the defendant’s culpability, the defendant’s risk of recidivism, and the practical consequences of the potential punishment. In turn, the courtroom communities’ perspective indicates that judges and practitioners in courtroom workgroups develop their own unique traditions and routines, which can explain some variations between courts in sentencing outcomes. Next, a literature review summarizes the results of prior empirical research on federal sentencing practices. The preexisting research was informative to building the statistical models presented herein.
Section IV sets forth an original empirical study of upward departure decisions. The data and variables are explained and the results from the multilevel models on upward departures are provided. In sum, the results demonstrate a statistically significant variance between district courts on upward departure outcomes. In a full model, a host of legal factors (e.g., final offense level, criminal history, offense type), extralegal characteristics (e.g., gender, race/ethnicity, citizenship), and case-processing variables (e.g., custody status) are predictive of upward departure outcomes in individual cases. Yet the influence of most of them varies across district courts, suggesting regional disparities in outcomes. The implications of the findings regarding factors correlated with individual outcomes and regional disparities are discussed in more detail. The results also substantively support the focal concerns and courtroom communities’ perspectives. A methodological Appendix attached hereto further demonstrates the empirical benefits of a multilevel regression modeling approach and describes foundational decisions underlying the final results reported in the main text.
This Article reports an original study using a sophisticated empirical modeling strategy to explore decisionmaking in criminal penalties. More specifically, the study is of discretionary upward departure outcomes in the federal sentencing system. A focus on criminal justice research specifically at the federal level is meaningful for several key reasons. In contemporary times, federal authorities act as a role model in the administration of justice.
[The federal government] provides resources, collects and develops best practices, and serves as the communicator and facilitator of these best practices throughout the country. . . . Because state, local, and tribal governments are limited by the need to devote resources to solving problems unique and endemic to their particular jurisdictions, the [f]ederal government plays [an] explicit role[] in advancing public policy to respond to gathering threats. N
Congress itself is often perceived as a leader in setting the criminal justice policy agenda for the country. Jerold Israel, John F. Pfaff,
Still, the federal guidelines are known for their extraordinary complexity James C. Oleson et al., Paul J. Hofer et al., Ben Grunwald, Douglas A. Berman,
There is another significant way that the federal system has influence on the evolution of criminal justice responses in the country. In part due to what some critics perceive as overcriminalization in Congress’ enactment of scores of new federal criminal laws over the last few decades, Rachel E. Barkow, N U.S. S
To situate the context of this study on upward departure decisions, a brief summary of the federal guidelines system is offered. Then the discussion outlines the case for why upward departures are noteworthy discretionary decisions that offer a valuable subject for research.
At the turn of the twentieth century, the federal sentencing system represented an indeterminate structure that awarded federal district judges broad discretion to determine criminal penalties in individual cases. Ilene H. Nagel, Kate Stith & Steve Y. Koh, Michael Tonry,
Congress was at the forefront of the country’s reform movement in the latter part of the twentieth century by adopting legislation which mandated more regimented sentencing practices. The Sentencing Reform Act of 1984 created a presumptive sentencing system to be engineered under the auspices of a newly formed United States Sentencing Commission (the “Commission” or “Sentencing Commission”). Sentencing Reform Act of 1984, Pub. L. No. 98-473, §§ 211-300, 98 Stat. 1837, 19872040. Frank H. Easterbrook,
An unforeseen and significant development recast how the Guidelines were to operate. Despite Congress’ intent for a presumptive Guidelines system, the United States Supreme Court rendered the Guidelines advisory in nature. In the seminal case of The Court ruled that such judicial factfinding violated the Sixth Amendment. 543 U.S. 220, 245 (2005). 543 U.S. at 249.
The Peugh v. United States, 186 L. Ed. 2d 84, 95 (2013).
At their heart, the Guidelines provide for a series of calculations in order to determine the defendant’s offense severity level and criminal history score. With these two numbers in hand, the district judge consults a single Guidelines grid to obtain the recommended prison sentence. U.S. S These are substantial assistance to authorities in investigating another potential offender (§ 5K1.1) and fast-track departures as a docket-clearing option (§ 5K3.1).
The Guidelines expressly provide for several types of upward departures, all of which are discretionary to the judge and do not require the prosecutor’s request. Technically, there are two types of upwardly varying sentences in the federal system. A “departure” is a term used in the Guidelines which refers to a sentence outside the recommended range from the sentencing grid but permitted by the Guidelines rules. United States v. Jeffers, 2015 U.S. Dist. LEXIS 132055, at *21-22 (N.D. Iowa 2015). A “variance” is a non-Guidelines sentence invoked to achieve statutory sentencing goals. U.S. S
Per the statutory framework and Guidelines policy, a judge may also depart for reasons not included in the Guidelines if “there exists an aggravating or mitigating circumstance of a kind, or to a degree, not adequately taken into consideration by the Sentencing Commission in formulating the Guidelines.” 18 U.S.C. § 3553(b) (2000); U.S. S Kimbrough v. United States, 552 U.S. 85, 108-11 (2007). U.S. S
In the end, a district judge in the individual case must determine a penalty that is reasonable and parsimonious, one that comprises “a sentence sufficient, but not greater than necessary.” 18 U.S.C. § 3553(a). The legislation specifies that district judges consider the following factors in determining a reasonable sentence in the individual case: (a) the recommended punishment range set by the sentencing guidelines and the Commission’s policy statements; (b) the nature and circumstances of the offense; (c) the history and characteristics of the defendant; (d) the need for the sentence imposed considering the seriousness of the offense, retribution, deterrence, protecting the public, and the offender’s rehabilitative needs; and (e) the need to avoid unwarranted sentencing disparities among similarly-situated offenders. Gall v. United States, 552 U.S. 38, 50 (2007).
The existence of greater discretion afforded by W
It is curious that there appear to be no other empirical studies comprehensively concentrating on upward departures in the federal system. Departures upward are extraordinary and consequential decisions for many reasons. First, an upward departure obviously is meant to increase the severity of the penalty. Prior studies in federal sentencing confirm such a result, and they demonstrate that the consequences are significant. Regression studies have found that the decision to upwardly depart multiplied the odds of a sentence involving incarceration by as much as 12 times compared to a sentence without an upward departure. Brian D. Johnson & Sara Betsinger, Tillyer & Hartley,
Second, to the extent that upward departures naturally leads to a greater number of defendants being incarcerated and for longer periods, these decisions worsen the federal system’s prison overpopulation problem. Since 1980, the federal prison population has grown 750%. S K
Third, upward departures uniquely signal that judges may be finding gaps in Guidelines policies and calculations, despite the Commission’s now decades of experience with studying sentencing practices and making relevant policy adjustments as needed. When a judge determines whether to depart upward from the Guidelines recommendation, it likely represents a compromise between uniformity and proportionality. Whereas downward departures are often for reasons other than proportionality concerns (for example, the repeated use of fast-track departures and substantial assistance departures are mainly for efficient case-processing purposes), upward departures are more attuned to calibrating the penalty to the defendant’s culpability and harm. Upward departures are even more surprising as many judges, practitioners, and researchers already assess the Guidelines as producing excessively harsh sentence recommendations as a general rule. Byungbae Kim et al.,
Fourth, because upward departures are relatively rare, it is therefore even more symbolic when one is issued in an individual case. Upward departures occur in three percent of cases. Data obtained from the Commission’s annual sourcebooks
An upward departure is also a particularly risky choice. In part because of its rarity and in part because of the substantive due process rights afforded criminal defendants, an upward departure practically invites the defendant to appeal. On review, the upward departure decision may well be overturned, particularly if the appellate court finds that the district judge did not provide sufficient reasons for the higher sentence.
Fifth, upward departures are surprising, too, as they violate the premise underlying the cognitive bias of anchoring. Silvio Aldrovandia et al., Jeffrey J. Rachlinski et al., Bettina von Helversen & Jörg Rieskamp,
Sixth, it is widely recognized that departure decisions as a general rule (upward and downward) are significant, if not primary, sources of perceived disparities in sentencing. Jawjeong Wu & Cassia Spohn, Michael S. Gelacak et al., Jeffery T. Ulmer et al.,
This suggested relationship between upward departures and discretion is highlighted by the likely impact of the Data analyses done by author using the Commission’s data files from fiscal years 1999-2015 and the Commission’s annual Sourcebooks for fiscal years 1989-2015. U.S. Sentencing Commission, 2015 Sourcebook tbl. N; 2008 Sourcebook tbl. N; 2006 Sourcebook tbl. N. Results from the author’s frequency distribution analysis run of the Commission’s datasets. The conclusion is derived from the Commission’s annual Sourcebooks from fiscal years 2008-2015.
Thus far, it has been argued that upward departures in federal sentencing are worthy of further analysis. The study was also led by relevant normative and theoretical foundations and informed by the results of previous studies.
The issue of disparities in sentencing practices is not a simple concept and not all agree on either whether it is necessarily a bad result. Challenges presented by potential disparities in penalties are discussed next. Then the Section reviews two major theoretical viewpoints relevant to the research herein, which are referred to as the focal concerns perspective and the courtroom workgroup perspective. Following that is a concise empirical literature review of relevant studies of federal sentencing practices.
The Sentencing Commission clearly values national uniformity in case-processing and outcomes. U.S. S Stephanos Bibas, R Ulmer & Light,
The Commission is not the only institution that works to normalize federal sentencing practices across judicial districts. The U.S. Department of Justice and the Federal Judicial Center are also centralized authorities providing educational opportunities to socialize judges into the federal government’s sentencing policies. Jeffery T. Ulmer, For a glimpse into the various instructional offerings, see the Commission’s training website: U.S. S
Though not all stakeholders would concur, it is not always clear what disparity means and whether it is necessarily a bad thing. According to Black’s Law Dictionary, disparity means “inequality” and “a difference in quantity or quality between two or more things.” B
When observers discuss disparity in sentencing outcomes, it is often based on identifying like individuals who commit like offenses. R
In any event, the Guidelines—despite U.S. S U.S. S Mandeep K. Dhami et al., F
The posited problems with disparities are particularly acute when judges base sentences on extralegal factors that the Guidelines were intended to more proactively forbid. J.C. Oleson, Pina-Sánchez & Linacre, Nutting, Bibas,
Nonetheless, it is still reasonable to acknowledge that not all variances from Guidelines recommendations constitute disparities, particularly in the negative sense of the term. Prior statisticians reviewing federal sentencing data rightly observe that a non-Guidelines-compliant sentence is not necessarily illegal considering the discretion that judges now lawfully maintain to deviate per Booker. R Rosemary Barkett, Michael S. Gelacak et al.,
There may well be something extraordinary in a particular case where a judge’s discretionary ability could work to better serve justice for all parties. Paul J. Hofer, United States v. Booker Amy Baron-Evans & Kate Stith, Booker Stuart S. Nagel,
In the end, this paper does not take the concrete position that even sophisticated statistical analyses of sentencing outcomes can prove that every upward departure represents disparity, at least to the extent the term holds a negative connotation, much less a discriminatory decision. Nor does the paper assign condemnatory blame to district judges for differences in sentencing for seemingly comparable offenses or offenders. As with any study of human behavior, no dataset can possibly account for all aspects of criminal conduct or of decisionmaking. Thus, different judges may sentence seemingly similar offenders to incomparable punishments for legitimate reasons that are simply not captured in the data.
Further, the source of any unwarranted disparity may arise from other actors anyway, such as based on the (legitimate or illegitimate) practices and decisions of other actors in the criminal justice process chain. Besiki L. Kutateladze et al., R F Douglas A. Berman,
Despite the choice not to assume all differences in outcomes establish unwarranted disparities, the observation that “some R
Another disparity matter needs to be addressed considering the study contained herein will focus on it: regional variations in sentencing outcomes. The issue here is where sentencing outcomes may be uniformly meted out within a region but vary from those in other regions. Regional disparities are viewed by some observers in unfavorable terms. The Sentencing Commission officially asserts that the federal Guidelines were meant to control local variations in sentencing practices, such that consistent practices were intended to be enforced nationwide when prosecuting federal crimes. F Paula M. Kautt,
Before reviewing potential sources of regional differences in federal sentencing outcomes, two limitations in the study’s design should be noted here. Federal district courts are comprised of more than one district judge.
There exist several potential sources of local variations in federal sentencing outcomes. One is that even though federal criminal law provides a single body of statutes covering the country equally, This reference excludes criminal laws solely focused on the District of Columbia, native American lands, and federal property. Bibas,
Another possibility for regional variations is if there is local hostility to a national policy concerning a particular crime or the Commission’s assessment of the severity of a crime. Observers may debate the propriety of a district judge’s ability to void a centralized policy. Such a rationale may be viewed reasonably in culturally sensitive terms to accommodate local priorities or, instead, as an inappropriate usurpation of the lawful powers of federal policymakers to make national policy decisions.
Other regional variations amongst federal courts in sentencing may be more or less benign, simply reflecting localized socialization in what are called courtroom workgroups. A cultural consensus unique to a courtroom workgroup may mean consistency in sentencing within that workgroup, but whose outcomes are uncorrelated (i.e., disparate) with outcomes generated by other courtrooms. This idea will be discussed further in the next Section that addresses two main theoretical foundations for between-court differences in criminal justice outcomes: the focal concerns perspective and the consequences of culturalized practices through the development of courtroom communities. For now, it is simply noted that the Sentencing Commission avers that regional variation in sentencing outcomes due to differing political climates or court cultures constitutes unwarranted disparity. F
The focal concerns perspective is now a popular theoretical framework for understanding sentencing outcomes. Kutateladze et al., Jeffery T. Ulmer, James Eisenstein, & Brian D. Johnson,
The Guidelines certainly address the focal concerns in their formalized rules regarding assessments of blameworthiness (e.g., offense level representing severity, offense type), future dangerousness (e.g., criminal history, acceptance of responsibility), and consequences of the penalty (e.g., substantial assistance reductions to conserve prosecutorial resources, fast-track departures to permit more efficient case processing). Yet, considering human nature cannot always be entirely automated and the potential for highly-educated and experienced federal judges to believe in their own qualities of judgment, the Guidelines likely do not entirely constrain discretion in considering the focal concerns.
Upward departures may rely more heavily on discretionary thought in that judges issuing them may be considering ideals or values not explicitly contained in the Guidelines rules. In addition, departure decisions beyond those expressed in the Guidelines presumably represent gaps in their set of rules. Thus, it is expected from the focal concerns perspective that there will be disparities in upward departure outcomes because of differences in judges’ situational assessment of the focal concerns in individual cases, the extent of their agreement with the Guidelines-driven proportionality judgment, and their relative concern about the practical consequences of the sentence.
The second theoretical perspective popular in sentencing research regards community courtroom cultures. “Court communities are distinct, localized social worlds with their own relationship networks, organizational culture, political arrangements, and the like. These localized social worlds, with their organizational cultures and political realities, shape formal and informal case processing and sentencing norms.” Jeffery T. Ulmer & Mindy S. Bradley, Robert R. Weidner et al., Ulmer & Bradley, Brian D. Johnson & Stephanie M. Dipietro,
Empirical researchers tend to assume there exists little interdistrict variation in the federal system, specifically, because of the uniform set of laws and policies provided by federal statutes and the sentencing Guidelines. Wu & Spohn, Johnson et al.,
We view the federal district court system not as a singular national legal structure with hierarchically arranged and geographically dispersed subunits, but rather as a semi-autonomous set of systems governed by the same formal rules, states, and procedural policies, while also embedded in localized legal cultures that are themselves shaped by regionally specific historical contingencies and norms. Mona Lynch & Marisa Omori,
Even though federal district courts operate at the national level, the practitioners within them are often plucked from their own locales. Idiosyncratic local practices within district court communities can impact federal sentencing as judges and prosecutors are often chosen from within the state in which the district court resides; plus, defense counsel and probation staff tend to have previously resided in or near the districts in which they become employed. Michael Tonry, F
Criminologists have aptly recognized that “offenders are sanctioned partially for what they have done (offense characteristics, criminal history), for who they are (race/ethnicity, age, gender) and also for what they may fail to do during the punishment process (plead guilty or express remorse).” Ronald S. Everett & Roger A. Wotkiewicz,
As for legal factors, prior research has confirmed that primary predictors of federal sentencing outcomes are offense seriousness, criminal history, Feldmeyer & Ulmer,
Much research has found that demographic characteristics, which are generally considered to be extralegal factors for punishment purposes, are still correlated with sentence length. As for race and ethnicity, multiple studies of federal sentencing show that whites receive sentences of shorter length than blacks Kim et al., Cyndy Caravelis et al.,
Studies of sentencing rather consistently indicate that males are sentenced to longer periods of incarceration. S. Fernando Rodriguez et al.,
In some studies, noncitizens are at a statistically significant greater likelihood of incarceration Michael T. Light, Light, scott E. Wolfe et al.,
Studies commonly indicate that older offenders are treated more leniently than their younger counterparts. Burrow & Koons-Witt, Franklin,
Two case-processing factors are relevant to predicting sentencing decisions. The so-called trial penalty occurs when being found guilty at trial (rather than plead) is correlated with more serious punishments. Michael M. O’Hear, Ulmer et al.,
As for the second case-processing factor, studies at the state and federal levels rather consistently show that pretrial detention is significantly and positively related to incarceration and sentence length. Oleson et al.,
Studies which include district or circuit variables in their models have generally found geographic disparity in federal sentences.
A significant majority of the foregoing studies on federal sentencing use the incarceration decision (in/out) and/or sentence length as their outcome of interest. Some researchers affirmatively, though, recognize the importance of investigating departure decisions. Almost all of the studies of federal departure decisions to date which model the dependent variable on departure outcomes address downward departures. U.S. S
This is curiously true, despite upward departures arguably being more substantial, such as leading to longer sentences in the face of the federal prison overpopulation. Plus, their relative rarity renders upward departures more symbolic in nature, perhaps perceived therefore as arbitrary. Almost all the studies to date which consider the upward departure decision as a variable at all simply add it as a control without further discussion of its significance because their interests concerned other aspects of sentencing.
It appears that only three studies (two of them by the same author) have so far utilized the upward departure decision as an outcome variable. Nevertheless, in these trio of studies the upward departure decision was one of multiple outcomes in single-level regressions and the authors did not spend too much space delving into the upward departure’s importance in federal sentencing outcomes. Crystal S. Yang, Mustard, Yang, Yang, Yang, Yang,
Due to the paucity of research with a concentration on the upward departure decision, the importance of it in the results of sentencing outcomes in terms of severity of sentence, and the symbolic nature of the discretionary decision with respect to potentially reflecting gaps in the Guidelines, the opportunity to fill the void was compelling. Then the recent availability of more aggressive computing resources to permit employing a sophisticated research design known as multilevel modeling would allow this study to also be able to test for possible regional disparities. Hence, the next Section offers such a study.
The most common type of advanced statistical analysis of sentencing outcomes is a single-level regression model with individual predictors. Cassia Spohn, R Paul Hofer,
Sentencing research now seems on the precipice to replacing single-level regressions with the more sophisticated technique of multilevel modeling.
The concept of multilevel modeling is a relatively recent development in the field of statistics. A Brian D. Johnson & Christina D. Stewart, Daniel A. Powers,
In discussing multilevel models, the terminology typically entails levels, usually in a linear fashion to signify the nesting structure. Level-1 is the most elemental. Level-1 units are clustered at Level-2. Three-level models involve Level-2 clusters that are nested into a higher order. For instance, as visually represented in Figure 1, federal sentencing entails a hierarchical structure in which individual defendants represent Level-1 units, with district courts at Level-2, and circuit courts representing Level-3.
Multilevel methods permit the researcher to specify an explanatory variable as a fixed effect, a random effect, or both. A fixed effect variable specifies a single value in the model and is applicable to each Level-1 unit, regardless of which Level-2 group the unit is situated. Andrew F. Hayes,
A random effect, on the other hand, allows an explanatory variable to vary between Level-2 units such that each Level-2 group has its own estimate of that variable. Tom A.B. Snijders,
A random effect coefficient for a predictor variable that is statistically significant, for purposes of the study herein, indicates that (a) the magnitude (i.e., strength) of the effect of the variable is weaker in some districts but stronger in other districts, and possibly (b) that the effect of that variable changes direction across districts units from positive to negative, or vice versa. John Wooldredge,
A multilevel study that includes both fixed and random effects is generally referred to as a mixed model. One of the strengths of specifying multilevel modeling is the ability to test whether a particular explanatory variable may have different effects at each level. An explanatory variable may be statistically signifi cant at Level-1 (the fi xed effect) and may—or may not—show statistical signifi cance at Level-2 (the random effect), or vice versa. Multilevel modeling can thereby overcome aggregation bias that exists when an explanatory variable shows different results at different levels. B
Overall, multilevel modeling presents an advancement for statistical research in criminal justice. In regards to penalty outcomes, it is particularly important to focus on both (a) individual level predictors because of the focal concerns perspective, and (b) on jurisdictional level variations because there may be relevant contextual differences stemming from unique cultural characteristics or peculiarities produced through discrete courtroom community practices. Gaylene S. Armstrong & Nancy Rodriguez,
Despite the many advantages of multilevel modeling techniques, relatively few multilevel studies have been conducted in federal sentencing. This does not mean that many other researchers have not been cognizant of the potential that geographical and jurisdictional differences may have significant impacts on individual sentencing outcomes. Typically, researchers realizing the potential for regional differences in federal sentencing simply control for these group-level variances in single-level regression models by adding districts
The rather scant number of studies which do apply a better specified model from a methodological perspective by adapting multilevel modeling to federal sentencing data have tended to focus on sentence length as the outcome of interest. Ulmer et al., Tillyer & Hartley,
This study used Commission datasets for the fiscal years 2008-2015 to represent a long period of sentencing practices and to account for post- C
There are three main research questions:
Is there significant variation across district courts in the use of upward departures?
To what extent do legal, extralegal, and case-processing factors account for upward departures in individual cases?
Do district courts vary from each other in the extent to which they weigh each of the legal, extralegal, and case-processing factors when issuing upward departures?
In the multilevel design, the outcome (dependent) variable is whether the judge issued a sentence that was an upward departure from the Guidelines recommendation. This outcome and a list of the multiple predictor variables (comprising legal, extralegal, and case-processing factors) which survived to the final multilevel model and their coding are summarized in Table 1.
Coding Scheme of Variables.Variable Coding Scheme Description Upward Departure 1 = yes Defendant received an upward departure Final Offense Level Scale Guidelines scale rating offense severity from 1-43 Criminal History Ordinal Guidelines ranking of criminal history from I-VI Number of Counts Log (scale) Natural log of the number of counts of conviction General Offense Type Five dummy variables Five dummy indicators with the reference category of drug offenses Acceptance of Responsibility 1 = yes Dummy indicator for having received a reduction in offense levels for accepting responsibility Male 1 = male Dummy indicator for gender Minority 1 = minority Dummy indicator for black, Hispanic, or other together coded as 1, with the reference category white U.S. Citizen 1 = citizen Dummy indicator for a U.S. citizen Age Over 50 1 = yes Dummy indicator for age 50 and above In Custody 1 = yes Dummy indicator for being in custody at time of sentencing Trial 1 = yes Dummy indicator for going to trial (versus a plea) Nominal 94 districts
In addition to the multilevel models, a statistical analysis was conducted concerning just the upward departure cases. Commission rules direct district judges when departing from the Guidelines to state the reasons for the departure and to specifically record them in the Commission-generated Statement of Reasons form that is submitted with the paperwork for each individual sentencing. U.S. S
The research questions posed earlier indicated a two-level design with district courts at Level-2. Descriptive statistics regarding the variables that survived to the resulting full model are provided in Table 2.
Descriptive Statistics.Upward Departure (2.0%) Final Offense Level 18.72 Criminal History 2.48 Number of Counts 1.42 General Offense Type Drugs (33.0%) Violent (5.9%) Firearms (10.6%) Immigration (29.9%) Property (16.5%) Other (14.0%) Acceptance of Responsibility (94.8%) Female (12.8%) Minority (73.5%) U.S. Citizen (58.7%) Age Over 50 (12.5%) In Custody (75.3%) Trial (3.5%)
Separate statistical analyses of Commission datasets (fiscal 2008-2015) indicated that an upward departure is typically of significant consequence to the receiving defendant’s sentence: the mean sentence for those defendants receiving an upward departure for the period of study was 84.44 months (about 7 years), with a range from probation to 4,253 months (about 354 years). The reader may wonder if the 354 year figure is a typographical error or a data error. It is not. This extreme sentence was handed to Corey Deyon Duffey in 2010 for a series of bank robberies. Two of Duffey’s co-defendants received similar sentences of 355 and 330 years. Perhaps not surprisingly, the district that sentenced them to these extreme sentences was the Northern District of Texas, the same district that has the highest rate of upward departures in the study period (2008-2015). For more information on the use of extreme sentences such as Duffey’s, see generally Hamilton,
The final multilevel model included 567,294 cases and is provided in Table 3. Eleven percent of the potential cases were excluded because of missing data on any one of the final predictor factors. There is no reason to believe the missing cases represent any bias.
Full Multilevel Model of Upward Departures.S.E. Odds Ratio S.E. Intercept -5.021 .152 ----- .064 .051 Final Offense Level -.072 .004 931 .001 .000 Criminal History .057 .013 1 059 009 .002 Number of Counts (log) .315 .018 1.370 .009 .003 General Offense Type --- --- Drugs (reference) Violent 1.576 .116 4.838 Firearms .694 .094 2.001 Immigration .199 .106 1.221 Property .532 .096 1.702 Other .503 .116 1.653 Acc. of Responsibility -.728 .070 .483 .045 .018 Female -.559 .047 572 .018 .014 Minority .045 .044 1.046 .035 .010 U.S. Citizen .509 .066 1.664 148 .031 Age Over 50 .311 .031 1.364 .010 .006 In Custody 1.403 .055 4.066 055 .016 Trial -.100 .084 .905 .063 .027 Random intercept .064 .051 ρ 1.9% -2LL = 4149605
The final model includes a substantial portion of the explanations for upward departures. Overall, the model poses a 98% correct classification rate. This section textually delineates the substantive results, with further discussion to follow in the next Section to explore how the theoretical background regarding focal concerns and the community workgroup thesis may help explain these results.
The results for the fixed effects (i.e., individual defendant predictors) will be addressed first. All of the legal factors achieved statistical significance in their individual effects on upward departures. The final offense level was negatively associated with the odds of an upward departure: the odds of an upward departure decreased 7% for every one level increase in the final offense level. The criminal history score had the opposite effect in being positively associated with an upward departure: the odds of an upward departure increased 6% for each one unit increase in criminal history category. The presence of multiple counts of conviction were associated with increased odds of an upward departure. Regarding crime type, compared to drug offenders as the reference category, the other offense types were more likely to receive upward departures. Violent offenders faced almost five times the odds of an upward departure while the odds for firearm offenders doubled. Only immigration offenses did not result in statistical significance. Acceptance of responsibility lowered the odds of an upward departure by a factor of two. As the coefficient is less than 1.00, we can interpret the effect on the odds by taking the reciprocal of the odds ratio = 1/.483.
Demographic variables were also modeled as fixed effects. Females were significantly less likely to receive upward departures than males, even after controlling for multiple factors: an upward departure for males was almost two times the odds as for females. U.S. citizens were more likely to be assigned upward departures, with the odds of citizens receiving upward departures being 66% greater as compared to noncitizens. There was also an age effect, with those age 50 and over being more likely to receive an upward departure compared to their younger counterparts.
Minorities were at higher risk of upward departures. The odds of a minority defendant receiving an upward departure increased 5% when controlling for the other legal and nonlegal variables. However, the result at the individual case level (Level-1) for the minority variable was not statistically significant. Still, as will be addressed further below, the minority factor was retained as there was a statistically significant random effect (districts at Level-2) for it, indicating that the lack of significance at the individual case level does not mean there is not a minority effect on increasing the odds of an upward departure in at least some districts.
Both case-processing factors were statistically significant. Custody status exhibited a large effect, increasing the odds of an upward departure by a factor of four for those in custody at sentencing. The trial penalty was not statistically significant at the individual level. However, the trial versus plea factor was retained because, as also addressed below, the random effect coefficient for the trial penalty at the district level indicated statistical significance, signifying that there are trial penalties in at least some districts.
The random effects (i.e., variations among districts) of the variables in the far right columns of Table 3 indicate whether the effect of each predictor varied across districts (except offense type which was excluded for statistical reasons per the Appendix). All but two of the predictor factors with random effects (being gender and age over 50) were found to vary across districts to a statistically significant degree.
Further information on the variability of each predictor factor that was modeled with fixed and random effects can be provided. Computations adding and subtracting one and two standard deviations indicated by each predictor variable’s random effect from the same variable’s fixed effect coefficient show whether the variability between districts concerns the strength of the correlation with the outcome and if the direction of the correction is positive in some districts yet negative in others.
For six of the random effects, the size of the effect across two standard deviations varied between districts (i.e., across 95% of the districts), but not the direction. The number of counts of conviction, age over 50, and being in custody at sentencing were each positively correlated with upward departures in at least 95% of districts. The final offense level, acceptance of responsibility, and being female were negative predictors of upward departures in at least 95% of districts.
In contrast, the effect of each of criminal history score, minority status, and trial penalty showed that the strength and the direction of its influence changed across just one standard deviation (i.e., two-thirds of districts). This means that not only the size of the effect of these three variables varied amongst districts but that each held a positive effect in at least some districts while indicating a negative impact in others. U.S. citizenship held a positive association with upward departures in one standard deviation, but across two standard deviations the effect was observed to be negative in at least a few districts.
A supplemental data analysis provides further information about the reasons for upward departure decisions derived from the judges’ Statement of Reasons forms filed with sentencing paperwork in individual cases. Table 4 contains the top ten cited reasons for upward departures capture through frequency analyses of the Commission’s data, along with their prevalence.
Specific Reasons Given by Judges for Upward Departures1 Criminal history issues 60.0% 2 Nature and circumstances of the offense and history and character of the defendant 53.5% 3 Reflect the seriousness of the offense, promote respect for the law, and provide just punishment 49.9% 4 Deterrence 42.6% 5 Protect the public from further crimes of the defendant 40.9% 6 Rehabilitation 9.3% 7 Avoid unwarranted disparities 8.0% 8 Dismissed and acquitted conduct 8.4% 9 General adequacy issue 5.5% 10 General guideline issue 4.4%
Importantly, considering the title of this Article, unwarranted disparities in upward departures as an external consequence was among the top ten rationales as observed in Table 4. Judges cited disparity issues in one out of twelve upward departure decisions. This result indicates that numerous judges remain cognizant of the potential downsides of the appearance of disparities in sentencing practices. It is also suggestive of gaps in the Guidelines to the extent these judges perceive that the Guidelines calculations in the instant cases failed to achieve proportionality with sentences for similarly-situated defendants. The other reasons judges gave as indicated in Table 4 as justifications for upward departures will be explored further in the context of the general discussion of the results that follows.
The results just provided can now be more fully addressed concerning the three research questions previously posed. Further, they can be better understood in the context of the theoretical perspectives offered implicating the focal concerns perspective and the courtroom workgroup thesis.
The first research question queried whether there existed significant variation between district courts in the use of upward departures. The answer is in the affirmative. Bivariate results that were the result of additional statistical analyses indicated a differential of twelve times the rate of upward departures between the lowest rate district and the highest. Significant variation was confirmed in a null multilevel model (see the Appendix) which indicated that 8% of the total variance in upward departure outcomes is explained at the district court level. This rate was statistically significant at the .001 level. In other words, this means that eight percent of the differences in upward departure decisions are accounted for by district court practices. This result of district differences was expected from the courtroom workgroup perspective in that cultures unique to certain districts may influence sentencing outcomes that contrast with outcomes from other cultures/ districts.
The second general research question asked to what extent legal, extralegal, and case-processing factors accounted for upward departures in individual cases. Generally the results support the influence of the focal concerns (concerning the defendant’s culpability and future risk and the consequences of the sentence) on individual outcomes with respect to upward departures.
The legal variables supported the focal concerns expectation that perceptions of the defendant’s blameworthiness are highly relevant to individual penalties. The results indicated an increased likelihood of an upward departure for a higher criminal history score, multiple counts of conviction, and violent and firearms offenses (compared to drug offenders). Criminal history and additional counts signify multiple crimes and perhaps perpetrated on multiple occasions, possibly demonstrating greater culpability and harm. The increased odds for violent and firearms offenses reveal culpability concerns in that crimes posing a risk to human life likely are considered more egregious than many nonviolent offences.
The decreased likelihood of an upward departure for acceptance of responsibility is also consistent with a concern for the defendant’s blameworthiness as well as with the focal concern of future risk. Accepting responsibility by admitting guilt at an early stage in the proceeding may be perceived to reduce one’s culpability while predicting positive rehabilitation potential. The negative correlation of acceptance of responsibility with upward departures was consistent across at least 95% of districts.
Curiously, the final offense level was negatively correlated with the upward departure decision. This result seems to be somewhat contradictory to the focal concern with greater offender culpability predicting more severe sentences. It may instead, then, suggest that in these cases judges find the Guidelines calculations to be more than sufficiently proportional to reasonable sentences as adjudging offense severity. This explanation is likely because stakeholders tend to find Guidelines recommendations are overly punitive as a general rule.
Further discussion of criminal history is warranted as it played a strong role throughout the results. There were multiple indications that judges perceive inadequacies in the criminal history calculations. As previously indicated, a higher Guidelines-calculated criminal history score increased the odds of an upward departure despite multiple controls. This result implies that judges in these cases do not believe the criminal history calculation is sufficiently proportional to prior offending evidence, at least when the defendant already has a substantial criminal history as officially calculated pursuant to Guidelines rules. This observation is buttressed by the reasons judges listed in explaining upward departures. In the list of rationales judges gave for upward departures from the frequency distributions provided in Table 4, the role of criminal background is salient. Criminal history calculation issues were expressly cited in 60% of the cases, earning the top ranked reason overall for upward departures. Relatedly, as a separately coded reason, evidence of dismissed and acquitted conduct was listed as an explanation for upwardly departing in 8% of upward departures. Further, past offending may be part of the second ranked reason, which includes the history and character of the defendant, cited in over half of the upward departures. Because of the broad nature of that particular reason as including the nature and circumstances of the offense, though, it is difficult to parse what portion of the fifty percent was for prior offending specifically. Still, the failure of the formal criminal history calculation to adequately account for prior offending was evident in a significant majority of upward departures. It is of particular note that judges candidly admitted the role of dismissed and acquitted conduct in their decisions to upwardly depart in one out of 12 (8%) cases. This finding might be of concern to critics of the real offense system in which individuals are penalized for conduct that is not the subject of conviction. Critics may be even more offended by increases in punishment for acquitted conduct. Here, it is not possible to tell exactly what percentage of those cases represented acquitted conduct, but it is likely that acquitted conduct played a role in at least some of them. These 8% of upward departure cases may also imply there are instances in which judges are countering plea bargaining to the extent that some percentage of these cases may represent increased penalties due to offenses dismissed as part of plea bargain deals. Perhaps this reflects judges acting as a check on prosecutorial authority in cases in which they view the plea bargains as overly lenient.
Overall, the salience of criminal history is theoretically important for another reason. The function of the defendant’s criminal history in the various results implicates the focal concern regarding the defendant’s future risk. The inclusion of criminal history in the Guidelines as a principal factor in the recommended sentence is often viewed as the Commission’s proxy to adjudge dangerousness. M
Regarding future risk as a focal concern, other reasons in Table 4 more directly address dangerousness. The inclusion of the character of the defendant within the second ranked reason may well include assessments of past antisocial behavior as reflective of future risk. Ranked fifth in the top reasons given, the need to protect the public, clearly a future risk rationale, represented 41% of the upward departures. In sum, the relevance of the focal concern of future risk to severity in sentences is strongly confirmed in the data.
The multilevel results concerning offense type likewise provide interesting information about compliance with Guidelines’ proportionality judgments. The dummy series for offense type indicated that all other offense types, except for immigration offenses, were more likely to receive upwards departures than drug cases as the comparator. This implies that district judges as a general rule tend to believe the Guidelines are sufficiently punitive for drug offenses and immigration offenses. As drug and immigration cases combined are the bulk of federal sentencing in percentage terms, this particularly result situate the Guidelines in a positive light in terms of proportionality, at least with respect to generally being sufficiently punitive for a majority of crimes. However, the greater likelihood of upward departures for violent and firearms offenses implies that the judges may perceive the Guidelines as insufficiently punitive in those cases.
Moving onto the impact of extralegal variables, demographic characteristics presented with some expected results, while others were more surprising. There was support for gender leniency as women were far less likely to receive upward departures than men at the individual case level. Plus, gender leniency for women did not vary among districts, even after controlling for a host of other variables. This was the case even though gender is an
Contrary to many studies, the results here indicate there was no individual-level minority discrimination in upward departure decisions. While the odds for minorities were 5% greater than whites, the result was not statistically significant. Indeed, minority status was the weakest individual predictor overall. This result derives from F statistic comparisons.
It was surprising that noncitizenship was not a positive predictor of upward departures. Perhaps the explanation for the statistically greater likelihood of United States citizens to receive upward departures is that (according to a supplemental data analysis) two-thirds of the noncitizens in federal sentencing during the period of study (fiscal 2008-2015) were immigration offenders. Noncitizen immigration violators are likely to be subject to deportation. Deportation as an incapacitating gesture may impact an assessment of future risk at least regarding the danger to U.S. residents. Thus, it is possible that for noncitizen immigration offenders, prosecutors typically did not request upward departures in those cases and/or judges may have perceived them as unnecessary because of the deportation option. Still, the random effect of citizenship was statistically significant, indicating that the strength of the effect of citizenship significantly varied between districts. At two standard deviations, the effect of noncitizenship shows that it is actually positive (i.e., noncitizens were at higher odds of upward departures) in at least some districts.
No age leniency was observed at least to the extent it means less punishment for older offenders. Indeed, those age 50 and above were more likely to receive an upward departure and, like gender, the strength of the effect did not vary across districts. This could be evidence of a policy dispute with the Commission’s rule that age should typically not be a relevant sentencing factor. An alternative explanation, and one more likely considering the existence of other studies affirming age leniency, U.S. S
In terms of case-processing variables, the failure to find a trial penalty at level-1 is inconsistent with much other research.
Still, the random effects coefficient was significant, and at one standard deviation, the results indicate a trial penalty in at least some districts, which is in line with prior research.
As the last predictor variable to be discussed, custody status was the strongest factor in elevating the odds of an upward departure among the predictor variables. This result derives from F statistic comparisons.
The third focal concern should also be mentioned regarding consequences of the penalty. Several of the top reasons judges indicated on the Statement of Reasons for upward departures (listed in Table 4) implicate external consequences. The third highest ranking justification includes respect for the law, which likely entails respect by the defendant individually and more broadly. The fourth reason cites a general deterrence function as a reason for the upward departure, being triggered in 43% of cases. Both reasons reflect upon the consequences of the penalty in its deterring potential offenders and promoting community safety. Another community consequence present among the top ten reasons relates to the rehabilitation of the offender. The frequency of the rehabilitation motive to justify an upward departure, present in 9% of cases, is curious as federal law specifically dictates that “imprisonment is not an appropriate means of promoting correction or rehabilitation.” 18 U.S.C. §3582(a).
Additional evidence exists that upward departure decisions are quite often about proportionality concerns. Rounding out the top ten reasons listed for upward departures are two categories that expressly indicate judicial perceptions that the Guidelines have gaps. Judges cited general guideline issues or general adequacy issues in up to 10% of upward departure cases.
The third broad research question queried whether district courts vary from each other in the extent to which they weigh each of the legal, extralegal, and caseprocessing factors when issuing upward departures. The results found numerous such variations, as has already been partly covered when discussing the second research question. Overall, significant random effects were observed for all but two of the predictor variables (excluding offense type which could not be modeled as random effects). The strengths of the effect of leniency for women and the lack of lenience for older offenders were consistent across districts. In contrast, minority status and the trial penalty, which were not statistically significant in individual cases (after controlling for other variables), achieved significance in their random effects. In general, these random effect results support the courtroom communities’ perspective which theoretically accounts for different regional sentencing patterns.
To cite two examples, criminal history score and U.S. citizenship were both significant positive predictors of upward departures in individual cases, yet they also held significant random effects, meaning that their relationship to upward departures varied between districts. Moreover, standard deviation computations indicated that criminal history and the citizenship effect were actually negative predictors in some regions.
The discussion shall end on an empirical note. Overall, the results provide strong reinforcement for modeling sentencing decisions with both fixed and random effects in a multilevel model to observe individual-and group-based factors. The statistical significance of multiple explanatory variables in fixed and random effects is itself informative. Then it is also of practical and empirical import that the statistical significance of four variables posed contrasts between their fixed and random effects. In sum, females and age over 50 were statistically significant at their fixed effects, with females and defendants under age 50 far less likely to be issued upward departures (controlling for other explanatory factors). However, there were no significant random effects for those two variables, meaning that the leniency to females and the lack of leniency for those over 50 years-of-age were consistent between districts. The fixed and random effects for two other variables were in the opposite directions. Minority status and going to trial, indicated no significant fixed effects, but their random effects were significant. For minorities and the trial penalty, this means that there are at least a few districts in which minority status is correlated with upward departures and that the trial penalty exists to some extent in at least some districts. The mixed multilevel model employed here was uniquely able to parse those contrasts between individual-level and group-level effects for these four explanatory variables.
This Article provided an original empirical study of a discretionary sentencing outcome that leads to more severe sentences. The results show that the focal concerns of culpability, risk, and consequences are significantly relevant to upward departure decisions. Legal and case processing factors regarding these focal concerns are predictive of upward departures and typically in the direction anticipated. The surprising result here was that while higher criminal history score increases the likelihood of an upward departure, the Guidelines offense severity measure produces the opposite effect. A likely explanation is evidence that Guidelines as a general rule offer sufficiently or overly punitive recommendations regarding offense severity. Yet for criminal history, the exclusion of various past crimes in the official Guidelines calculations insufficiently values past antisocial behavior.
It was also of interest that the trial penalty, relevant to culpability and caseprocessing consequences, is not evident at the individual case level. The explanation is the inclusion of the acceptance of responsibility factor which mediates the trial penalty as a predictor across individual cases. Still, the random effects results also indicate that there exists a trial penalty in at least some districts, even with the acceptance of responsibility variable.
The results confirm that extralegal variables impact non-Guidelines sentences. Leniency for women is strongly supported and systematic, being significant and present across districts. The effect defies the Guidelines policy prohibition consideration of gender. For those who believe gender disparities equal gender discrimination, these results suggest such discriminatory practices. An age effect exists with older age (operationalized as 50 years) being more likely to receive upward departures and, like gender, it was systematically present.
No minority effect is observed at the individual level, though the random effects indicates its presence in at least some districts, even with multiple control variables. Thus, the study finds some racial/ethnic disparities which might constitute implicit or explicit discrimination in some regions. The failure to find that minority status as a consistent predictor of more severe sentences in this study could be due to the multitude of variables measured as fixed and random effects. In turn, citizenship produces an odd result with U.S. citizens more likely to receive upward departures. This result is likely due to the deportation option for non-citizens who commit crimes. On the other hand, this rationale appears to challenge the Guidelines policy that national origin should never be relevant.
Overall, the study suggests reasons for individual disparities in federal sentencing. Likely these embody a mix of warranted and unwarranted disparities, depending upon how one defines and values those terms. The research demonstrates the existence and salience of regional disparities, as well. The multilevel mixed model was able to parse differences between district courts concerning the impact of various legal and extralegal explanatory factors. The results indicate that while gender and age reflect systematic effects, districts vary significantly in their judgment about the relevance of the other predictor factors on upward departure decisions. These variations are consistent with the courtroom workgroup perspective. The results also support the observation that federal courts do not necessarily exhibit a singular culture, share an affinity toward the reasonableness of Guidelines recommendations, or regard national uniformity as the primary goal in sentencing.
This Article contributes to the empirical legal studies literature regarding sentencing practices. It may likewise be helpful more broadly to stakeholders and researchers across criminal justice contexts. The theoretical, policy, and empirical offerings herein may inform about more modernized ways to conceptualize, shape, and study criminal justice outcomes. The study further provides more data in the overall debate about the divergent values of disparity and uniformity.
This Appendix contains additional information about the practical benefits and statistical specifications for multilevel models. It provides the results of several null models (i.e., before explanatory variables were included), further explains some of the independent factors that were transformed in the full model provided in the text of this Article, and discusses why certain other variables were tested yet excluded from the final model.
Most sophisticated research on sentencing outcomes utilizes single-level regression analysis. While these types of regressions have confirmed values in being able to test the effect of each independent variable in the model while holding constant other variables, there may be an empirical flaw to be recognized in a single-level design as applied to certain datasets. A statistical presumption of a single-level regression model is that the outcomes are independent from one another. Peter C. Austin et al., U.S. S Michael T. Light, Michael Massoglia, & Ryan D. King,
Defendants within individual districts are more likely to share sociodemographic characteristics than with defendants in other districts because of the tendency in at least some parts of the United States to be more heterogenic in their populations. Traditional regression models unfortunately tend to ignore these kinds of correlations between defendants sentenced in the same jurisdiction.
In addition, the theory of courtroom communities is relevant. Sentences of defendants in the same district may be more correlated because they share the same courtroom cultures and sentencing judges than they are correlated with sentences issued in other districts exhibiting different cultures and judges. These group-based factors, resulting from individuals nested in districts, may also impact sentencing outcomes.
The statistical issue, then, when criminal defendants are nested in a higher level, such as district courts in the federal context, is that assuming that penalty outcomes for the dependent variable are independent from the higher level may be erroneous. Noelle E. Fearn, Austin et al., Weidner et al.,
Multilevel analyses, when suitable for the data, are able to provide numerous benefits over single-level regression models. First, multilevel methods can account for the lack of independence when individuals are nested in groups. Brian D. Johnson, Fearn, Porter & Umbach,
Third, multilevel models are not limited to two levels; they can accommodate additional levels. As an illustration, multilevel regressions are popular in educational research where students are nested in classrooms which are nested in schools. The current challenge of including multiple levels is the substantial increase in computer resource capacity that is necessary to run a model with numerous explanatory factors included. An attractive feature is that there need not be the same number of units at each level. Nor must the levels be strictly hierarchical in nature. They may merely be nested. Thus, a multilevel model can be cross-level, such as defendants nested in years and nested in districts. Such a design would account, then, for both annual and regional variables.
Fourth, multilevel models partition the overall variance in the outcome of interest among the levels of analysis (e.g., at the individual level and then at the group level). The result indicates how much of the variation in the outcome is accounted for by the grouping.
The initial step in a multilevel model project is to run a null model. The null model is also referred to as an unconditional model because it has no explanatory factors included. The purpose is to statistically obtain the intraclass correlation coefficient (“ICC”) to determine if multilevel modeling is appropriate for the data. The ICC provides the proportion of the total variance in the outcome that is accounted for by the clustering at the nested group level. In other words, for purposes of this study, the statistic is a measure of how much of the differences in upward departure decisions are attributable to variations in district court practices. If the ICC indicates that intraclass correlation exists with statistical significance, the assumption of independence required by the single-level regression model may be rejected and the data are appropriate for multilevel modeling. J. Kyle Roberts, Tom A.B. Snijders,
Multilevel models, like single-level regression models, are commonly tested on continuous dependent variables. But when the outcome of interest is binary in nature, different modeling must be employed because a binary dependent variable means that the normal assumptions of a normally distributed response variable and homoscedatic errors are violated. Joop J. Hox & Cora J.M. Maas,
A statistical model to fit data with a binary dependent variable is called a generalized linear model with three components: (1) a linear regression equation, (2) a specific error distribution, and (3) a nonlinear link function that transforms the predicted values for the dependent variable to the observed values.
For the study herein, the binary response variable for the
The transformation of the dichotomous dependent variable for an upward departure presented herein utilizes the logit link function.
RLogit Link Function
In the logit link function, the Greek letter eta (η) represents the transformed linear predictor. Exponentiating the resulting η parameter provides the odds ratio. The
At the outset of this study, it was considered that a three-level model might be appropriate considering district courts are nested within the higher level circuit courts of appeal and/or within years, with the latter perhaps accounting for changes in sentencing patterns over time and using annual time periods as the temporal division.
A few statistical notes should be briefly mentioned before addressing the models. The software utilized for the study presented herein, including the three-level models that follow, was SPSS version 24. Further, there is no issue of selection bias and therefore no need for the so-called Heckman correction. Selection bias may occur when the researcher obtains data from a non-random sub-sample of the population of interest. Shawn Bushway et al.,
In any event, the specification for a three-level null model is as follows:
Hη Level-1 β0jk = γ00k + μ0jk Level-2 γ00k = γ000 + μ00k Level-3
It was of interest, then, to test for whether the final model ought to account for serious nesting patterns which may introduce bias from the circuit courts of appeal as Level-3. The initial step in creating a multilevel model with three levels is to estimate the null model, which is provided in Table 5.
Null Model for Upward Departures with Districts Nested in Circuits.Fixed Effects S.E. Intercept -3.934 .087 Random Effects S.E. ρ Level-1 3.29 Level-2 .250 .042 6.94% Level-3 .060 .162 1.67% -2LL=4324243 n=623,947
From Table 5 it is estimated that 7% of the variation in upward departures is between district courts and almost 2% of the variation is between circuit courts of appeal. The ICC was statistically significant for Level-2 district courts, yet was not significant for the Level-3 circuit courts. Practically, it was not surprising that there was not shown to be statistical significance with circuit courts. An earlier scan of bivariate data for the proportion of upward departures in the districts did not reveal consistencies for districts nested in circuits. Instead, the circuits tended to encompass a mix of low and high use of upward departures within their nested districts. For example, while three of the districts within the Fifth Circuit yielded the highest proportions of upward departures (Northern District of Texas at 6.5%, Western District of Louisiana at 5.7%, and Eastern District of Louisiana at 4.8%), the Fifth Circuit also included one district with a below-average rate of upward departures (Southern District of Texas at 1.5%). Overall, the Fifth Circuit ranked as the fifth highest among the 12 circuits in its total proportion of upward departures. The First Circuit ranked first overall, with a total of 3.3% of sentences with upward departures. But the First Circuit also presented with vastly different practices within its district court outcomes, as well. Most of the upward departures in the First Circuit were issued in the District of Puerto Rico (at 4.4%), yet this circuit also included the District of Rhode Island which issued one of the lowest rates of upward departures (at 0.5%).
While circuit court variation was not statistically significant, it alternatively was likely that there might be variations by time. Thus, a three-level null model was run for district courts nested in fiscal years, which is presented in Table 6.
Null Model for Upward Departures for Districts Nested in Years.Fixed Effects S.E. Intercept -3.937 .057 Random Effects S.E. ρ Level-1 3.29 Level-2 .282 .046 7.69% Level-3 .093 .010 2.54% -2LL=4328082 n=623,947
This null model with district courts nested in fiscal years demonstrated that 8% of the variation in upward departures is between district courts. It was also found that there is a statistically significant variation with Level-3 being an annual indicator. Yet, for several reasons, the nesting of upward departure outcomes at a level with years was dropped to proceed with a more developed two-level model. The ICC for years was, in practical terms, indicating a low degree of variation by year at less than 3%. As multiple explanatory variables were expected to be included in the final model with both fixed and random effects, a three-level model including years would present as an extremely complicated model from a computing resource perspective. Indeed, as will be indicated below, even in a two-level design with district courts at the higher grouping, the final model had to be curtailed a bit because of convergence issues when attempting to model all independent variables as both fixed and random effects. An additional concern is that there were only 8 groups involved for years (i.e., eight consecutive fiscal years), an extremely low number for multilevel modeling purposes. In any event, as a primary interest for this study was regional variations in discretionary sentencing decisions, the Level-3 variation with years was dropped. Still, the three-level model indicated in Table 6 was presented herein for informational purposes.
As the three-level designs just summarized were vetoed, a null model with two levels to account for nesting in districts could be run. The null model for two-level design with a dichotomous dependent is specified with the following equations.
η Level-1 Null Model β0j = γ00 + μ0j Level-2 Null Model
In these null models for this study, the term β0j is the intercept, which is the average log odds of an upward departure in group H
In a generalized linear multilevel model using a logit link because of a binary response variable, the Level-1 residuals are assumed to follow the standard logistic distribution, with a mean of 0 and a variance (
Intraclass Correlation Coefficient (ICC)
The term τ00 represents the between-group variance at Level-2.
Table 7 provides for the null model results for upward departures where Level-1 are individual defendants and Level-2 are district courts. Table 7 is the basis for the final model contained in Table 3 in the main body of this Article.
Null Model for Upward Departures Nested in Districts.Fixed Effects S.E. Intercept -3.921 .058 Random Effects S.E. ρ Level-1 3.29 --- Level-2 .301 .047 8.38% -2LL=4324129 n=623,947
The ICC computed for the two-level null model means that 8% of the variability in upward departures is accounted for by districts. This leaves 92% of the variability to be accounted for at the individual case level (or other unknown factors). Light,
As expected from the courtroom communities’ perspective, the Level-2 random effect is significant at the .001 level, which indicates that the probability of an upward departure significantly varies between districts. Indeed, in a separate analysis to compare district means, wide variation in proportions were observed. The proportion of upward departures at the district court level ranges from a low of 0.5% (Northern District of Oklahoma, District of New Mexico, and District of Rhode Island) to a high of 6.5% (Northern District of Texas). Thus, the district with the greatest proportion of upward departures is more than twelve times that of the district with the lowest percentage, indicating a stark district level differential.
The intercept in the two-level null model represents an estimate that can be converted to the overall probability of an upward departure. The random effect represents the degree to which the outcome varies across federal districts. The estimated probability of a defendant receiving an upward departure in the average district is approximately 2%. The formula to obtain the overall expected proportion is an inverse of the logit link function: [(1/(1 +
Once the researcher chooses the null model with the appropriate higher level(s), the researcher can add explanatory factors. In a very simple model, we can add a Level-1 explanatory variable and a Level-2 predictor, such as the following equation illustrates.
η Level-1 β0j = γ00 + γ01Wj + μ0j Level-2 β1j = γ10 + μ1j
Now γ00 is the log odds that the outcome = 1 when explanatory variable X = 0 and μ = 0. β1, is the log odds effect that the outcome is = 1 for every one unit increase in the variable X in group
In this study, the null model with district courts at Level-2 was the choice and the independent variables that survived into the final model are provided in Table 3 in the main body of the text. In Table 3, the ICC statistic indicates that 2% of the overall variance remains with district courts. The intraclass coefficient is no longer statistically significant when accounting for multiple fixed and random effects. Nonetheless, the substantial reduction in the -2 Log-Likelihood statistic between the null model and the full model indicates a significantly better fit of the full model for this dataset. Further discussion on methodological choices along the way to the final model is next.
Some variables were transformed for the final model as explained below. In addition, other factors were tested yet eliminated in the end for the reasons ascribed to them herein.
For purposes of the descriptive statistics in Table 2, the variables for final offense level, criminal history, and number of counts are in their original metrics. For the multilevel model in Table 3, these three variables are each grand mean centered for ease of interpretation as none of them can have zero as a real value. In federal sentencing, defendants must have at least one count of conviction, the lowest criminal history category is I (i.e., 1), and the minimum offense severity level is 1. In a logistic model, the intercept is interpreted to mean the value of the outcome when all predictors are equal to 0. This has no practical meaning for variables that cannot actually have a real world value of 0, which is the case for these three variables. Grand mean centering is the statistical convention for adjusting the metrics to have a more interpretable intercept in such a case.
The number of counts (of conviction) variable was transformed for statistical purposes. In the original data, the number of counts variable was skewed to the right. This variable was first centered at the grand mean. Then to enable a natural log transformation to adjust for the skew and more closely approximate a normal distribution, the value of .1 was added to the mean centered variable because log transformations are not possible on values of 0.
Race/ethnicity was originally coded as dummy variables of black, Hispanic, and other, with white as the reference category. In a full multilevel model with such coding with all fixed effects, the only statistically significant result was for the category of other as compared to whites. This result is practically meaningless because the grouping of “other’ includes a heterogeneous mix of native Alaskan, native American, non-U.S. American Indians, Asian, Pacific Islander, multi-racial, and a smaller subset of other. U.S. S
The full model includes all 94 district courts. This is mentioned because many studies that incorporate district courts in their variables exclude the districts that are in the U.S. territories (Puerto Rico, Virgin Islands, Guam, North Mariana Islands). These researchers argue the territories are viewed as different because states enjoy greater rights than them and, thus, the inclusion of the territories may introduce nonrandom bias. Gail Iles et al.,
The general offense type was excluded from the random effects due to the complexity of the algorithm necessary to compute a multilevel model with them included. In other words, the model with the offense type having random effects was overly complicated for computational iterations, resulting in a failure of convergence. Convergence was achieved after excluding offense types at Level-2, while still retaining their Level-1 fixed effects.
It is noted that four additional independent variables were tested but removed before the final model for reasons of parsimony and specific statistical challenges. The applicability of a mandatory minimum statute was not statistically significant (at the .001 level) at Level-1 in any model and thus was removed as there was no theoretical justification to retain it as a factor in a study on
A series of dummy variables to distinguish fiscal years of sentencing were also dropped. While the annual rates of upward departures were statistically significant compared to 2008 as the dummy, the overall statistical impact (according to F statistic results) on explaining upward variances for the timing factor was among the weakest among the various explanatory variables. The statistical resources necessary to account for the seven dummy variables for years did not then seem worthwhile.
Another variable was tested and also dropped. No statistically significant effects of education level on upward departures were observed in any tested model. Without any pressing need to focus on educational level as it does not represent the most egregious type of discriminatory category, it was discarded as an explanatory factor.
As a final methodological note, the results here may advise other researchers that it might be preferable to model the main Guidelines proxies for crime severity and criminal background with the two separate factors of final offense level and final criminal history category, respectively, rather than their combination as indicated by the Guidelines’ minimum sentence recommendation. As shown herein, the two variables may actually have the opposite effect on the outcome of interest, which would unfortunately be indiscernible when using the minimum sentence combination instead.