Indicators for Missing Data on Baseline Covariates
Certain key demographic variables that had limited numbers of missing data were recoded to retain cases with intermittent missing data. Two individuals who had missing data for
racial/ethnic status were included in a combined category: Hispanic, biracial/multiracial, other racial/ethnic status, or missing. Nine individuals who were missing data on number of times previously imprisoned were included in the category for no previous prison terms, due to their young ages when entering prison to complete their SVORI-related sentences.
Group-Based Trajectory Model
The trajectory model retained cases that had missing data for some observation periods (in cases where men were too young to have been eligible for arrest), but these cases contributed fewer observation periods to the fitting of the trajectory model. Approximately half of the time-
invariant explanatory variables included in the trajectory model were created using lifetime arrest records. The remaining time-invariant explanatory variables come from the baseline interview, which was completed by all of the men recruited into the sample. However, most items had little or no missing data. Categorical variables that had missing data for a small number of cases (e.g., racial/ethnic status, previous imprisonments) were recoded as described above to retain cases.
Propensity Score Matching and Duration Models
The indicator for participation status had no missing data (n = 1,575): One man did not indicate whether he had received vocational education/job training, but all of the men provided
information on educational service receipt. The duration models use data from official arrest records that were compiled for all men in the original sample (n = 1,575). The multilevel logit model and duration models used listwise deletion, due to incidental patterns of missing data for items collected at the baseline interview. These models include race and prison variables that
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were recoded to retain cases with missing data, as described previously. The logit participation model eliminates four cases with missing data on covariates in the model (n = 1,571). The duration models exclude 10 cases from the matched sample that had missing data on covariates (n = 1,521).
Confirmatory Factor Analysis
The maximum likelihood (ML) estimation procedure retained cases with incidental missing data patterns, although cases with extensive missing data (e.g., attriters from all three follow-up interviews) were excluded from the sample.
Structural Equation Modeling
This study uses full-information maximum likelihood (FIML) estimation for the structural equation models, which assumes that data are missing at random (Allison, 2003; Yuan, Yang- Wallentin, & Bentler, 2012). FIML estimation using the full sample is preferable to statistical techniques that use complete cases when data are not completely missing at random (Allison, 2003). Listwise deletion introduces the possibility of bias into estimates, while the reduced sample size increases the size of standard errors and reduces the power of hypothesis tests (Allison, 2003). FIML generates parameter estimates that are often more efficient than multiple imputation techniques and do not rely on multiple random draws of data sets (Allison, 2003, 2012; Larsen, 2011). Because FIML addresses missing data as part of the estimation process, the parameter estimates, standard errors, and test statistics are stable and do not vary (Allison, 2012).
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Table 3.1 Variable Descriptions by Analysis
Variable GTM PSM DM LSEM
In-person interviews
Linear age at release X Xa Xa X Squared age at release X
Cubed age at release X
Years of education Xa Xa X
Racial/ethnic status (ref. African American)
White X X X X
Hispanic, multiracial, other, miss X X X X SVORI term: Sentencing offense
Drug offense X X X
Property offense X X X
Person/violent offense X X X
Parole/probation violation X X X SVORI term: Time served (years) Xa X
Log-transformed time served Xa
Prior prison terms X
No previous terms/missing X ref. ref.
1 previous term X X X
2 previous terms ref. X X
3 or more previous terms ref. X X Pre-SVORI income: Family X
Pre-SVORI: Longest job (ref. Never/1 year)
1 to under 2 years X X
2 to under 5 years X X
More than 5 years X X
Prosocial peers (W2-W4) X
Job search difficulties (W2-W4) X
Stable employment (W2-W4) X
Recent job: Hours worked (W2-W4) X Recent job: Permanency (W2-W4)
Permanent position X
Temporary employment X
Recent job: Stability (W2-W4)
Formal pay X
Casual pay/self-employment X
Financial need items (W1-W4) X
Personal mastery scale X
Average anxiety score (W1-W4) X
Average depression score (W1-W4) X Average hostility score (W1-W4) X
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Table 3.1 Variable Descriptions by Analysis
Variable GTM PSM DM LSEM
In-person interviews
Pre-SVORI recent alcohol/drug use X X
Global Severity Index X
General physical health status X
Health limits activities (ref. None)
A little X
A lot X
SVORI participant status X
Educational program participation X
Employment program participation X
Prison industry job X
Work release job X
SVORI site location (ref. South Carolina) Level-2
Iowa random X X Indiana effect X X Kansas X X Maryland X X Missouri X X Nevada X X Ohio X X Oklahoma X X Pennsylvania X X Washington X X
NCIC Arrest Files Pre-release arrest files
Age at first arrest X X
Lagged arrest, drug offense X X
Lagged arrest, property offense X X Lagged arrest, violent offense X X Years with any recorded arrest X
Lifetime sum of recorded arrests X X
Arrests count, year before prison X X
Post-release arrest files
Time to first arrest X
Time to first drug arrest X
Time to first property arrest X
Time to first violent arrest X
Arrest within 3, 9, 12 months X
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Table 3.1 Variable Descriptions by Analysis
Variable GTM PSM DM LSEM
Model-Generated Variables
Trajectory group (ref. Group 1)
Group 2 X X X
Group 3 X X X
Linear age*Trajectory group Xa
Education*Trajectory group Xa
Prison terms*Trajectory group X
Prob. participation, Education/Employment services X Probability of participation* Trajectory group X
Note: GTM = Group-based trajectory model. LSEM = Longitudinal Structural Equation Model. NCIC =
National Crime Information Center. PSM = Propensity score methods. DM = Duration Models. SR = Self- report. SVORI = Serious and Violent Offender Reentry Initiative. In-person interview items were collected at baseline unless noted. “a” indicates continuous variables centered on state means.