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Prison Size and Inmate Rule Violation 
 
 

Alex Martinez 
Department of Sociology 

California State University, Los Angeles 
 
 

In recent decades the prison industry has grown at an 
unprecedented rate. Prisons have become overcrowded and 
underfunded. Because of the demographics of those housed in 
prisons, it is important to understand how increased overcrowding 
has affected their behavior and tendency to break prison rules. In 
this study we look at a data set collected by the Ohio Department 
of Rehabilitation to analyze any possible connections between 
prison size and inmate rule violation. Three distinct sizes were 
examined while also taking into consideration other factors such 
as age, ethnicity and education level. For our analysis we used a 
negative binomial regression model. Findings showed a 
relationship between ethnicity/age and prison size at smaller 
prisons. No significant relationships were found within medium 
and large prisons. Nevertheless, a more comprehensive study of 
prison size affects is needed to address the potentially disastrous 
effects of overcrowded prisons.  

 
 

INTRODUCTION1 
 
Today the prison industrial complex is a 
huge and profitable industry in the 
United States. The industry provides 
many jobs not only in the area where a 
particular prison is located, but 
                                                 
Alex Martinez is a graduate student at 
the Department of Sociology, California 
State University. He is currently working 
on his Master’s Thesis under the 
supervision of Professors Hyojoung Kim 
(Chair), Cristina Bodinger-deUriarte, 
and Gretchen Peterson. The current 
paper was initially submitted to Soc. 410 
(Advanced Statistics), taught by 
Professor Hyojoung Kim in Fall 2007. 

nationally as well. The prisons them-
selves provide jobs for prison guards 
however the entire industry provides 
jobs in construction, uniforms, security, 
and other industries. The prison in-
dustrial complex also has a very 
powerful lobby machine in Washington 
D.C that requests funding from the 
federal government which ensures its 
continued growth and survival. With the 
recent media coverage on the over-
crowding of prisons and prison riots, the 
question arises: Is there a relationship 
between prison size and rate of inmate 
rule violation?  The purpose of this 
paper is to find out if the size of the 
prison (based on number of prisoners)

CALIFORNIA SOCIOLOGY JOURNAL, 2008, VOL. 1 (November: 22-26) 
 



INMATE RULE VIOLATIONS by Alex Martinez 23

 affects the rate of inmate rule violations 
inside prisons. This topic is important 
because if research indicates that pris-
oners at larger prisons violate rules at a 
higher rate could eventually lead to 
policy change. If findings can exhibit 
that prison size is correlated or has a 
causal relationship between prison size 
and the rate of inmate rule violation, it 
could lead to a change in how prisons 
are built and how they are occupied. 
 
RESEARCH HYPOTHESIS  
 
Based on the Inmate Data Set the 
following hypothesis can be formed: 
prisoners in medium sized prisons (those 
having 1000 to 1999 prisoners) receive a 
greater number of class III tickets, than 
those inside smaller prisons (those 
having one thousand or less). 
 
DATA AND VARIABLES 
 
This paper will make use of the “Inmates 
Dataset” that was collected by the Ohio 
Department of rehabilitation. The dataset 
consists of information on 1,485 male 
inmates admitted to the Ohio 
Department of Rehabilitation and 
Correction during September and 
October 1985. The “variables reflect 
demographic and criminal history 
information for each inmate as well as 
individual lifestyle data and correctional-
institution information regarding rule 
infractions during incarceration” 
(DeMaris, 2004:16).  

Our dependent variable in this 
analysis is the number of class three 
tickets that prisoners receive. NUM-
3TIX, number of Class three tickets, is a 
measure of inmate rule-violation 
behavior while incarcerated. The NUM-

3TIX variable has a range of 0 to 28. A 
greater number of tickets reflect more 
rule-breaking.  

Our independent variables in the 
analysis are prison size, either small or 
medium sized prisons. The variable for 
small prisons (SMALL) is a dummy 
variable in which 1 = prison has 1000 
inmates or less and 0=other. The var-
iable for medium sized prisons 
(MEDIUM) is also a dummy variable in 
which 1 = prison has 1000 – 1999 
inmates and O=other.  Prison size and 
rate of inmate rule violation will be 
analyzed and checked for a possible 
relationship.  

A number of variables will be 
controlled for beginning with the amount 
of time a prisoner has served in jail. We 
will code time served the following way: 
Time will range from 2.3 to 4.1 months. 
Ethnicity will also be controlled as a 
dummy variable in which 1=black and 
0=white. Years of formal schooling will 
range from 2 to 22 years. Age at first 
arrest will range from 6 to 71 years of 
age. Centered age at admission, and the 
square of centered age at admission will 
also be coded. 
 
STATISTICAL MODELS 
 
The best model of analysis to use is the 
Poisson or Negative Binomial 
Regression model which makes use of a 
count dependent variable.  If an 
Ordinary Least Squares (OLS) model 
was to be used, the assumption of 
homoscedasticity is inherently violated. 
Also, the assumption of zero covariance 
between residual and covariates would 
be violated making the OLS estimates 
biased. Because the outcome would 
provide non-normal distribution of 

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INMATE RULE VIOLATION by Alex Martinez 24 

Table 1. OLS Regression Analysis of the Number of Class III Tickets 
 

Variable Coef. (s.e.) Variance Inflation 
Factor (VIF) 

Intercept  
Small size prison 
Medium size prison 
Time served  
Ethnicity 
Education  
Age at first arrest 
Centered age at admission 
Centered age at admission squared 

1.10
0.68

-0.01
0.04
0.27

-0.03
-0.01
-0.07
0.002

(0.35)* *  
(0.17)* * 
(0.13)  
(0.02) 
(0.11)* *  
(0.02) 
(0.01) 
(0.01)* * 
(0.001)* *  

0.00 
1.19 
1.31 
1.06 
1.05 
1.08 
1.42 
2.64 
2.33 

N 
F statistic 
Adjusted R-squared 
Breusch-Pagan Test 

1,485 
18.60 * * 

0.08 
42.62 * * 

*p<0.05; **p<0.01  
 
  
residuals, the F-test and t-test could not 
be used. However, if robust conditions 
are present, the OLS model may be used. 
Robust conditions are met if the count 
variable has big enough counts or 
heteroscedasticity of error terms does 
not cause serious trouble and the number 
of observations (N) is large. This paper 
will make use of OLS model for its 
analysis.  
 
FINDINGS 
 
Table 1 reports the OLS regression 
coefficients for each of the independent 
variables. The F-test evaluates the 
overall fit of the model on the data. The 
F-test is statistically significant at least at 
the 0.01 level showing that at least one 
ofthe independent variables has 
statistical significant effect on the 
number of class three tickets that the 
inmates receive. Furthermore, the 

Adjusted R-squared is 0.08, indicating 
that a total of 8 percent of the variance in 
the dependent variable is successfully 
explained by the model.  
 Table 1 shows the regression 
coefficient for small sized prisons is 
positive and statistically significant at 
least at the 0.01 level. For small sized 
prisons, the number of class three tickets 
is larger by 0.68, in comparison to 
prisons with 2000 or more inmates, net 
of all other independent variables in the 
model. Because both dummy variables 
were used in the OLS model, the 
contrast group is prisons with 2000 or 
more inmates. 
 The regression coefficient for 
medium sized prisons is negative and 
statistically insignificant at the 0.05 
level. In other words, medium sized 
prisons have no significant effect on the 
number of class three tickets that an 
inmate receives.  

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INMATE RULE VIOLATION by Alex Martinez 25 

 The time served variable has a 
positive regression coefficient which is 
statistically insignificant at the 0.05 
level. The amount of time served has no 
significant effect on the number of class 
three tickets that an inmate receives.  
 Table 1 shows that ethnicity has 
a positive regression coefficient which is 
statistically significant at least at the 
0.01 level. In other words, for Blacks the 
number of class three tickets is larger by 
0.27, in comparison to Whites, net of all 
other independent variables in the 
model.  
 Education has a negative 
regression coefficient and it is statis-
tically insignificant at the 0.05 level. In 
other words, the amount of education 
that an inmate acquires has no 
significant effect on the number of class 
three tickets he receives.  
 The age at first arrest variable 
has a negative regression coefficient 
which is statistically insignificant at the 
0.05 level. The age at which the prisoner 
was arrested has no significant effect on 
the number of class three tickets that he 
receives.  
 The centered age at admission 
variable has been de-meaned, meaning 
that the mean has been subtracted from 
the variable itself. Table 1 shows that the 
centered age variable has a negative 
regression coefficient and it is 
statistically significant at least at the 
0.01 level. To compensate for this issue 
the variable has been squared (see Table 
1). The squared centered age at 
admission has a positive regression 
coefficient and it is statistically 
significant at least at the 0.01 level. In 
other words, for one unit increase in 
centered age at admission squared, the 
number of class three tickets is expected 

to increase by 0.002, net of all 
independent variables in the model.  
 
DIAGNOSIS OF OLS REGRESSION 
ASSUMPTIONS  
 
Although OLS estimates are BLUE 
(best, linear, and unbiased estimates), the 
properties only hold true when OLS 
assumptions are satisfied. The OLS 
assumptions are assessed by examining 
the partial regression residual plots and 
by examining the variance inflation 
factors (VIF) (see Table 1).  
 The Variance Inflation Factors 
are close to 1, indicating that the 
independent variables are not collinear 
with each other and much less perfect 
multicollinearity.  
 The Breusch-Pagan test checks 
for homoscedasticity. The test assumes a 
null hypothesis of homoscedasticity, and 
since the outcome for this analysis 
shows statistical significance (see Table 
1), this indicates that the residuals are 
heteroscedastistic. In other words the 
assumption of homoscedasticity is 
violated thus making the OLS regression 
coefficients still unbiased but no longer 
best or efficient. The assumption 
violation of homoscedasticity can be 
resolved by testing the statistical 
significance of heteroscedasticity while 
using robust standard errors that take 
into consideration heteroscedastistic 
disturbances. We can also use a weight-
ed least square estimator and regress this 
estimator on the variables associated 
with heteroscedasticity.  
 No test was conducted to check 
for the assumption of zero covariance 
with regressors, but the partial regression 
residual plots seem to indicate linear re-
lationships for the independent variables. 

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INMATE RULE VIOLATION by Alex Martinez 26 

CALIFORNIA SOCIOLOGY JOURNAL, 2008, VOL. 1 (November: 22-26) 

If variables are omitted the assumption 
of zero conditional mean is most likely 
violated. Since other ethnicities have 
been omitted, we concluded that the 
assumption of zero conditional mean has 
been violated. No test was conducted for 
the assumption of no autocorrelation. 
However since our data is not time 
series, we conclude that the assumption 
of no autocorrelation has not been 
violated.  

OLS estimates are also sensitive 
to the influence of outliers. To check for 
influential outliers the partial regression 
residual plots are examined. The partial 
regression residual plots for all the 
independent variables show that there is 
a possible influential outlier. However 
when the observation is omitted and the 
OLS model is run again, the outcome 
shows that the original findings hold 
true. All the independent variables have 
the same statistically significant 
coefficients. Interestingly, the direction 
of the medium sized prison variable 
changes from negative to positive. 
However, the statistical significance 
shows no change.  

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Also, the magnitude for ethnicity 
changes but not the significance.  
 
CONCLUSION  
 
The OLS regression analysis shows that 
the number of class three tickets that an  
inmate receives in not affected by; 
medium sized prisons, amount of time 
served, education, and the age at first 
arrest. The analysis does show that small 
sized prisons, ethnicity, and centered age 
at admission do have a significant effect 
on the number of class three tickets that 
an inmate receives. While we have 
learned much from our analysis, further 
research is needed. To have solid 
conclusions on whether there is a re-
lationship between the size of prisons 
and the rate of inmate rule violations, 
more research needs to be conducted that 
includes prisons of different sizes. There 
also needs to be an analysis that includes 
other race/ethnicities and female in-
mates. Also, there needs to be a 
comparison done between prisons in 
different states.  
 


