Supplementary Measurement Appendix
Education: A variable indicating the last grade completed: High school or less = 1, some college or
technical school = 2, college = 3, or post-college degree = 4.
Income: “Which of the following groups includes the income of all members of your immediate
household for the past year before taxes. Less than $15,000, $15,000 to $35,000, $35,000 to
$50,000, $50,000 or more?”
Religious activity: “How often do you attend church or some other religious service? “Never” = 1,
“sometimes” = 2, “often” = 3.
Ideology: “Would you say that your views in most political matters are liberal, conservative or
somewhere in the middle?” Liberal = 0, moderate = 1, conservative = 2.
Party Identification: “Which of the following categories best describes what political party
represents your political views? The Democratic Party, The Republican Party, or do you consider
yourself an Independent?” Democrat = 0, Independent = 1, Republican = 2.
Discrimination Index: An additive index of responses to the following three questions (Cronbach’s
 = .85): “Do you feel the opportunity for fair treatment by the [police, prosecutors, judges] is
equal for blacks and whites?”
Crime concern Index: An additive index of responses to the following three questions (Cronbach’s
 = .45): “In the last year, do you think crime in this country has increased, decreases, or stayed
about the same?” “How much do you personally worry about crime and violence? A great deal, a
fair amount, only a little, or not at all?” “Is there any area where you live---that is within a mile--where you would be afraid to walk alone at night?”
Criminal Past: “Have you personally, at anytime in the past, been under some sort of correctional
supervision such as prison, parole, or house arrest?” No = 0, yes = 1.
Dispositional Attribution: “Do you agree or disagree with the following statements: People become
criminals because they don’t care about the rights of others or their responsibility to society?”
Strongly agree = 4, agree = 3, neither agree or disagree = 2, disagree = 1, strongly disagree = 0.
Knowledge: An additive index of responses to the three questions, coded as either correct = 1 or
incorrect = 0 (Cronbach’s  = .61). “Whose responsibility is it to determine if a law is
constitutional or not?” “What job or political office is now held by John Roberts?” “Of all of the
countries in the world, do you happen to know which country has the highest number of its citizens
under some form of correctional supervision, that is prison, parole, or probation?”
Inner-city: Inner city region = 1; rural region = 0.
Supplementary Estimation Appendix
An item response theory model provides a direct test of the theory concerning intra-issue
constraint as well as efficient and unbiased estimates of each respondent’s latent support for
punitive and preventative anti-crime policies. Item refers to the individual measures or indicators of
a particular latent concept, in this research ordinal-scaled questions about support for specific
punitive or preventative policies. The IRT model provides estimates of the probability of choosing
a specific “response” category (e.g., favor, oppose) across levels of policy support (commonly
referred to as item difficulty) and the ability of each policy item to discriminate between
respondents with similar levels of policy support.
Item response theory models have been used to measure expert opinions (Clinton and
Lewis 2008), democracy (Treier and Jackman 2008), political knowledge (Delli Carpini and Ketter
2001; Jerit, Barabas, and Bolsen 2006), and elite voting (Clinton, Jackman, Rivers 2004; Voeten
2004). In most of these instances, a latent trait was estimated from multiple dichotomous-scaled
items using a two-parameter logistic item response theory model or 2PLM. Formally, the 2PLM is,
where Pj(i) denotes the probability that a respondent at some level of the latent trait, denoted by
the Greek letter theta (i), will choose to endorse item j. The item can be any binary choice such as
a roll call vote or a survey question. The probability of endorsing an item, Pj (i), is a function of
the disposition of the respondent (i.e., their latent trait i) and characteristics of the item j.
The first item characteristic in the 2PLM above is its difficulty denoted by the Greek letter
kappa (). This is the item difficulty parameter. The item difficulty parameter indicates the level of
the latent trait necessary for a respondent to endorse item j. An item with a difficulty of 1 indicates
that an individual with a latent trait of 1 has a 50% chance of endorsing the item (see Fraley,
Brennan, and Waller 2000). In theory, only individuals with a high score on the latent trait will
endorse an item with a high difficulty parameter and almost everyone will endorse an item with a
low difficulty parameter.
The second item characteristic in the 2PLM model is the item discrimination parameter.
The discrimination parameter, denoted by the Greek letter alpha (), indicates the ability of an item
to differentiate between individuals with similar trait levels (i.e., similar values of theta). Similar to
a factor loading for a normally distributed latent variable, items with higher discrimination
parameters represent a better indicator of the latent trait with the typical item discrimination
parameters for dispositional traits falling between .5 and 2.5 (Kim and Pilkonis 1999).
In order to make the binary item response linear to the latent trait denoted by theta, the
model uses the familiar logistic link function of
that produces the same S-shaped curve
that links binary responses to a set of independent variables in logit models. However, the 2PLM
also estimates the probability of endorsing an item as a function of the difference between an
individual’s latent trait and the item difficulty multiplied by the inverse of the item’s discrimination
parameter rather than a linear combination of independent variables as in a logistic regression.
This research uses an expansion of the 2PLM to include items with ordinal-scaled response
options (e.g., strongly favor, favor, neither, oppose, or strongly oppose). This graded item response
model, where graded refers to the ordinal-scaling, estimates the probability that a respondent will
choose a response category denoted by c (e.g., favor, oppose) on a specific policy item j (e.g., death
penalty, tougher sentencing) as a function of their latent support for punitive (or preventative)
policies denoted by , the discrimination parameter for that specific item denoted by j, and the
category threshold estimates for that specific item denoted by j. The key difference between this
model and the 2PLM above is the item response scale is estimated as a series of C-1 response
dichotomies, where C is the number of response categories for an item. This essential amounts to
estimating the probability that a respondent chooses category c minus the probability that the
respondent chooses the adjacent category c-1. Instead of a single difficulty parameter as in the
2PLM, the model estimates a threshold parameter for each response category cutpoint. These
threshold parameters represent the probability of selecting a specific response category c (e.g.,
favor, oppose) based on a respondent’s latent policy support ().
Formally, the probability of a respondent, denoted by i, of selecting response category c on
item j given their latent policy support i, the item discrimination j, and the item threshold
parameter j is,
where  is the same S-shaped cumulative normal distribution function used in probit and ordered
probit models to link the non-linear ordinal-scaled responses to the latent policy support variable.
The final parameter denoted by the Greek letter sigma (i) is the variability in each respondent’s
policy support, an indicator of each respondent’s intra-issue constraint.
The latent policy support variable is simultaneously estimated from a set of respondent
dispositional characteristics and demographic variables by setting  as a function of a set of
independent variables. Formally,
  1 X1  2 X 2 
where 1 describes the relationship between an independent variable X1 and the latent trait ,
 regression.
similar to an ordinary least squares
The application of this IRT model is unique in that it also estimates the variability
surrounding each respondent’s latent policy support. Specifically, I estimate the log square root of
the variance as,
log
    Z  
i
1
1
2
Z2
where 1 represents the relationship between an independent variable Z1 and the variability in policy
support. A positive andstatistically significant 1 coefficient would indicate that an increase in the
variable Z1 would also increase the variability in the latent trait. Estimating the log of the square
root of the variance in this equation constrains the variance to be a positive value. This is similar to
the specification of any heteroskedastic choice model (regression, probit, ordered probit).
Supplementary Appendix References
Clinton, Joshua, Simon Jackman, and Douglas Rivers. 2004. “The Statistical Analysis of Roll Call
Data.” American Political Science Review, 98(2): 355-370.
Clinton, Joshua D. and David E. Lewis. 2008. “Expert Opinion, Agency Characteristics, and
Agency Preferences.” Political Analysis, 16(1): 3-20.
Delli Carpini, Michael X. and Scott Keeter. 2001. “Measuring Political Knowledge: Putting First
Things First.” American Journal of Political Science, 37(4): 1179-1206
Fraley, R. Chris, Niels G. Waller, and Kelly A. Brennan. 2000. “An Item Response Theory
Analysis of Self-Report Measures of Adult Attachment.” Journal of Personality and Social
Psychology, 78(2): 350-365.
Jerit, Jennifer, Jason Barabas, and Toby Bolsen. 2006. “Citizens, Knowledge, and the Information
Environment.” American Journal of Political Science, 50(2): 266-282.
Kim, Yookyung and Paul A. Pilkonis. 1999. “Selecting the Most Informative Items in the IIP
Scales for Personality Disorders: An Application of Item Response Theory.” Journal of
Personality Disorders, 13(2): 157-174.
Treier, Shawn and Simon Jackman. 2008. “Democracy as a Latent Variable.” American Journal of
Political Science, 52(1): 201-217.
Voeten, Erik. 2004. “Resisting the Lonely Superpower: Responses of States in the United Nations
to U.S. Dominance.” Journal of Politics, 66(3): 729-754.