30
International Journal of Security and Terrorism • Volume: 4 (1)
(OLR) model. This model is “estimated by a method called Maximum Likelihood Estimation
(MLE)” (Aldrich & Nelson, 1984: 49) that deals with “picking parameter estimates that imply
the highest probability or likelihood of having obtained the observed sample Y” (p. 51; see
also Agresti, 2002).
An ordered response model can be developed as a linear probability model with the
use of a continuous latent
5
variable (Long & Freese, 2006). One assumption of the ordered
response model is that an unmeasured (latent) variable, y
*
, that ranges from – ∞ to + ∞
exists, and is “mapped to an observed variable y” (Long, 1997: 116), where the mapping
from the latent variable is done with the response categories of not utilized, utilized some,
and highly utilized in the current study. This division of y* into three “values of the observed
y” (Long, 1997: 117) is done by thresholds, or cut points, that are denoted as
τ
. Here a
linear equation model is created by using log odds, where standardized coefficients are used
the same way that the coefficients are used in a linear regression model (LRM).
Another way of interpreting the results of ordinal-level outcomes is to use a non-
linear model—specifically, odds ratios—rather than standardized coefficients. In that regard,
one assumption of the ordinal regression model is the “parallel regression assumption
[italics original] and, for the ordinal logit [logistic regression] model, the proportional odds
assumption” [italics original] (Long & Freese, 2006: 197) where the intercepts may change,
but the coefficients for the independent variables are unchanged for each equation (see also
Powers & Xie, 1999). When “the assumption of parallel regressions is rejected, alternative
models should be considered that do not impose the constraint of parallel regressions”
(Long, 1997: 145). All of the three models in this study (i.e., command, patrol, and detective
models) were tested with the likelihood-ratio test, particularly with a model
6
command in
Stata (Long & Freese, 2006; Wolfe & Gould, 1998). It is “an omnibus test that the coefficients
for all variables are simultaneously equal” (Long & Freese, 2006: 199), and it evaluates
“how the log likelihood of the ORM would change if the constraint…was removed” (Long,
1997: 143). The test results also showed that all three models in the current study are
appropriate for the data.
3.2. Findings
3.2.1.Descriptive Statistics
The descriptive statistics of all variables (i.e., dependent, explanatory independent, and
control) used in the models are presented in the Table 2.
5
In this section, the “latent” concept does not represent the same thing as it represented in the factor
analysis section.
6
This is not an official Stata command.
31
Intelligence - Led Policing:
How the Use Of Crime Intelligence Analysis Translates in to the Decision-Making
Table 2. Descriptive Statistics for Dependent, Explanatory Independent, and Control Variables
3.2.2. Multivariate Analysis
As indicated in the previous sections, the results from nonlinear models are not easy to
interpret. The ordered logit is mostly “interpreted in terms of odds ratios for cumulative
probabilities” (Long, 1997: 138). In the current study, the results of ordered logit models are
presented in terms of the percent change in odds. In other words, the percent change of the
metric values in the odds of “higher versus lower outcomes” (Long & Freese, 2006: 218) in
the dependent variable will be provided in this section.
Variable
N
Measure
Min.
Max.
Mean
SD
Dependent
Command-level use CAa efforts
519
Ordinal
0
2
1.28
0.621
0 = not utilized
1 = utilized some
2 = highly utilized
Detectives use CAa efforts
521
Ordinal
0
2
1.25
0.627
0 = not utilized
1 = utilized some
2 = highly utilized
Patrol officers use CAa efforts
518
Ordinal
0
2
1.05
0.607
0 = not utilized
1 = utilized some
2 = highly utilized
Explanatory
Factor 1: Statistical analysis
423
Continuous
-2.02
3.94
0
1
Factor 2: Crime analysis
423
Continuous
-2.29
3.3
0
1
Factor 3:
Intelligence analysis
423
Continuous
-2.21
3.64
0
1
Factor 4: Survey analysis
423
Continuous
-1.94
4.21
0
1
Factor 5: Patrol strategy analysis
423
Continuous
-2.56
3.12
0
1
Factor 6:
Displacement analysis
423
Continuous
-3.06
3.74
0
1
Control
Crime analysis unit
517
Dummy
0
1
0.65
0.479
(yes = 1, no = 0)
Unions in the agency
535
Dummy
0
1
0.61
0.489
(yes = 1, no = 0)
Agency size
493
Continuous
0.09
6.32
1.637
0.983
(# of sworn x 1,000
⁄ population)
Total operating budget
535
Continuous
4,554
1,492,567
153,366
112,401
(dollars in 12-month period)
Organizational hierarchy b
535
Continuous
0.19
4.65
1.33
0.627
[(min - max salary)
⁄ min salary]
Crime rates
500
Continuous
0
421.47
61.27
39.17
(# of crimes x 1,000
⁄ population)
a
CA = crime analysis.
b
Unit in dollars.