Stepwise Regressions

described insection 3.4.

be dropped due to singularity problems). A first regression, using all variables determined 44 variables to be significant at a five percent level. Since k must be arbitrarily chosen, we take k=50 for the inclusion- and a less conservative choice of k=80 for the exclusion threshold and set c=493. So, instead of using 0.05 and 0.2 as the in- and exclusion probabilities, we try to lessen the selection bias by using the adjusted thresholds of p₁= 0.05₄₉₃⁵⁰ ≈0.005 and p₂=0.2₄₉₃⁸⁰ ≈0.03.

Hendrey and Krolzig(2000) show that these adjustment can be avoided when the data mining algorithm accounts for the selection bias as is the case with their software PcGETS. However, this accumulation of statistical tools didn’t achieve any better results for a restricted test set of 200 studies⁴⁹. Therefore, we resort to the well studied stepwise regression methods.

Backward Stepwise Regression

The basic procedure of the stepwise regression algorithms implemented in STATA is rather simple.

Both methods, backward and forward are very similar.

1. start with the full model,

2. exclude the least significant variable if its p-value is above p₂,

3. include the most significant excluded variable if its p-value is belowp₁, 4. exclude the least significant included variable if its p-value is abovep₂, 5. re-estimate and repeat steps 3 to 4 until neither is possible.

Forward Stepwise Regression

The forward procedure typically finds less variables than the backward procedure but is method-ologically almost identical:

1. start with the empty model,

2. include the most significant variable if its p-value is belowp₁,

3. exclude the least significant included variable if its p-value is abovep₂, 4. include the most significant excluded variable if its p-value is belowp₁, 5. repeat steps 3 to 4 until neither is possible.

The stepAIC-Algorithm

The applied algorithm is similar to the sw-algorithm. It adds and drops variables but evaluates the changes in the model-fit (the Aikaike Information Criterion) instead of the significance values.

The algorithm stops as soon as any further improvement is smaller than a certain threshold-value;

see alsoVenables and Ripley(2002) for more detailed information.

We use the implementation in R with the default settings. Each algorithm is applied to the whole data set (backward) and to the empty data set (forward). The results of these two algorithms are given intable 3.52.

49One reason may be that it does fit time series models better than our data set of very heterogenous cross sections.

Table 3.52: Multivariate analysis - stepwise regressions

sw stepAIC

Variable var 1c 1t 2c 2t 3c 3t 4c 4t

Study: publication, page begin 99.8 0.01 4.0 0.01 3.9

Study: publication, page end 100.0 −0.01 −4.3−0.01 −4.1

Study: not explorative 4.0 −0.49 −2.6−0.44 −2.4

Study: measuring points 97.4 0.00 3.1 0.00 3.1

Study: year of first measure 84.4 0.00 −2.9

Study: time span in months 63.2 −0.00 −3.0−0.00 −2.9

Study: size of first population 24.9 0.00 2.9 0.00 2.3

Study: size of second population 0.9 0.00 4.8 0.00 3.8 0.00 1.6

Study: size of first sample 25.6 0.00 −3.7 0.00 −1.7

Study: size of second sample 1.2 0.00 4.9 0.00 −1.7

Study: size of first realized sample 58.8 0.00 −3.8 0.00−4.9 0.00 −9.2 0.00 −7.8

Study: size of second realized sample 2.4 −0.00−14.1−0.00−7.6−0.00 −7.7 0.00 −5.5

Study: rate of return of first sample 13.0 0.00 1.6

Study: rate of return of second sample 0.9 −0.02 −2.3

Study: maximum age in first sample 5.7 −0.02 −4.3−0.02 −3.5

Study: mean age in first sample 5.0 0.02 3.0 0.02 1.8

Study: check for validity 2.1 −0.43 −1.4

Study: tests of significance 9.4 −0.67 −3.4−0.59−2.6−0.58 −4.5−0.64 −4.8

Study: number of bivariate estimates 32.4 0.01 3.2 0.01 3.3 0.01 3.0

Study: user, tr 48.6 −1.11−5.0−0.53 −3.4−0.65 −3.8

Study: user, aw 29.3 0.42 3.1 0.45 3.1

Study: user, mw 1.4 0.77 3.5 0.48 2.0

Study: publication, journal article 13.7 0.53 3.0 0.36 1.9

Study: publication, working paper, report 4.9 −0.97 −4.1−1.11 −4.6

Study: publication, miscellaneous type 3.3 −0.48 −1.7−0.60 −2.0

Study: publication, not a dissertation or master thesis, etc. 2.3 −1.63 −4.3−1.53 −3.8

Study: author, Steven D. Levitt 1.7 1.94 6.3 1.75 5.3

Study: author, William C. Bailey 2.7 0.62 2.8

Study: author, David W. Rasmussen 1.3 −1.45 −4.6−1.85 −5.5

Study: author, Theodore G. Chiricos 1.2 0.64 1.7

Study: author, Dale O. Cloninger 1.5 0.81 2.9

Study: author, Simon Hakim 1.0 −1.36 −4.1−1.74 −4.9

Study: author, Raymond Paternoster 2.4 −0.76 −2.5−0.83 −2.7

Study: author, Isaac Ehrlich 1.0 −1.63 −4.1−1.70−2.8−0.71 −2.0−1.17 −3.2

Study: author, Matti Vir´en 0.8 −1.54 −3.4−2.54 −5.8

Study: author, Ann Dryden Witte 1.0 0.71 1.8

Study: author, Maynard I. Erickson 0.6 1.06 3.9 1.27 1.7

Study: author, Jack P. Gibbs 0.9 −1.42 −2.4

Study: author, Alex R. Piquero 1.3 −0.69 −2.0−1.33 −3.6

Study: author, other author 22.5 −0.38 −3.2

Study: journal, Criminal Justice 2.2 0.54 2.0

Study: journal, Criminal Law and Criminology 2.2 −0.41 −1.8

continued on the next page. . .

. . . last page oftable 3.52continued

sw stepAIC

Variable var 1c 1t 2c 2t 3c 3t 4c 4t

Study: journal, Social Forces 2.2 −0.47 −1.8−0.77 −2.9

Study: journal, Law and Society Review 2.8 0.55 2.4

Study: journal, American Journal of Economics and Sociology 1.7 0.50 1.9

Study: journal, Public Economics 1.1 1.07 2.4

Study: journal, Social Problems 1.6 0.53 1.7

Study: journal, Accident Analysis and Prevention 2.2 −0.82 −3.1−0.98 −3.2

Study: journal, Studies on Alcohol 1.1 −0.99 −2.6

Study: journal, Criminology 4.5 0.43 2.5 0.51 2.8

Study: journal, Social Science Quarterly 2.2 −0.84−4.3−0.60 −2.5−0.47 −1.9

Study: journal, Legal Studies 2.0 −0.49 −2.0

Study: publication, United Kingdom 8.3 0.60 4.3 0.69 4.8

Study: publication, Canada 3.6 −0.83 −2.8

Study: publication, Netherlands 2.6 0.61 2.8 0.64 2.9

Study: author, Germany 3.2 2.51 4.5 0.91 2.5

Study: author, USA 21.3 0.27 1.7

Study: author, Switzerland 1.0 1.41 4.6 3.25 5.2 3.35 5.3

Study: author, Finland 0.8 −0.43 −3.1−0.97−2.7

Study: author, Netherlands 1.3 1.50 2.6 1.02 3.0 1.56 3.8

Study: author, Australia 2.0 0.68 2.6 1.02 2.9

Study: author, Sweden 0.9 2.02 4.3 2.73 7.1 2.79 5.4

Study: author, other country 3.7 0.73 3.7 0.82 3.4

Study: author, criminology 11.3 0.63 5.1 0.61 4.3

Study: author, psychology 4.2 −0.43 −2.1−0.58 −2.4

Study: author, law 3.6 0.27 1.5

Study: publication, economics 36.0 −0.58 −5.5−0.46 −4.3

Study: publication, type not applicable 0.4 −1.40 −3.5−2.07−3.6−2.67 −4.6−2.97 −4.9

Study: publication, criminology 20.5 1.03 6.4

Study: publication, sociology 19.4 0.70 3.9

Study: publication, miscellaneous 14.1 −0.44 −3.3

Study: publication, psychology 2.8 −1.42 −5.3−0.82 −2.8

Study: institute, sociology 21.3 −0.19 −1.6

Study: institute, miscellaneous 14.9 0.88 4.2 0.74 3.7 0.94 8.5 0.86 7.2

Study: cross section 23.2 0.48 2.7 0.39 3.8 0.29 2.6

Study: single survey 17.8 −0.51−2.8 −0.73 −3.1

Study: repeated survey 3.1 0.93 3.6 0.45 1.5

Study: panel survey 5.6 −0.87 −3.2

Study: experiment (laboratory) 4.4 −1.47 −4.4

Study: experiment (field, researcher initiative) 1.6 1.39 4.3

Study: experiment (field, institutional initiative) 1.6 −0.97 −3.4−1.23 −3.8

Study: experiment (natural) 3.0 0.47 2.3

Study: not experimental 15.9 −0.60 −2.1

Study: quasi experimental 8.8 −0.63 −2.2

Study: first population, Germany 2.7 −1.98 −3.6

continued on the next page. . .

. . . last page oftable 3.52continued

sw stepAIC

Variable var 1c 1t 2c 2t 3c 3t 4c 4t

Study: first population, United Kingdom 5.0 0.76 3.0

Study: first population, USA 23.3 0.61 2.3 1.00 4.8

Study: first population, Canada 4.3 0.56 2.7 1.39 4.6 2.04 8.3 1.98 7.9

Study: first population, Sweden 1.4 −1.00 −2.2

Study: first population, Finland 0.9 −0.42 −2.6

Study: first population, Switzerland 1.0 0.61 2.8 −1.24 −1.8−1.40 −2.2

Study: first population, Australia 1.7 −1.10 −3.0

Study: first population, Netherlands 1.3 −1.22 −2.8

Study: first population, other country 6.2 1.31 3.4 1.48 5.7 0.56 3.2

Study: second population, other country 3.3 0.97 2.4

Study: sample base, first population, complete country 36.9 −1.82 −3.4−1.77 −3.2

Study: sample base, first population, partial country 37.4 −2.16 −4.2−2.05 −3.8

Study: sample base, second population, complete country 2.4 −3.60−9.2−2.99 −5.5−2.22 −4.0 Study: sample base, second population, partial country 2.2 −3.51−5.6−3.95 −5.9−3.78 −5.4

Study: sample unit, first population, states 21.9 0.45 2.6 0.40 4.2 0.37 3.8

Study: sample unit, first population, miscellaneous 7.4 0.97 6.5 0.92 6.0

Study: sample unit, second population, individuals 1.7 1.78 3.0 2.72 4.3

Study: sample individuals, first population, population 36.2 0.40 3.7−0.51 −4.0

Study: sample individuals, first population, students 11.7 −0.55 −3.1

Study: sample individuals, first population, pupils 3.0 1.53 6.7 1.00 3.7

Study: sample individuals, second population, population 2.6 4.28 8.2 4.70 7.7 3.68 5.8 Study: sample individuals, second population, miscellaneous 1.2 4.71 6.5 3.70 5.4 3.36 4.4 Study: sample individuals, second population, students 0.5 −3.44 −3.5 1.80 2.9

Study: sample individuals, second population, pupils 0.2 3.44 6.0 1.59 1.4

Study: sample of extreme groups 0.5 1.21 2.2

Study: complete sample 9.8 −0.64 −5.2−0.73 −5.8

Study: PKS is public data base 1.2 1.07 2.6 3.45 7.0 2.35 4.6

Study: miscellaneous public data base 40.1 0.96 6.9 0.83 5.6

Study: UCR is public data base 22.9 0.63 4.0 0.56 3.4

Study: no public data base 26.3 0.61 4.3 0.66 4.5

Study: income representative 1.1 0.58 1.5

Study: education below average 0.1 −1.69 −1.4

Study: no class overrepresented 0.9 1.62 3.2

Study: no social fringe group 0.6 −0.99−3.1−2.13 −3.6−1.65 −2.7

Study: percentage of convicted>75% 0.6 1.50 4.1 2.02 3.7 1.31 2.3

Study: percentage of convicted>51−75% 0.3 −1.28 −2.9 1.13 1.8

Study: main location>500000 inhabitants 3.5 −1.68−2.3−1.84 −9.1−1.87 −8.9

Study: main location<5000 inhabitants 0.2 −3.04−10.2−2.80−4.9−7.38 −7.7−6.92 −7.0

Study: small cities overrepresented 1.1 1.00 2.6 0.74 1.8

Study: does not claim to be representative 32.5 −0.36 −4.0−0.26 −2.9

Study: claims to be representative 19.4 −0.57 −4.5−0.47 −3.5

Study: does not check representativeness 26.9 0.47 3.0 0.45 4.8 0.49 5.0

Study: checks representativeness 2.9 −0.63 −3.1

continued on the next page. . .

. . . last page oftable 3.52continued

sw stepAIC

Variable var 1c 1t 2c 2t 3c 3t 4c 4t

Study: does not report representativeness checks 2.2 −0.80−3.2−0.75 −2.5−0.92 −3.0

Study: reports representativeness checks 0.4 −1.34 −2.4

Study: closed questions for pretest 21.5 1.10 4.2 0.81 4.5 1.20 5.9

Study: mixed questions for pretest 2.1 2.06 5.0 1.43 4.5 1.56 4.7

Study: open questions for pretest 1.4 −1.04 −3.2−0.76 −2.2

Study: Guttman reliability method 0.2 5.74 4.0 5.82 4.0

Study: miscellaneous reliability method 0.3 −4.42−4.0−3.87 −4.2−4.45 −4.4

Study: correlational reliability method 0.2 −1.77−10.6−1.18−5.5−2.91 −3.6−3.52 −4.2

Study: variables reliable 3.9 1.06 4.5 1.22 4.6

Study: validity test of all variables 0.2 3.88 2.9

Study: miscellaneous validity check 0.4 −1.85 −1.6

Study: criteria validity 1.0 1.32 2.7

Study: the variables are not valid 0.2 −1.64 −3.8

Study: conditions for significance check fulfilled 49.2 0.15 1.6

Study: conditions for significance check not fulfilled 3.6 0.52 2.6 0.44 1.9

Study: quality index 100.0 −0.09 −3.7−0.06 −2.4

Estimate: exogenous, number of categories 35.3 0.00 2.0

Estimate: endogenous, begin of observation (year) 78.5 0.00 2.2

Estimate: endogenous, number of categories 17.3 −0.01 −1.8

Estimate: deterrence is focus-variable 14.8 −0.30 −2.8−0.35 −3.4

Estimate: complete sample 14.9 −0.20 −1.9−0.17 −1.7

Estimate: sub-sample of males 1.4 −0.51 −1.7−0.50 −1.6

Estimate: sub-sample of adults 0.5 −0.66 −1.4

Estimate: sub-sample of youths 1.3 −0.59 −1.8−0.68 −2.0

Estimate: sub-sample of non-urban area 0.8 −1.02 −3.0 −1.79 −4.2−1.68 −3.8

Estimate: exogenous, index multiplicative 1.9 1.03 3.1

Estimate: exogenous, index additive 0.6 −1.05 −2.1

Estimate: exogenous, index mean 0.0 −1.15 −3.8−3.76−5.4

Estimate: exogenous, index items unprocessed 2.8 1.19 3.1 0.43 1.5 1.21 5.5

Estimate: exogenous, index items miscellaneous 0.2 1.79 2.2

Estimate: exogenous, index items standardized 0.2 0.63 3.4 2.26 2.8

Estimate: study type, crime data 45.3 −1.13 −8.8−1.46 −4.3

Estimate: study type, survey 24.4 −2.13 −2.9−3.10 −3.6

Estimate: study type, experiment 12.7 −2.65 −2.8

Estimate: study type, death penalty 8.2 1.20 4.5

Estimate: exogenous, death penalty, existence of death penalty 1.0 1.26 3.6 1.03 3.1 0.65 1.4

Estimate: exogenous, death penalty, execution rate 4.8 −0.52 −1.5

Estimate: exogenous, death penalty, other 1.5 −0.45 −1.6−0.85 −2.0

Estimate: exogenous, crime data, clearance rate 5.3 0.56 3.3 0.57 3.2

Estimate: exogenous, crime data, arrest rate 9.5 −0.83 −3.4

Estimate: exogenous, crime data, conviction rate 3.9 −0.36 −2.1−0.39 −2.2

Estimate: exogenous, crime data, parole rate 0.2 −1.09 −4.4

Estimate: exogenous, crime data, incarcerations (absolute or per capita) 0.9 1.61 4.7 1.50 4.3

continued on the next page. . .

. . . last page oftable 3.52continued

sw stepAIC

Variable var 1c 1t 2c 2t 3c 3t 4c 4t

Estimate: exogenous, crime data, incarceration rate 0.6 0.77 2.0 0.67 1.8

Estimate: exogenous, crime data, mean sentence length (sentenced) 2.0 0.89 3.9 1.06 4.6 1.15 5.0 Estimate: exogenous, crime data, mean sentence length (served) 1.7 0.73 2.9 0.77 3.0

Estimate: exogenous, crime data, police expenditures 4.0 1.43 3.3 1.54 8.3 1.48 7.8

Estimate: exogenous, crime data, police strength 7.9 1.53 4.1 1.44 10.1 1.37 9.6

Estimate: exogenous, crime data, other 8.5 0.69 5.0 0.63 4.5

Estimate: exogenous, crime data, probation rate 0.2 1.08 1.5 1.11 1.6

Estimate: exogenous, crime data, incarceration per crime 0.9 −0.61 −1.8−0.57 −1.6

Estimate: exogenous, crime data, convicted per crime 0.6 −0.88 −2.2−0.83 −2.1

Estimate: exogenous, survey, surveyed is delinquent 2.9 0.55 2.5

Estimate: exogenous, survey, is experiment 23.1 0.94 1.6 0.94 1.5

Estimate: exogenous, survey, is no experiment 0.9 2.43 2.7 3.01 4.3 2.66 3.6

Estimate: exogenous, survey, probability of detection by police 7.1 −0.85−4.2−0.65 −4.0−0.75 −4.5 Estimate: exogenous, survey, probability of punishment by justice 4.5 −0.93−4.6−0.79 −4.0−0.83 −4.3 Estimate: exogenous, survey, prob. of punishment by employment law 0.6 −0.87−2.9

Estimate: exogenous, survey, prob. of detection by friends or family 0.2 −1.10 −3.1−2.24−3.9−1.51 −2.1−1.41 −1.9 Estimate: exogenous, survey, prob. of punishment by friends or family 1.6 −0.87 −3.5−1.52−5.8−1.21 −4.4−1.34 −4.7 Estimate: exogenous, survey, probability of punishment by others 0.9 0.54 1.5

Estimate: exogenous, survey, severity of punishment by others 0.4 1.49 3.0 1.35 2.7

Estimate: exogenous, survey, time between offense and clearance 0.1 −1.49−2.8−1.11 −1.4−1.10 −1.4

Estimate: exogenous, survey, relates to the present 21.3 0.80 2.6 1.44 2.1 2.01 2.5

Estimate: exogenous, survey, relates to the past 2.7 1.08 4.0 1.13 3.5 1.92 2.6 2.60 3.2

Estimate: exogenous, experiment, yes 7.2 3.02 3.4

Estimate: exogenous, experiment, no 5.4 1.01 3.1 2.93 3.3

Estimate: exogenous, experiment, experimental variation of probability of detection

2.1 −1.72−3.9−1.42 −5.4−1.17 −4.0

Estimate: exogenous, experiment, other 2.2 0.46 1.8 0.44 1.5

Estimate: exogenous, experiment, relates to the present 13.9 −0.79 −3.3

Estimate: exogenous, experiment, relates to the past 0.5 −1.37 −2.2

Estimate: exogenous, relates to one year 42.7 0.39 2.3 0.86 7.4 0.64 4.8

Estimate: exogenous, relates to more than one year 12.1 −0.47 −2.8

Estimate: exogenous, metric category 36.8 1.55 3.4

Estimate: exogenous, interval category 9.1 1.57 3.2

Estimate: exogenous, binary category 18.8 1.56 3.4

Estimate: exogenous, nominal category 0.3 −3.59 −3.1−2.62 −2.1

Estimate: exogenous, ordinal category 7.4 0.52 3.0 1.90 3.9

Estimate: exogenous, in logs 20.2 −0.21 −1.5−0.28 −2.0

Estimate: exogenous, in differences 3.1 0.77 3.2 2.01 3.4 1.73 7.0 1.73 7.1

Estimate: exogenous, not in differences 0.2 1.25 1.8

Estimate: exogenous, not other transformation 10.1 −0.59 −3.9−0.70 −4.3

Estimate: endogenous, index miscellaneous 0.1 3.06 6.2 2.09 1.9 2.06 1.9

Estimate: endogenous, index multiplicative 0.2 3.79 2.7 1.38 1.5 1.98 2.0

Estimate: endogenous, number of reported crimes (absolute numbers) 11.1 0.30 2.3

continued on the next page. . .

. . . last page oftable 3.52continued

sw stepAIC

Variable var 1c 1t 2c 2t 3c 3t 4c 4t

Estimate: endogenous, number of registered suspects 0.6 1.35 3.1 1.50 3.3

Estimate: endogenous, number of convicted to prison sentence 0.2 1.33 3.8 2.19 3.1 2.16 2.9 Estimate: endogenous, probability of future delinquency (surveyed is

delinquent)

4.1 −0.31 −1.5

Estimate: endogenous, probability of delinquency of fictitious offense (surveyed is delinquent)

1.2 0.68 2.0 1.36 3.6

Estimate: endogenous, recidivism 0.7 1.26 2.5 1.94 3.6 2.24 3.9

Estimate: endogenous, accidents 4.2 0.83 2.9 1.09 5.2 0.82 3.5

Estimate: endogenous, violating prescriptive limits 2.9 −0.71 −2.5

Estimate: endogenous, relates to less than one year 29.2 0.58 4.7 0.45 3.3

Estimate: endogenous, relates to more than one year 11.5 0.22 1.6 0.51 3.0

Estimate: endogenous, lifelong self reported delinquency 3.8 −0.46 −2.3

Estimate: endogenous, one year of self reported delinquency 8.2 0.41 2.3

Estimate: endogenous, self reported delinquency since age of fourteen 0.6 2.34 4.8 2.01 4.0 Estimate: endogenous, less than one year of unlimited future self

re-ported delinquency

1.2 −0.56 −1.5

Estimate: endogenous and exogenous relate not to the same offense 6.3 0.58 3.8 0.69 4.4

Estimate: crime category, misdemeanors 9.5 −0.98 −6.6−0.96 −5.9

Estimate: crime category, formal deviant behavior 2.5 0.75 3.1 0.77 3.0

Estimate: crime category, violation of game-rules 2.4 0.74 2.7

Estimate: crime category, other 1.5 0.73 2.4 0.95 2.9

Estimate: offense, assault 10.1 −0.24 −2.1−0.29 −2.4

Estimate: offense, negligent assault 1.8 0.64 2.4 0.79 3.0

Estimate: offense, burglary 12.2 0.22 1.9 0.29 2.5

Estimate: offense, larceny (severe) 3.2 −0.37 −1.8−0.57 −2.7

Estimate: offense, drug possession (soft) 0.7 2.58 3.0 2.27 5.2 2.42 5.0

Estimate: offense, drug possession (hard) 0.5 −3.27−2.4−3.01 −5.0−3.39 −5.4

Estimate: offense, drug related crime (general) 4.4 −0.52 −2.6

Estimate: offense, other sexual related crimes 0.8 0.59 1.5

Estimate: offense, speeding 1.1 0.74 2.2 0.72 1.8

Estimate: offense, drunk driving 12.1 0.30 2.0 0.46 2.6

Estimate: offense, fare dodging 0.4 1.19 2.0 1.03 1.8

Estimate: offense, fraud 3.9 0.34 1.8 0.31 1.5

Estimate: offense, tax evasion 7.3 0.49 2.8 0.53 2.9

Estimate: offense, embezzlement 0.1 −1.87−2.9

Estimate: offense, other 7.1 −0.70 −4.3−0.83 −4.6

Estimate: offense, vehicle theft 8.5 0.35 2.6 0.28 2.1

Estimate: offense, environmental crimes, Violations of prescriptive limits 2.3 1.43 4.7 1.14 4.3

Estimate: property and violent characteristics 48.8 0.37 2.3 0.37 4.6 0.44 4.6

Estimate: violent characteristics 15.1 0.21 1.7

Estimate: endogenous, metric category 19.5 −1.16 −2.1

Estimate: endogenous, interval category 4.1 −0.85 −1.4

Estimate: endogenous, ordinal category 4.6 −1.25 −5.6−2.46 −4.2

continued on the next page. . .

. . . last page oftable 3.52continued

sw stepAIC

Variable var 1c 1t 2c 2t 3c 3t 4c 4t

Estimate: endogenous, binary category 9.6 −0.63−2.5−1.17 −8.8−2.46 −4.4

Estimate: endogenous, nominal category 0.3 −1.40 −1.6

Estimate: endogenous, not in logs 32.0 0.59 3.0 0.68 3.3

Estimate: endogenous, in logs 26.8 0.57 2.5 0.68 2.9

Estimate: endogenous, other transformation 7.8 −1.26−2.4−1.49 −9.3−1.62 −9.7

Estimate: endogenous and exogenous relate to the same time 28.0 −0.57 −2.4−0.92 −3.8 Estimate: endogenous occurs after exogenous (lagged exogenous) 25.6 −0.43 −1.7−0.68 −2.7

Estimate: covariate, age 20.2 −0.33 −3.3−0.35 −3.4

Estimate: covariate, marital status 5.6 0.43 2.5 0.53 3.1

Estimate: covariate, profession 0.4 0.87 1.6 1.04 1.9

Estimate: covariate, social integration 1.5 0.51 1.7 0.84 2.5

Estimate: covariate, religion 1.7 0.49 1.7 0.56 1.9

Estimate: covariate, social class 0.8 −1.06 −2.9−1.51 −4.0

Estimate: covariate, drug usage 1.3 −1.22 −3.6−1.38 −4.1

Estimate: covariate, acceptance of norms 2.2 −0.47 −1.7

Estimate: covariate, morality 1.6 0.52 2.9 1.05 3.5 1.00 3.1

Estimate: covariate, personal characteristics 3.0 −0.57 −2.5−0.76 −3.1

Estimate: covariate, fixed effects (spatial) 10.0 −0.58 −4.4−0.39 −2.8

Estimate: covariate, fixed effects (time) 12.0 −0.30 −2.4

Estimate: covariate, random effects 1.0 1.02 3.1 1.00 3.0

Estimate: covariate, other 35.8 0.15 1.6 0.21 1.8

Estimate: covariate, time trend 5.4 0.35 2.2 0.35 2.1

Estimate: covariate, poverty, welfare 6.4 1.03 3.5 0.97 3.3 0.69 4.8 0.73 4.9

Estimate: covariate, urbanity 8.2 0.80 3.2 0.41 3.2 0.44 3.4

Estimate: covariate, GDP 1.4 −0.98 −3.2−1.04 −3.4

Estimate: covariate, population (-growth) 11.5 0.47 4.0 0.44 3.7

Estimate: covariate, alcohol (consumption) 1.7 0.67 2.5 0.92 3.2

Estimate: covariate, labor force 2.5 −0.34 −1.6−0.35 −1.6

Estimate: covariate, consumption 2.0 −0.68 −2.7−0.81 −3.2

Estimate: covariate, risk propensity 0.8 0.85 3.4 1.27 3.9 2.39 5.6 2.22 5.1

Estimate: not linear model 15.1 −0.41 −2.1

Estimate: additive model 6.3 0.26 1.4 0.35 1.5

Estimate: not additive model 1.6 0.81 2.1

Estimate: correction for simultaneity (with variables) 9.1 −0.40 −2.1

Estimate: no correction for simultaneity 19.3 −0.69−3.3−1.00 −8.9−1.18 −7.6

Estimate: no error correction 12.8 0.22 2.0

Estimate: weighted model 6.8 0.41 2.8 0.35 2.4

Estimate: bivariate method, bivariate regression 0.6 −1.36−2.9−1.30 −3.4−1.80 −4.3

Estimate: bivariate method, other nonparametric test 0.1 −2.08 −1.8

Estimate: bivariate method, correlation 9.5 0.59 4.0 −0.52 −2.6

Estimate: bivariate method, differences (means, percentages, etc.) 4.0 −0.56 −2.3

Estimate: bivariate method, point biserial correlation 0.4 −0.69−3.0−1.02 −1.9−1.59 −2.8

Estimate: bivariate method,ρ 0.5 −2.23 −4.3−3.03 −4.6

continued on the next page. . .

. . . last page oftable 3.52continued

sw stepAIC

Variable var 1c 1t 2c 2t 3c 3t 4c 4t

Estimate: bivariate method, t-test for independent samples 0.5 −1.43 −2.7−1.77 −3.2

Estimate: bivariate method, t-test for dependent samples 0.6 −0.99 −1.9

Estimate: bivariate method,τ 0.9 −0.64 −1.7−1.33 −3.2

Estimate: bivariate method, ANOVA 2.1 0.82 3.2

Estimate: bivariate method, other 1.0 1.13 3.2

Estimate: bivariate method, Wilcoxon 0.2 −0.74 −2.8

Estimate: bivariate method, binomial 0.2 1.51 10.2 0.85 3.6

Estimate: multivariate method, OLS 24.2 −0.61 −3.2

Estimate: multivariate method, 2SLS 9.8 −0.60−2.5−0.64 −5.0−1.39 −6.1

Estimate: multivariate method, GMM 0.8 0.78 2.0

Estimate: multivariate method, poisson regression 1.1 −0.43 −1.4−1.07 −2.9

Estimate: multivariate method, other ML method 1.1 1.11 2.9

Estimate: multivariate method, other 5.1 −0.75−2.3−0.61 −3.9−1.26 −6.6

Estimate: multivariate method, ANOVA 0.4 −1.69 −3.4−1.57−4.6 −1.69 −2.8

Estimate: multivariate method, GLS 1.7 −0.97−2.5−1.70 −6.2−2.36 −7.0

Estimate: multivariate method, VAR 0.6 −1.07 −2.3

Estimate: multivariate method, path analysis 1.3 −0.60 −2.1−1.30 −3.8

Estimate: multivariate method, ARIMA 4.2 −0.62 −3.4−1.24 −5.0

Estimate: multivariate method, COX regression 0.3 1.89 8.2 2.63 4.9 1.82 2.7 1.66 2.4

Estimate: test of significance 5.5 0.54 3.0 0.52 2.8

Estimate: square root of sample size for negative values 79.2 −0.02 −4.2−0.01−4.5−0.01−12.5−0.01−13.3 Estimate: square root of sample size for positive values 82.5 0.05 6.9 0.05 8.2 0.05 28.8 0.05 26.5

Constant −1.36 −6.5−1.89−5.0 0.04 0.0 1.12 4.1

The numbers in the headline are: 1=forward (R²=0.282, 44 variables), 2=backward (R²=0.369, 81 variables), 3=forward (R²=0.4415, 215 variables), 4=backward (R²=0.4442, 258 variables). The first two regressions (1 and 2) have clustered standard errors (each study is one cluster), the last two do not. The selection criteria is the significance of each variable in the first two regressions and the AIC improvement in the latter. candtare the coefficients and the corresponding t-values of the included variables. The adjusted in- and exclude probabilities are 0.005 and 0.03 in the first two regressions. The columnvar refers to the variation of a variable (i.e., the percentage of valid observations); the maximum variation for dummy variables is fifty percent. The reference category for dummies is usually the opposite property or, in the case of multiple categories, the missing values.

end of thetable 3.52

As expected, both backwards methods yield more variables (84 by the sw and 270 by stepAIC algorithm) than those methods which start with an empty set (44 and 234). Due to the unavailabil-ity of an existing implementation in R, the stepAIC-method does not use clustered standard errors and therefore yields even more significant variables. Out of the 270 (234) variables 203 (174) are significant at a 0.03 level and still 156 (141) are significant at a 0.005 level.

It is somewhat surprising that the stepAIC-algorithm has selected so many authors to be of ma-jor influence. While most of the coefficients have the same sign as in the bivariate comparison (table 3.36), some do not: Piquero has published significantly larger (i.e., less negative) normal-ized t-values but his dummy has a negative sign in regression three and four. This means that much

of his larger (normalized) t-values can be explained by other factors. There are only two authors who are included in all four regressions: Ehrlich and Vir´en (the Vir´en-dummy and the Finnish author dummy are identical) and both are negative. All other authors are either in line with the bivariate results or appear only in one regression. Whether these author dummies should be inter-preted as evidence of a publication bias or are more associated with unobserved heterogeneity is difficult to judge in this context. Among the nationality of the authors, Sweden, Switzerland and the Netherlands stand out, all bearing large positive coefficients, all being highly significant.

Concerning the discipline of the authors, experience suggests that criminologists and sociolo-gists have larger (i.e., more positive) normalized t-values than economists. While this is supported by the bivariate analysis (table 3.27), the stepwise regressions show a more differentiated picture.

Although the general trend is supported by the publication- and discipline-dummies, there are differences within each discipline. For example, studies published in “Criminology” have larger (normalized) t-values while those in “Criminal Law and Criminology” are smaller. The same can be observed for “Social Problems” and “Social Sciences Quarterly”.

Among the implemented deterrence variables, the clearance rate seems to be very interesting.

While it is associated with more negative (normalized) t-values in the bivariate case, its influence has been reversed in the regressions above. The mean sentence length has now a positive effect on the (normalized) t-values (i.e., is less in favor of the deterrence hypothesis) while it is ambiguous in the bivariate case. The same applies to the ‘other” deterrence variables. The rest of the deterrence variables are in line withtable 3.44.

Furthermore, it is interesting to note that those models which use transformed exogenous vari-ables tend in different directions. Untransformed varivari-ables or those in logarithms are associated with more negative results. The opposite is the case for the endogenous variables. Most covari-ates have still the same influence as intable 3.45, but some change. Age and especially personal characteristics and the social class switch their signs and are now associated with more negative (normalized) t-values. Marital status and the time trend also switch, but in the opposite direction.

Intable 3.40it seems to be that studies using surveys or crime data are associated with larger (normalized) t-values. This picture is put into perspective by the results above. When other factors are accounted for (e.g., disciplines of authors or publishers), results based on surveys and crime data are even associated with more negative (normalized) t-values. As expected, the results for studies about the death penalty yield larger t-values.

Results based on misdemeanors are significantly related to more negative (normalized) t-values, while the opposite can be found for results which are based on accidents. This fits very well to the common expectation that offenses based on utility considerations are more readily accessible by deterrence measures, while drunk driving is often committed by people who do not react to deterrence. The latter is also supported by the inclusion and the positive sign of the drunk driving variable. Only vehicle theft does not fit into this picture. Regarding the studied offenses, some in-teresting observations emerge: although only based on very few observations, the deterrent effects based on the possession of hard drugs are strongly negative, while those based on the possession

of soft drugs are almost equally strong but positive. This supports the view that possession (and usage) of marijuana, for example, is less affected by anti-drug laws, while people more readily react when, for example, crack is involved. Obviously, this might be partially explained by the more severe penalty for possessing hard drugs and by the larger public acceptance of soft drugs.

It is somewhat surprising that almost all included variables describing the method of analysis bear a negative sign. The correlation-dummy is a rare exception with inconsistent results (positive sign by the sw-algorithm, negative sign by the stepAIC-algorithm). Although COX-regressions are only rarely used, the associated dummy stands out because it is chosen by all four regressions.

The opposite effect is found for 2SLS and GLS models which are significantly associated with smaller (i.e., more negative) estimates. Furthermore, it seems to be the case that methods which do not consider simultaneity overestimate deterrent effects.

Other noteworthy observations are that results from studies using Canadian data are less in favor of deterrence. The same applies when the nation under study does not belong to the most frequent nations. Results which are entered by the user tr into the data base appear to be significantly more negative. This is probably explained by the fact that he entered all economic studies while all other users entered the sociological and criminological studies; tr also worked at a different location, while all other users worked in the same department. The possibility of any intentional bias can be excluded. Positively signed offenses included in the regressions are drunk driving, environmental offenses, fraud, tax evasion, negligent assault, burglary, vehicle theft. Negatively signed are severe larceny, assault, drug related crimes, as well as assault. Results are more in favor of the deterrence hypothesis if deterrence is the focus of the study. The high significance of the realized sample sizes is a bit odd. These variables are not diversified by the sign of the results, as is the case with the number of observations. Since the latter are included in every regression, the relationship, explained insection 3.4, should already be taken care of. Again, also the stepwise regression methods include some variables with only very little variation. These seem to catch some oddities in the data which cannot be explained sufficiently by more general variables.

Im Dokument Meta Analysis of Crime and Deterrence : A Comprehensive Review of the Literature (Seite 166-177)