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The Conjunctive Analysis of Case Configurations: An Exploratory Method for Discrete Multivariate Analyses of Crime Data

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Abstract

Derived from comparative approaches in both qualitative and quantitative research, the current study describes a simple exploratory technique for the multivariate analysis of categorical data. This technique is referred to as the conjunctive analysis of case configurations. After describing the logic and underlying assumptions of this conjunctive method, it is applied and illustrated in the study of the federal sentencing of drug offenders. The relative value of this conjunctive approach for purposes of exploratory data analysis and its overall utility as a method for confirmatory research are also discussed.

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Notes

  1. Technically, there are no limits on the number of case configurations to be included in conjunctive analysis. Miethe and Regoeczi (2004), for example, studied the nature of homicide situations by examining a maximum number of 32,768 possible case configurations involving the conjunctive interrelationships among 15 dummy variables. Most of their major analyses, however, focused on a substantially smaller number of dominant case configurations (n = 25) that represented at least 1,000 homicides per decade. Practical problems of greater interpretative complexity and small cell sizes often limit most applications of conjunctive methods to the analysis of far less than 100 distinct case configurations.

  2. Appendix 1 illustrates the computer syntax and procedures for constructing a conjunctive table of case configurations within several common software packages (e.g., SPSS, STATA, SAS).

  3. These data were collected by the Federal Sentencing Guidelines Commission and are available for secondary analysis through ICPSR at the University of Michigan.

  4. As the initial step in any quantitative inquiry, a brief inspection of the univariate frequency distributions shows that many of these variables are highly skewed. The modal categories for each variable in this sample include drug trafficking (94% of the cases), having a prior record (83%), race (Black = 59%), gender (Male = 86%) and type of sentence (Prison = 92%).

  5. When a saturated model of all possible main and interaction effects was estimated on the full sample (n = 1,358), many of the estimated interaction effects were highly unstable, resulting in unusually large standard errors (e.g., se = 17,974 for the gender x trafficking interaction) and extreme odds ratios (e.g., odds ratio of 2.5 million-to-1 for this same interaction). These dubious estimates are due directly to the adverse impact of the non-random distribution of case attributes within the low-frequency cells (e.g., 18/22 of these cases involve non-drug traffickers without prior records and the majority of them also involve offenders who are white and/or female). No statistically significant interaction effects are found in this saturated model and the type of drug crime (i.e., trafficking vs. other offenses) is the only variable with a significant main-effect on imprisonment risks. This absence of any interaction effects in the saturated model is in sharp contrast to the observed patterns of interaction visually revealed in the conjunctive matrix of Table 4 and confirmed by estimating the “modified” saturated model in Table 5.

  6. The research group for comparative methods for the advancement of systematic cross-case analysis and small-n studies (COMPASS) provides numerous bibliographic sources and software links for conducting various types of comparative configurational analyses (e.g., QCA, fs/QCA (fuzzy set), and mvQCA (multi value). Software for conducting QCA that has been developed by Charles Ragin and associates can be downloaded from reference links in the COMPASS website (http://www.compasss.org).

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Authors and Affiliations

  1. Department of Criminal Justice, University of Nevada, Las Vegas, 4505 Maryland Parkway, Las Vegas, NV, 89154-5009, USA

    Terance D. Miethe & Timothy C. Hart

  2. Department of Sociology, Cleveland State University, 2121 Euclid Avenue, RT1733, Cleveland, OH, 44115-2214, USA

    Wendy C. Regoeczi

Authors
  1. Terance D. Miethe
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  2. Timothy C. Hart
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  3. Wendy C. Regoeczi
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Corresponding author

Correspondence to Terance D. Miethe.

Appendix 1: Software Syntax for Conjunctive Analysis

Appendix 1: Software Syntax for Conjunctive Analysis

For each of the following examples, ABCD = categorical independent variables and Y = categorical dependent variable.

  • SPSS Syntax for Generating Conjunctive Data Matrix:

    • AGGREGATE

    • /OUTFILE = ’cdmatrix_file’

    • /BREAK = A B C D

    • /Y_mean = MEAN(Y)

    • /N_Cases = N.

  • STATA Syntax for Generating Conjunctive Data Matrix:

    • egen N_Cases = count(Y), by (A B C D)

    • collapse (count) N_Cases (mean) Y_MEAN = Y, by (A B C D)

    • list A B C D Y_MEAN N_Cases

  • SAS Syntax for Generating Conjunctive Data Matrix:

    • proc means data = yourdata nway;

    • class a b c d;

    • var y;

    • output out = cdmatrix(drop=_type_ _freq_) mean = n= / autoname;

    • run;

    • proc print data = cdmatrix;

    • run;

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Miethe, T.D., Hart, T.C. & Regoeczi, W.C. The Conjunctive Analysis of Case Configurations: An Exploratory Method for Discrete Multivariate Analyses of Crime Data. J Quant Criminol 24, 227–241 (2008). https://doi.org/10.1007/s10940-008-9044-8

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  • DOI: https://doi.org/10.1007/s10940-008-9044-8

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