NCJ Number
60747
Date Published
1979
Length
446 pages
Annotation
TO ACQUAINT CRIMINOLOGISTS WITH THE MATHEMATICAL TOOLS NOW BEING USED TO DO RESEARCH IN CRIME, RECENTLY DEVELOPED METHODS AND THOSE NEWLY ADAPTED TO THE SOCIAL SCIENCES ARE EMPHASIZED.
Abstract
INTENDED FOR CLASSROOM USE, THE TEXT IS ORGANIZED INTO THREE PARTS. THE FIRST PART, SUITABLE FOR A ONE-SEMESTER COURSE IN MULTIVARIATE METHODS, BEGINS WITH BASIC STATISTICAL TECHNIQUES--REGRESSION AND CORRELATION. THESE TECHNIQUES ARE EXTENDED IN SEVERAL WAYS, SUCH AS NONINTERVAL DATA AND DUMMY VARIABLE REGRESSION, SIMON-BLALOCK CAUSAL MODELS AND THE INTERPRETATION OF CORRELATIONS, AND RECIPROCAL CAUSATION. A DISCUSSION FOLLOWS OF PATH ANALYSIS, WHICH APPLIES MULTIPLE REGRESSION TO THE ANALYSIS OF CAUSAL MODELS AND THE ANALYSIS OF DATA COLLECTED AT DIFFERENT TIMES. ALSO DESCRIBED ARE LOGLINEAR MODELS, WHICH CAN BE USED FOR ANALYZING QUALITATIVE VARIABLES. WHEREAS THE FIRST SECTIONS OF THIS PART ARE CONCERNED WITH DIFFERENT WAYS OF PREDICTING ONE VARIABLE FROM A KNOWLEDGE OF OTHERS, THE SECTION ON PRINCIPAL COMPONENT AND FACTOR ANALYSIS IS CONCERNED WITH CLARIFYING THE STRUCTURE OF THE RELATIONSHIP BETWEEN A SET OF VARIABLES. THIS IS PARTICULARLY IMPORTANT IN FORMING COMPOSITE INDEXES THAT CAN SERVE AS NEW VARIABLES. FINALLY, DIFFERENT METHODS FOR CLASSIFYING INDIVIDUALS INTO GROUPS OR CATEGORIES ARE DISCUSSED, A SUBJECT PARTICULARLY INTERESTING IN CONNECTION WITH ATTEMPTS TO PREDICT CRIMINALITY. THE SECOND PART OF THE VOLUME EXPLAINS MODELS OF PROCESSES THAT ARE STOCHASTIC, I.E., PROBABILISTIC. THESE MODELS DO NOT PREDICT INDIVIDUAL EVENTS WITH CERTAINTY; INSTEAD, THEY ASSIGN PROBABILITIES TO EVENTS AND ARE CONCERNED PRIMARILY WITH SEQUENCES OF EVENTS AND THE DISTRIBUTION OF TIME INTERVALS BETWEEN EVENTS. PROBABILITY THEORY IS REVIEWED, AND TWO PARTICULARLY IMPORTANT KINDS OF STOCHASTIC PROCESSES, MARKOV CHAINS AND POISSON PROCESSES, ARE EXAMINED. THE LAST PART OF THE TEXT DISCUSSES ANALYTICAL METHODS DEALING WITH PROPERTIES OF CONTINUOUS (SMOOTH) FUNCTIONS. AREAS COVERED INCLUDE DIFFERENTIAL CALCULUS, INTEGRAL CALCULUS AND ITS APPLICATION TO SPECIFIC PROBLEMS, DIFFERENTIAL EQUATIONS, AND LAPLACE TRANSFORMS. THESE FINAL SECTIONS ARE SUITABLE FOR A ONE-SEMESTER COURSE IN MATHEMATICAL MODELS, WITH EMPHASIS ON THE MODELING OF PROCESSES OF SPECIAL INTEREST TO CRIMINOLOGISTS. EACH CHAPTER IS INDIVIDUALLY REFERENCED. FIGURES, TABULAR DATA, A BIBLIOGRAPHY, NAME AND SUBJECT INDEXES, AND APPENDIXES (ON LEAST SQUARES SOLUTION IN LINEAR REGRESSION, MATRIX ALGEBRA RULES, USEFUL ALGEBRAIC IDENTITIES, DETERMINANTS AND MATRIX INVERSION, AND THE CONTAGIOUS POISSON PROCESS) ARE PROVIDED. (AUTHOR ABSTRACT MODIFIED--PRG)