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NCJ Number: 68159 Find in a Library
Title: ESTIMATION AND TESTING FOR A MARKOV MODEL OF REINFORCEMENT
Journal: SOCIOLOGICAL METHODS AND RESEARCH  Volume:8  Issue:4  Dated:(MAY 1980)  Pages:434-453
Author(s): P D ALLISON
Date Published: 1980
Page Count: 20
Type: Statistics
Format: Article
Language: English
Country: United States of America
Annotation: NEW METHODS MAKING USE OF EVENTS COUNTS FROM TWO OR MORE ADJACENT INTERVALS OF TIME ARE PROPOSED FOR ESTIMATING AND TESTING A MATHEMATICAL MODEL OF REINFORCEMENT.
Abstract: REINFORCEMENT THEORIES HOLD THAT AN EVENT REINFORCES THE TENDENCY FOR THE SAME EVENT TO RECUR. THE CONTAGIOUS POISSON PROCESS IS A MARKOV PROCESS WHICH HAS BEEN USED TO REPRESENT THE REINFORCEMENT OF EVENTS. STANDARD METHODS FOR ESTIMATING AND TESTING THE MODEL ARE GENERALLY INEFFICIENT AND USUALLY INCONSISTENT. NEW METHODS ARE PROPOSED FOR ESTIMATING THE PARAMETERS OF THE CONTAGIOUS POISSON PROCESS AND FOR TESTING THE MODEL AGAINST THE MORE RESTRICTED COMPOUND POISSON PROCESS. THE PROPOSED METHODS ARE MORE STATISTICALLY EFFICIENT THAN THOSE PREVIOUSLY USED, AND THEY MAKE LESS STRINGENT ASSUMPTIONS ABOUT THE DATA. SINCE THE COMPOUND POISSON IS A VERY RESTRICTIVE HYPOTHESIS, ITS COMPARISON WITH THE CONTAGIOUS POISSON PROCESS ONLY TESTS WHETHER THE RATE OF EVENT OCCURRENCE DOES OR DOES NOT INCREASE WITH TIME. WHETHER REINFORCEMENT DOES OR DOES NOT OCCUR IS NOT DETERMINED. ON BALANCE, THE CONTAGIOUS POISSON PROCESS IS A LIKELY FIRST APPROXIMATION OF REINFORCEMENT, EVEN WHEN MANY OF ITS ASSUMPTIONS APPEAR UNREALISTIC. AT LEAST IT SERVES AS A USEFUL BASELINE FOR DETERMINING WHETHER AND WHAT ELABORATIONS ARE NECESSARY. MATHEMATICAL EQUATIONS, NOTES, AND REFERENCES (CA. 25) ARE PROVIDED. (AUTHOR ABSTRACT MODIFIED)
Index Term(s): Evaluation; Mathematical modeling; Statistical analysis
To cite this abstract, use the following link:
http://www.ncjrs.gov/App/publications/abstract.aspx?ID=68159

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