The “numerical method ” in medicine goes back to Pierre Louis ’ study of pneumonia (1835), and John Snow’s book on the epidemiology of cholera (1855). Snow took advantage of natural experiments and used convergent lines of evidence to demonstrate that cholera is a waterborne infectious disease. More recently, investigators in the social and life sciences have used statistical models and significance tests to deduce cause-and-effect relationships from patterns of association; an early example is Yule’s study on the causes of poverty (1899). In my view, this modeling enterprise has not been successful. Investigators tend to neglect the difficulties in establishing causal relations, and the mathematical complexities obscure rather than clarify the assumptions on which the analysis is based. Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C,... hold, then H can be tested against the data. However, if A, B, C,... remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work—a principle honored more often in the breach than the observance. Snow’s work on cholera will be contrasted with modern studies that depend on statistical models and tests of significance. The examples may help to clarify the limits of current statistical techniques for making causal inferences from patterns of association. 1.

For nearly a century, investigators in the social sciences have used regression models to deduce cause-and-effect relationships from patterns of association. Path models and automated search procedures are more recent developments. In my view, this enterprise has not been successful. The models tend to neglect the difficulties in establishing causal relations, and the mathematical complexities tend to obscure rather than clarify the assumptions on which the analysis is based. Formal statistical inference is, by its nature, conditional. If maintained hypotheses A, B, C,... hold, then H can be tested against the data. However, if A, B, C,... remain in doubt, so must inferences about H. Careful scrutiny of maintained hypotheses should therefore be a critical part of empirical work-- a principle honored more often in the breach than the observance.

Abstract not found

The Dirichlet Model has been fitted to purchase behaviour in many product categories. The model uses the Dirichlet multinomial distributions to account for heterogeneity between customers in brand choice. The research reported here applies the concept of heterogeneity, developed in the Dirichlet Model, to other areas in marketing. It works through a range of classic market research techniques showing the changes and improvements that result from the consideration of heterogeneity in brand choice. The analysis has implications for (1) sample size calculations (2) the estimation of variance and reliability for nominal variables, (3) the evaluation of logistic and multinomial logit models, (4) the method and design of research which uses discrete choice models, (5) the evaluation of the similarities and differences between product categories and (6) the analysis and measurement of purchase feedback effects. The work also examines methods for identifying if a set of data conforms to the Dirichlet distribution. The work develops a concept of heterogeneity for a nominal variable, which was always known but the implications not fully understood. Discrete choice is a random Bernoulli trial based on a probability. The thesis embodied in the work presented here is that: across the population there is not a single probability, but a probability variable. The probability distribution of this variable is known as the mixing distribution. Analysis should focus on the attributes of this probability variable, and in particular its heterogeneity, rather than on the specific discrete brand choice. If all choice is based on the one, single underlying probability then there is no heterogeneity in the probabilities; there is no mixing distribution. If there is no heterogeneity in the probabilities then an analysis of the discrete choice is an analysis of random data evolving from repeated Bernoulli trials. The Dirichlet and Dirichlet multinomial distributions provide a strong framework for the analysis of the probability variable.