- Email: [email protected]
A prescriptive method for rating models
Industrial
Marketing
Management
E.V.A.F., London and Elsevier Publishing Company,
A Prescriptive A. Edward Associate
Method
- Amsterdam
for Rating
Models
Spitz
Professor of Marketing,
Eastern Michigan
INTRODUCTION
This is the age of the model builder. Models are often labeled as such, but they also assume aliases. For instance, the very popular technique of simulation wherein a computer performs as if it were the subject system, is a model. Also, the increasingly popular technique of gaming which uses decisions made by humans as inputs is a model. As the mathematical subculture grows, the complexity of models grows also. Many models are constructed only with an eye toward the advancement of science. There should be and are uses for models in the business areas. But how is one to select a model for use, keeping in mind that in business there is little time for trial and no time for error? In this article a framework for a qualitative test and subsequent rating of models will be proposed. WHAT IS A MODEL?
The strict academician might say that a model is just a currently popular term meaning theory. Definitions of models to suit a variety of outlooks are to be found in the literature. Kaplan (1964) tells us that one usage of the term model is “. . . only those theories which explicitly direct attention to certain resemblances between the theoretical entities and the real subject matter”. Another source, (Cohen and Cyert, 1965), defines a model as “, . . a set of assumptions from which a conclusion or a set of conclusions is logically deduced”. Since the interest here is in the field of behavioral science, the meaning of models to users and pedagogues is significant. One such meaning of a model is a formal 358
- Printed in the Netherlands.
University,
Ypsilanti,
Michigan
statement of a theory of market behavior and the tools for collection and analysis of relevant data (see Langdoff, 1965). Another is a set of equations, each describing the interrelationship between the factors which determine the market mechanism (see Bass, 1961). Still another is a symbolic description of a phenomenon from which observable characteristics are deduced (Lazer, 1961). The term model as used in the behavioral sciences does not carry the connotation of ideal as it does in the U.S. Department of Health, Education, and Welfare’s Model Cities Program. An ideal is also expressed in a model home or a fashion model where the audience is treated to a visual display glamorized beyond the usual or everyday example. Even if not an ideal, one may argue that a model is, or should be, normative, i.e. prescriptive of how things (events, people, life) should be. But implicit in all definitions of a model is a requirement for interrelationship of structure between it and the subject matter. So the model must relate to events in the real world as they are happening now and the model can be normative only to the extent that the model builder (or user) agrees with the ideal nature of that real world. If a conception is an individual’s interpretation of a term, and a concept is a family of conceptions (see Kaplan, 1964), then a’salient guide to usage of the concept of, for instance, a marketing model, is the way marketing men think of it. In simplistic terms, a statement or statements, usually in mathematical terms describing the relationship of causal factors and effects in a real world situation, is a marketing model. Theories state that a certain structure exists in the subject matter, but the theory need not have that Ind. Mark.
Manage.,
3 (1972)
structure itself. Theories make abstractions about the subject, but the theory need not go so far as to consider all but the structure irrelevant (Kaplan, 1964). Models, like theories, make abstractions about the subject matter, but they must satisfy the further requirements of negating all but the structure of the subject matter and mirroring in themselves that structure. It may be concluded that models, or at least semantical models, are a special type of theory. WHY
MODELS?
One may be expected to ask why the term model has come to enjoy such popularity if it is so nearly synonymous with theory. There appear to be two major reasons. The first and the one which is readily attested to in the literature, is the advent of the highspeed electronic computer. The computer used as a data processor enables the analysis of huge quantities of input and output data. This is low-level usage, however. It is when the computer is used as a thinking machine that its real benefits are realized. In this case the computer, with the appropriate program, becomes the model and the language of the computer becomes the language of the model. The painfully slow pace of hypothesis testing has been greatly speeded by the computer, but so has been the rate of hypothesis generation. The other reason for the popularity of the term model and the one which receives little mention in the literature is the semantic advantage of model over theory. Theory has become known, in nonacademic circles at least, as an antonym of practical or useful. Theory has become a long-haired term (Langhoff, 1965). Model, on the other hand, conjures visions of miniature bridges or airplanes being tested in wind tunnels, all eminently practical and worthwhile. Generally, most models qualify as theories and there should be little lost in using the term models when it is not incorrect to do so. There is, on the other hand, a great deal to be gained if, by using the term model, one attracts the interest of those who would balk at trying business or experimental applications of a “theory”. Also, the potential user can expect to find in the model a particularized formula relating cause to effect and therefore predictive enough that formerly relied upon guesswork can be improved. Of course, if the mistake is made of applying the results of model manipulation to the wrong real world system, then the user can be led further astray than if he had Id
Mark.
Manage.,
3 (1972)
suffered abstract
the mental agonies required but more general theory.
MODEL
RATING
to apply
an
A most obvious rating is a scaling method using a cardinal number system. Numbers, however, bear a definite and commonly understood relationship to one another. Ten is twice as great as five, etc. Implicit in such a system that rates an object as six, for instance, is a mechanism sufficiently accurate to assure that the object is at neither a seven nor a five level, and moreover, that the object is doubly endowed with attributes when compared with an object scaled at three. No such accuracy is herein claimed and therefore, numerical ratings are considered inappropriate. What is required is an entirely new conceptual framework tailored to describe a model’s usefulness. To avoid premature closure of ideas (see Kaplan, 1964) a rating system is suggested that is at once familiar and at the same time vague in its individual applications. In rating movies, military generals, and corporations, stars are used usually one through four or five. This star rating does not imply the exactness of a one to ten scale, and yet, being a familiar use it does ascribe to a definite feeling of preference. Also, the open-end nature of a star rating is an asset allowing more stars to be added upon the arrival of one deserving them. Those who revere mathematics might ask why there is a need to go further than tests of statistical significance. After all, the model generates a probability distribution similar to that inferred from experimental data or measured empirically, and various techniques are available for measuring the correspondence between the two. However, if sample size can be adjusted (and it usually can), then any reasonable model can be accepted or rejected at any desired level of confidence. The considerations determining the required power of a test are unclear without a statement concerning the practical significance of various discrepancies (see Massarik and Rotoosh, 1965). A NONMETRTC
TEST
,I Kaplan (1964) identifies several shortcomings of models. Among them are what he calls an overemphasis on symbols, overemphasis on form, oversimplification, and overemphasis on rigor. To these could be added inadequate proof, not that it is a 359
fault of the model itself, but rather of the model builder to sell his product. It is possible that the possibilities held out by the model are so great that it is worthy of testing by the user but in the usual case it is incumbent upon the model builder to provide a convincing example of successful usage if he is to have any buyers. Each of the above shortcomings is discussed with key questions formulated about models. Overemphasis on Symbols-An unconscious belief in the magic of symbols can have an effect on both the constructor and the reviewer of a model. Speaking of the reviewer’s side, witness the number of people who can recite E = MC’ and think that they are informed on the theory of relativity. There is more to the theory than the relationship between energy and mass, but many feel that being familiar with those famous symbols somehow imparts to them some of Einstein’s insight, and so it is that mathematical formulae lend some glamour. But formulae cannot lend content. If a proposition is useless, codifying it won’t help. Therefore one may properly ask if there are any symbolic formulae in the model which can be omitted without changing the nature of the model. Overemphasis on Form-Kaplan (1964) points out that “science advances on the basis, not of what is logically possible, but of what is actually available to it in the concrete problematic situation”. A model may be built upon faultless logic, and it may even be an accurate representation of the workings of a small slice of the real world, but if that slice is so small that it constitutes only an insignificant subset of an important class then the model may not represent the class. And if it doesn’t, then its very existence may serve to delay the search for the answer to the class behavior. The desire to build a model may have preceded any knowledge of the class in question. Or it is quite possible that a definition of the class was never obtained or even looked for. Perhaps there were available some statistics regarding the behavior of the subset. That availability might be the impetus for model generation. Instantly the statistics become data and the small slice of the real world becomes the subject matter. One should ask, therefore, whether there are any obvious shortcomings or limitations on the conceptualization of the model’s subject matter. Oversimplification-A model cannot be simplified too much. The requirements of explanation or prediction are sufficient determinants of com360
plexity. But a model can be simplified improperly. Certain variables must be set aside (neglected) when building a model, but adequate knowledge of the variable is necessary to determine the validity of the omission. If the variable is in fact crucial to the model then the crime of oversimplification has been committed. A variation is assuming without evidence that a causal or some other relationship exists between a physical isomorph and the subject system. One should ask if an improper assumption regarding scale relations or omission of variables has been made. Overemphasis on Rigor-It should not be necessary to say that scientists, especially those in the behavioral fields, are at times limited by the available techniques of observation and measurement. Yet to judge by the types of input required by some models, one might conclude that there is no limit to the type and sophistication of data to be had just for the asking. It is a safe game, constructing models for which there is little data, but in the absence of empirical proof credibility goes out the window. Even when sufficient and proper data exists, and this data is processed through a complex series of manipulation, one may not be learning anything new. As Kaplan (1964) puts it, “The ratio of significant theorems to the number of postulates and definitions is disappointingly low”. Credibility-Assume for the moment that the reader of the literature is interested in more than just gaining a familiarization with models, that he might put one to task if he could match a model with a task (decision problem, etc.). This being the case the model builder should, in the interest of selling, provide a description and results of a real world test case. The empirical data that may have been used to formulate the model does not satisfy this requirement. The test case or cases would generate confidence thus promoting actual use of the model in business situations. Also they would serve to point out the type of situations in which the model applies.
THE TEST SUMMARIZED
1. Is the model devoid of symbolic formulae which may be verbalized or omitted with no loss of rigor? If yes, award one star. 2. Is the model devoid of any serious shortInd. Mark. Manage.,
3 (1972)
comings or limitations on the conceptualization of the subject matter? If yes, award one star. 3. Is the model devoid of improper assumptions regarding relationships of scale or omission of variables? If yes, award one star. 4. Can the required data be obtained and will processing the data reveal anything new and important? If yes, award one star. 5. Is the model accompanied by a description of convincing test cases and of the situation in which it should work? If yes, award one star. If enough doubt exists so as to prevent answering a question with either yes or no, then award onehalf a star. If an affirmative answer is earned on all questions, then the model receives the highest rank,
Ind. Mark.
Manage.,
3 (1972)
five stars, (for the time being). This type of model rating is simple, succinct and lucid. The programming of model applications may only require some minor adjustments for the various users. REFERENCES Bass, F. M. (1961). Mathematical Models and Methods in Marketing, p. 4. Homewood, Ill.: Richard D. Irwin. Cohen, K. J. and Cyert, R. M. (1965). Theory of the Firm: Resources Allocation in a Market Economy, p. 18. Englewood Cliffs, N.J.; Prentice-Hall. Kaplan, A. (1964). The Conduct of Inquiry, pp. 265, 49, 70, 279, 284, 277-283. San Francisco: Chandler. Langhoff, P. (1965). Models, Measarement and Marketing p. 3 & 13. Englewood Cliffs, N.J.: Prentice-Hall. Lazer, W. (1961). “An Investigation of Marketing Models”, in Bell, M. L., ed., Proceedings of the Winter Conference of the American Marketing Association, p. 48. Chicago: Am. Market. Assoc. Massarik, F. and Rotoosh, P. (1965). Mathematical Ex plorations in Behavioural Science, p. 3. Homewood, Ill.: Richard D. Irwin.
361
Marketing
Management
E.V.A.F., London and Elsevier Publishing Company,
A Prescriptive A. Edward Associate
Method
- Amsterdam
for Rating
Models
Spitz
Professor of Marketing,
Eastern Michigan
INTRODUCTION
This is the age of the model builder. Models are often labeled as such, but they also assume aliases. For instance, the very popular technique of simulation wherein a computer performs as if it were the subject system, is a model. Also, the increasingly popular technique of gaming which uses decisions made by humans as inputs is a model. As the mathematical subculture grows, the complexity of models grows also. Many models are constructed only with an eye toward the advancement of science. There should be and are uses for models in the business areas. But how is one to select a model for use, keeping in mind that in business there is little time for trial and no time for error? In this article a framework for a qualitative test and subsequent rating of models will be proposed. WHAT IS A MODEL?
The strict academician might say that a model is just a currently popular term meaning theory. Definitions of models to suit a variety of outlooks are to be found in the literature. Kaplan (1964) tells us that one usage of the term model is “. . . only those theories which explicitly direct attention to certain resemblances between the theoretical entities and the real subject matter”. Another source, (Cohen and Cyert, 1965), defines a model as “, . . a set of assumptions from which a conclusion or a set of conclusions is logically deduced”. Since the interest here is in the field of behavioral science, the meaning of models to users and pedagogues is significant. One such meaning of a model is a formal 358
- Printed in the Netherlands.
University,
Ypsilanti,
Michigan
statement of a theory of market behavior and the tools for collection and analysis of relevant data (see Langdoff, 1965). Another is a set of equations, each describing the interrelationship between the factors which determine the market mechanism (see Bass, 1961). Still another is a symbolic description of a phenomenon from which observable characteristics are deduced (Lazer, 1961). The term model as used in the behavioral sciences does not carry the connotation of ideal as it does in the U.S. Department of Health, Education, and Welfare’s Model Cities Program. An ideal is also expressed in a model home or a fashion model where the audience is treated to a visual display glamorized beyond the usual or everyday example. Even if not an ideal, one may argue that a model is, or should be, normative, i.e. prescriptive of how things (events, people, life) should be. But implicit in all definitions of a model is a requirement for interrelationship of structure between it and the subject matter. So the model must relate to events in the real world as they are happening now and the model can be normative only to the extent that the model builder (or user) agrees with the ideal nature of that real world. If a conception is an individual’s interpretation of a term, and a concept is a family of conceptions (see Kaplan, 1964), then a’salient guide to usage of the concept of, for instance, a marketing model, is the way marketing men think of it. In simplistic terms, a statement or statements, usually in mathematical terms describing the relationship of causal factors and effects in a real world situation, is a marketing model. Theories state that a certain structure exists in the subject matter, but the theory need not have that Ind. Mark.
Manage.,
3 (1972)
structure itself. Theories make abstractions about the subject, but the theory need not go so far as to consider all but the structure irrelevant (Kaplan, 1964). Models, like theories, make abstractions about the subject matter, but they must satisfy the further requirements of negating all but the structure of the subject matter and mirroring in themselves that structure. It may be concluded that models, or at least semantical models, are a special type of theory. WHY
MODELS?
One may be expected to ask why the term model has come to enjoy such popularity if it is so nearly synonymous with theory. There appear to be two major reasons. The first and the one which is readily attested to in the literature, is the advent of the highspeed electronic computer. The computer used as a data processor enables the analysis of huge quantities of input and output data. This is low-level usage, however. It is when the computer is used as a thinking machine that its real benefits are realized. In this case the computer, with the appropriate program, becomes the model and the language of the computer becomes the language of the model. The painfully slow pace of hypothesis testing has been greatly speeded by the computer, but so has been the rate of hypothesis generation. The other reason for the popularity of the term model and the one which receives little mention in the literature is the semantic advantage of model over theory. Theory has become known, in nonacademic circles at least, as an antonym of practical or useful. Theory has become a long-haired term (Langhoff, 1965). Model, on the other hand, conjures visions of miniature bridges or airplanes being tested in wind tunnels, all eminently practical and worthwhile. Generally, most models qualify as theories and there should be little lost in using the term models when it is not incorrect to do so. There is, on the other hand, a great deal to be gained if, by using the term model, one attracts the interest of those who would balk at trying business or experimental applications of a “theory”. Also, the potential user can expect to find in the model a particularized formula relating cause to effect and therefore predictive enough that formerly relied upon guesswork can be improved. Of course, if the mistake is made of applying the results of model manipulation to the wrong real world system, then the user can be led further astray than if he had Id
Mark.
Manage.,
3 (1972)
suffered abstract
the mental agonies required but more general theory.
MODEL
RATING
to apply
an
A most obvious rating is a scaling method using a cardinal number system. Numbers, however, bear a definite and commonly understood relationship to one another. Ten is twice as great as five, etc. Implicit in such a system that rates an object as six, for instance, is a mechanism sufficiently accurate to assure that the object is at neither a seven nor a five level, and moreover, that the object is doubly endowed with attributes when compared with an object scaled at three. No such accuracy is herein claimed and therefore, numerical ratings are considered inappropriate. What is required is an entirely new conceptual framework tailored to describe a model’s usefulness. To avoid premature closure of ideas (see Kaplan, 1964) a rating system is suggested that is at once familiar and at the same time vague in its individual applications. In rating movies, military generals, and corporations, stars are used usually one through four or five. This star rating does not imply the exactness of a one to ten scale, and yet, being a familiar use it does ascribe to a definite feeling of preference. Also, the open-end nature of a star rating is an asset allowing more stars to be added upon the arrival of one deserving them. Those who revere mathematics might ask why there is a need to go further than tests of statistical significance. After all, the model generates a probability distribution similar to that inferred from experimental data or measured empirically, and various techniques are available for measuring the correspondence between the two. However, if sample size can be adjusted (and it usually can), then any reasonable model can be accepted or rejected at any desired level of confidence. The considerations determining the required power of a test are unclear without a statement concerning the practical significance of various discrepancies (see Massarik and Rotoosh, 1965). A NONMETRTC
TEST
,I Kaplan (1964) identifies several shortcomings of models. Among them are what he calls an overemphasis on symbols, overemphasis on form, oversimplification, and overemphasis on rigor. To these could be added inadequate proof, not that it is a 359
fault of the model itself, but rather of the model builder to sell his product. It is possible that the possibilities held out by the model are so great that it is worthy of testing by the user but in the usual case it is incumbent upon the model builder to provide a convincing example of successful usage if he is to have any buyers. Each of the above shortcomings is discussed with key questions formulated about models. Overemphasis on Symbols-An unconscious belief in the magic of symbols can have an effect on both the constructor and the reviewer of a model. Speaking of the reviewer’s side, witness the number of people who can recite E = MC’ and think that they are informed on the theory of relativity. There is more to the theory than the relationship between energy and mass, but many feel that being familiar with those famous symbols somehow imparts to them some of Einstein’s insight, and so it is that mathematical formulae lend some glamour. But formulae cannot lend content. If a proposition is useless, codifying it won’t help. Therefore one may properly ask if there are any symbolic formulae in the model which can be omitted without changing the nature of the model. Overemphasis on Form-Kaplan (1964) points out that “science advances on the basis, not of what is logically possible, but of what is actually available to it in the concrete problematic situation”. A model may be built upon faultless logic, and it may even be an accurate representation of the workings of a small slice of the real world, but if that slice is so small that it constitutes only an insignificant subset of an important class then the model may not represent the class. And if it doesn’t, then its very existence may serve to delay the search for the answer to the class behavior. The desire to build a model may have preceded any knowledge of the class in question. Or it is quite possible that a definition of the class was never obtained or even looked for. Perhaps there were available some statistics regarding the behavior of the subset. That availability might be the impetus for model generation. Instantly the statistics become data and the small slice of the real world becomes the subject matter. One should ask, therefore, whether there are any obvious shortcomings or limitations on the conceptualization of the model’s subject matter. Oversimplification-A model cannot be simplified too much. The requirements of explanation or prediction are sufficient determinants of com360
plexity. But a model can be simplified improperly. Certain variables must be set aside (neglected) when building a model, but adequate knowledge of the variable is necessary to determine the validity of the omission. If the variable is in fact crucial to the model then the crime of oversimplification has been committed. A variation is assuming without evidence that a causal or some other relationship exists between a physical isomorph and the subject system. One should ask if an improper assumption regarding scale relations or omission of variables has been made. Overemphasis on Rigor-It should not be necessary to say that scientists, especially those in the behavioral fields, are at times limited by the available techniques of observation and measurement. Yet to judge by the types of input required by some models, one might conclude that there is no limit to the type and sophistication of data to be had just for the asking. It is a safe game, constructing models for which there is little data, but in the absence of empirical proof credibility goes out the window. Even when sufficient and proper data exists, and this data is processed through a complex series of manipulation, one may not be learning anything new. As Kaplan (1964) puts it, “The ratio of significant theorems to the number of postulates and definitions is disappointingly low”. Credibility-Assume for the moment that the reader of the literature is interested in more than just gaining a familiarization with models, that he might put one to task if he could match a model with a task (decision problem, etc.). This being the case the model builder should, in the interest of selling, provide a description and results of a real world test case. The empirical data that may have been used to formulate the model does not satisfy this requirement. The test case or cases would generate confidence thus promoting actual use of the model in business situations. Also they would serve to point out the type of situations in which the model applies.
THE TEST SUMMARIZED
1. Is the model devoid of symbolic formulae which may be verbalized or omitted with no loss of rigor? If yes, award one star. 2. Is the model devoid of any serious shortInd. Mark. Manage.,
3 (1972)
comings or limitations on the conceptualization of the subject matter? If yes, award one star. 3. Is the model devoid of improper assumptions regarding relationships of scale or omission of variables? If yes, award one star. 4. Can the required data be obtained and will processing the data reveal anything new and important? If yes, award one star. 5. Is the model accompanied by a description of convincing test cases and of the situation in which it should work? If yes, award one star. If enough doubt exists so as to prevent answering a question with either yes or no, then award onehalf a star. If an affirmative answer is earned on all questions, then the model receives the highest rank,
Ind. Mark.
Manage.,
3 (1972)
five stars, (for the time being). This type of model rating is simple, succinct and lucid. The programming of model applications may only require some minor adjustments for the various users. REFERENCES Bass, F. M. (1961). Mathematical Models and Methods in Marketing, p. 4. Homewood, Ill.: Richard D. Irwin. Cohen, K. J. and Cyert, R. M. (1965). Theory of the Firm: Resources Allocation in a Market Economy, p. 18. Englewood Cliffs, N.J.; Prentice-Hall. Kaplan, A. (1964). The Conduct of Inquiry, pp. 265, 49, 70, 279, 284, 277-283. San Francisco: Chandler. Langhoff, P. (1965). Models, Measarement and Marketing p. 3 & 13. Englewood Cliffs, N.J.: Prentice-Hall. Lazer, W. (1961). “An Investigation of Marketing Models”, in Bell, M. L., ed., Proceedings of the Winter Conference of the American Marketing Association, p. 48. Chicago: Am. Market. Assoc. Massarik, F. and Rotoosh, P. (1965). Mathematical Ex plorations in Behavioural Science, p. 3. Homewood, Ill.: Richard D. Irwin.
361