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Statistics in Marketing
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A new metric multidimensional scaling model is developed to accommodate the analysis of three-mode dominance and nonsymmetric proximity data. One of many possible marketing applications is presented concerning the modeling of consumer preference for various breakfast and snack foods.
Most clustering techniques used in product positioning and market segmentation studies render mutually exclusive equivalence classes of the relevant products or subjects space. Such classificatory techniques are thus restricted to the extent that they preclude overlap between subsets or equivalence classes. An overlapping clustering model, ADCLUS, is described which can be used in marketing studies involving products/subjects that can belong to more than one group or cluster simultaneously. The authors provide theoretical justification for and an application of the approach, using the MAPCLUS algorithm for fitting the ADCLUS model.
The college choice behavior of graduate business school applicants is studied. A stochastic utility model is proposed and estimated by use of a sample of students admitted to Carnegie-Mellon University. The specific formulation used is the conditional logit model. Results indicate that such factors as net cost, quality, and distance of applicant's home from school are important determinants of college choice. Specific probability computations are used to illustrate the results for a typical decision maker.
This paper presents a comparative analysis of the findings of two field studies and three recent laboratory experiments that assessed the efficacy of judgment based models in aiding marketing decision making. This analysis indicates factors that may affect the effectiveness of these models. The implications of the findings for users of judgment based marketing decision models as well as model builders are discussed, and suggestions are made for future research to improve the models' effectiveness.
This article presents a brief description of the development and use of log-linear models. Current research in areas of screening effects, partitioning chi-square statistics, stepwise procedures, and model fitting and selection is discussed. An analysis of inherent model ambiguities is provided, identifying potential problem areas for marketing applications.
A model is developed for incorporating the long-standing marketing research effort of explaining variation in observed consumption behavior into the more recent notion that such behavior has an inherent component of randomness. The model recognizes that consumption behavior on any given occasion will fluctuate around some mean consumption level and that this mean consumption level will vary across the population in a systematic manner which is related to the characteristics of the consuming unit. However, it is not assumed that the relationship is exact, but that it contains an element of randomness. The properties of the model are examined and it is compared with ordinary least squares models of the same phenomenon.
Traditional market share models can be elaborated by combining nonstationary stochastic models of brand choice with econometric models. A variable Markov model is described which allows assessment of marketing decision variables' influence on the underlying composition of market share.
Most empirical work on Markov processes for brand choice has been based on aggregative data. This article explores the validity of the crucial assumption that underlies such analyses, i.e., that all the families in the sample follow a Markov process with the same or similar transition probability matrices. The results show that there is a great deal of diversity among families' switching processes, and that many of them are of zero rather than first order.
0.5 to 7.5. Whenever it falls in the range 0.5 to 1.5, the subject checks Level 1; from 1.5 to 2.5, he checks Level 2, and so on. This procedure gives a perfect scaling technique. The assumption of a perfect model is merely that when the true attribute has a value x (anywhere in the continuum from 0.5 to 7.5), the model predicts this same value. The question is now very simple, since correlation between the true attribute value and the predicted value has been defined as 1.0. However, what
The author comments on Fornell and Larcker's article in the February 1981 issue of "JMR". He indicates some limitations of the analyses, pinpoints where they can be misleading, and introduces some new notions.
The existence of multiple observations within several cross sections gives rise to both opportunities and problems in the application of regression analysis. In this article the issues associated with the decision of whether or not to pool the data for purposes of estimation are explored and examples of marketing applications are provided.
This article describes a method of predicting the market share for newly launched brands and the future equilibrium share of established brands after major promotional activity. The method is dependent on the continuous purchasing data obtainable from consumer panels and is developed from numerous case histories from the Attwood Consumer Panel in Great Britain to illustrate the use of the technique and its refinements.
A mathematical model is presented of consumer behavior in the marketplace under advertising stimulation. The model relates advertising effort to attitude changes and consumer purchases, using a nonstationary Markov process. A new analytical method of handling nonstationary stochastic matrices is developed. The behavior of brand shares under different market conditions is considered along with numerical examples of how the model operates.
Logit and log-linear models are new techniques for analyzing categorical data. Each of these models is described and applied to a problem involving consumer adoption of a new telecommunications service. The models provide probability-of-adoption predictions that can be used to select favorable market areas for promoting the service.
Chakravarti, Mitchell, and Staelin (CMS) draw a number of conclusions about judgment based models that agree with our field experience. However, we question whether their experiments form an adequate basis for ascribing negative effects to decision calculus models. A key part of the laboratory task is to estimate five model parameters, given between six and 18 observations of a share-advertising time series and no further market information. By contrast, in our field experience a major advantage of decision calculus models is that managers base their calibrations on multiple information sources and detailed knowledge of market and consumer behavior.
Conjoint measurement is a new development in mathematical psychology that can be used to measure the joint effects of a set of independent variables on the ordering of a dependent variable. In this (primarily expository) article, the techniques are applied to illustrative problems in marketing. In addition, a number of possible areas of application to marketing research are discussed, as well as some of the methodology's limitations.
This study investigates the relationships among attitude change, advertising exposure, and choice of a new brand on an individual basis. Results indicate that although attitudes change both before and after choice of the new brand, the post-choice attitude change is greater in magnitude and correlated more highly with choice.
This article describes novel methods of using consumer panel statistics to predict the success of new grocery products. Since about four out of five such products fail, even modest improvements in early identification of successes is important. The authors show how greater attention to successive waves of repeat buying and to intervals between purchases make significant improvement practical. They link these somewhat neglected statistics to a mathematical model of penetration.
In this article Mr Ehrenberg shows how data on purchases of non-durable consumer goods can be fitted by the negative binomial distribution, and discusses applications of this finding. He also considers a simple model for purchases made in different periods of time and some quick and easy methods for calculating standard errors.
Recent developments in numerical taxonomy appear to show applicability for many classification problems in marketing. This review article describes some of the approaches to numerical classification and presents illustrative marketing applications. Current limitations of the procedures are also discussed.
Some of the recent developments in sample survey methodology that are relevant to marketing research are reviewed. These innovations, all involving probability sampling, concern (1) methods of minimizing the total survey error, (2) methods of estimating the sampling errors in complex surveys, (3) more efficient methods of sampling from complex frames, (4) the selection of telephone household samples, and (5) methods to protect the privacy of respondents and increase response validity. These innovations are described in terms of actual methods and potential applications.
The purpose of this study is to formulate and test a model which can assess the impact of advertising on sales, rather than just produce sales forecasts. The proposed model, which incorporates many of the models and concepts previously suggested, is found through predictive tests to be consistent with empirical evidence.
This article reports on a study of the incidence of telephone ownership and telephone directory listings that was based on random-digit dialing (RDD). Various considerations important in the design and selection of RDD samples and in the execution of surveys based on such samples are presented.
Two methods are given for estimating future demand for durable goods. Both require detailed information on past consumer purchasing behavior but not on future intentions. The first method considers the different segments of the total market, and the second deals with household preferences and priority patterns. The replacement component of the market is considered in terms of a life distribution.
This article demonstrates the application of simultaneous equation regression methods in analyzing limited time series data for sales and advertising. In testing a model with sales and advertising relationships for filter and non-filter cigarette brands, we could not reject a model in which the advertising elasticity for filter brands is substantially greater than that for nonfilter brands.
This paper initiates an investigation into the statistical significance of results obtained by analysing data through the Automatic Interaction Detection technique. A test statistic which is asymptotically independent of the sample size is examined and critical values are obtained for a special case. The asymptotic results are compared with the exact distribution for varying sample size in a specific example. A brief discussion on the application of the results to a particular case study concludes the paper.
The purpose of this article is to suggest that, for some studies, samples which include only published numbers may be adequate.
When a triangle taste test, i. e., "Which of these three stimuli is different from the other two?", is given twice to each subject, a natural question to ask is: "Are the subjects who got both tests correct really better discriminators than the other subjects who got 0 or 1 correct?" Surprisingly enough, the answer to this question has nothing to do with the number of subjects who got both correct, i. e., the twos. Rather, it is the ratio of the ones to the zeroes that supplies the necessary information. This information on the subject's abilities to discriminate can be used to develop a weighted voting procedure for subsequent preference tests.
MDS techniques have now reached a mature stage in development and application to marketing. Green takes a critical look at the early promises of the methodology, and points out problems still to be solved and potentials still to be realized.
This paper assesses the state-of-the-art of the diffusion models of new product acceptance. A number of issues related to the further development and validation of these models are discussed.
A new stochastic choice model is proposed which can incorporate any number of explanatory variables. The model combines logit regression, heterogeneity, and product class purchase incidence concepts. The authors describe an exploratory study of the model, in which it is found to fit a certain situation very well.
Conventional telephone directory sampling techniques fall short of producing a perfect sample of domestic telephone subscribers. Near the end of the 1963-64 local telephone directory year, when the number of new, but as yet unlisted, telephones was at its maximum, 18 percent of private telephones in use in the Greater Cincinnati area were not listed in the current directory. By means of a new technique for obtaining numbers, one large source of sampling error can now be virtually eliminated in sampling private telephone subscribers, whether listed or not.
A depth of repeat model is presented that can forecast the demand for new consumer products. The relation of the model to other forecasting models is noted. Data analysis, estimation procedures, and the observed accuracy of forecasts are discussed.
When the selection of a sample of stores or cities requires a high degree of similarity among the test units in order to ensure a sensitive experiment, the sample may no longer represent the market. These conflicting requirements can be satisfied by choosing the sample from clusters displayed in a reduced space representation of the market.
A method for exploring and quantifying the value systems of consumers through conjoint measurement is described. Since it is concerned with value systems of individual consumers, the method is most appropriate for product categories where consumers' desires are heterogeneous and where markets are highly segmented.
Analysis and interpretation of higher order cross-tabulation data are of recurring concern in marketing research. The authors present a parsimonious new approach to this data analysis problem. Specifically, a model-free approach is proposed which helps to identify differences in the response distribution of a criterion variable based on segments of respondents defined by characteristics of the predictor variables. The approach, which relies on Bonferroni adjusted chi square statistics to direct a sequential search process, is illustrated in a segmentation analysis of data from a national consumer survey. The results of analyzing the same data by using AID and LOGIT procedures are also examined. The article concludes with a discussion of potential applications, limitations, and extensions of the new approach.
With the availability of "canned" computer programs, it is extremely easy to run complex multivariate statistical analyses. However, it is not as easy to interpret the output of these programs. This article offers some comments about the well-known technique of linear discriminant analysis; potential pitfalls are also mentioned.
The tradeoffs among product attributes typically are estimated from data on preferences toward several product concepts. The "no-yes" data on intentions to buy a product concept in relation to a previously intended purchase of an existing brand are perhaps more useful for computing these tradeoffs. These measurement concepts are explored by means of the multivariate probit model, which is suited to the analysis of dichotomous data. Results of a pilot application indicate that procedures can be developed which will convert these data into probit coefficients applicable to each product attribute in the formation of market segments.
Specific multivariate statistical techniques, such as factor analysis and discriminatory analysis, are finding increasing application in marketing research investigations. Canonical analysis, a less well-known multivariate technique, is an appropriate procedure to use when sets of criterion and predictor variables are to be correlated. This article describes the objective of canonical analysis, its relationship to other multivariate techniques and the major limitations of the method. The procedure is applied to a problem involving the relationship of certain behavioral measures to personality test scores.
A method of analyzing the components of a trend in consumer purchasing is described. An empirically-based mathematical model is first used to predict the purchasing pattern in the absence of a trend. Comparison between the observed data and these predicted norms permits a detailed evaluation of the trend. Two examples of practical applications of the technique are presented.
Conjoint analysis has been applied in a large number of commercial projects as well as in many noncommercial studies. Often MONANOVA, a nonmetric technique, is applied to a preference rank order obtained for a set of hypothetical objects. The authors report simulation results obtained for four alternative estimation procedures, ANOVA, LINMAP, LOGIT, and MONANOVA. The results suggest, within the limitations of the simulation study, that ANOVA may be the preferred procedure for compensatory models, whereas LINMAP is most likely to provide the best predictive validity for models with a dominant attribute.
Buyer usage behavior data are used to compare the relative performance of a linear discriminant analysis and several multinomial classification methods. The potential shortcomings of each of the procedures investigated are cited, and a new method for determining the contribution of a variable to discrimination in the context of the multinomial classification problem also is presented.
The author's stochastic evolutionary adoption model (STEAM) is briefly described. Methods for estimating its parameters from panel data covering the first part of the introductory period are outlined. A method by which the future purchase history of each panel household can be simulated and the results projected into a total market forecast is reported. Results obtained by applying the model and simulation procedure to live data for a new product are shown and compared with the product's actual sales during the years after its introduction.
This study investigates the influence of advertising exposure on individual brand attitude change. Results indicate that past exposures, brand familiarity, and prior attitude are significantly related to attitudinal response.
A new brand choice model that has the capacity to include explanatory variables is described and its use illustrated in an application to a particular brand. In this application, pricing and certain consumer demographics provide an explanation of the purchase behavior for the brand studied. The model provides a good fit to empirical data as well as some important insights for marketing decision making.
A multivariate extension of AID is presented for use in market segmentation studies where the criterion consists of multiple measures of behavioral response. The procedure is illustrated with an example employing several measures of long distance telephone expenditures.