# A Conjoint Model For Analyzing New Product Positions in a Differentiated Market With Price Competition

^{[ to cite ]:}

Jordan J. Louviere (1986) ,"A Conjoint Model For Analyzing New Product Positions in a Differentiated Market With Price Competition", in NA - Advances in Consumer Research Volume 13, eds. Richard J. Lutz, Provo, UT : Association for Consumer Research, Pages: 375-380.

^{[ direct url ]:}

http://acrwebsite.org/volumes/5951/volumes/v13/NA-13

[Jordan Louviere was Associate Professor of Marketing, University of Iowa when this paper was written.]

[The author gratefully acknowledges the assistance of a major chemical company, who wishes to remain anonymous, in the form of a grant to the Department of Marketing, University of Iowa for data collection associated with this project. The author also wishes to acknowledge the assistance in data collection and analysis provided by Mike Zenor, Tim Heath and Tim Eliason as part of an MBA Marketing Research Project. Dave Curry, Gary Gaeth and Mark Moriarty read the first draft and provided useful comments and suggestions which this version incorporates. Faults remaining, however, are my own.]

This paper extends existing conjoint choice techniques to handle problems involving the positioning of new product concepts in existing, competitive product markets. It permits explicit competition for customer choices among a number of existing products and one or more new entrants. The approach therefore is useful for analyzing both positioning and repositioning strategy in competitive product markets. Use of split-plot or incomplete block designs together with the multinomial logit choice model permit considerable flexibility in both design and analysis. An illustrative application to an agrochemical marketing problem is provided.

INTRODUCTION

In 1975 D.F. Jones described a simple survey technique that could be used to anticipate changes in the demand for a product or service under different pricing policies. As Jones (1975, p. 75) expressed the problem:

"One of the more challenging tasks that confronts marketing researchers is that of determining the probable effect of different pricing policies on the sale of a new or existing product. Closely allied to this problem is that of determining how the modification of a product or its image will affect sales if price remains constant or if it, too, is modified in some manner."

Jones' approach permitted one to estimate the own-elasticity of the price of the product or service of interest, assuming constant prices of existing competitors and/or other brands for the same manufacturer.

Jones' (1975) approach was extended by Mahajan, Green and Goldberg (1982) to explicitly consider the simultaneous manipulation of the prices of all competitors, not just a single competitor. Furthermore, Mahajan, Green and Goldberg (1982) linked the estimation of these effects to a conjoint choice experiment, the results of which could be analyzed by means of the multinomial logit choice model (Theil 1971; McFadden 1974; Hensher and Johnson 1981; Amemiya 1981). Thus, Mahajan, Green and Goldberg (1982) succeeded in linking multiattribute conjoint concepts with an explicit competitive choice experiment, the analysis of which was consistent with a particular theoretical choice model. [Although relying on an orthogonal design plan to vary absolute levels of prices, the design used by Mahajan, Green and Goldberg is not orthogonal in price differences, as required by the linear logit model they employed.] In their 1982 paper, Mahajan, Green and Goldberg (p.341) suggested that the simple pricing model could be extended to include non-price competition:

"... it is straightforward to extend the technique to other classes of product-service attributes, such as physical characteristics, pack aging, distribution and advertising. In principle, the same kind of procedure would be followed, but attributes other than (or in addition to) price would be systematically varied for both the firm's offering and various explicitly defined competitive offerings."

Louviere and Woodworth (1983) provided a systematic extension of the Mahajan, Green and Goldberg (1982) ideas to a wide variety of choice experiments, including those in which the set of competitive products-services varies. Louviere and Woodworth also prove that certain classes of choice experiments provide near optimally efficient estimates for multinomial logit choice models. Louviere and Hensher (1983, p. 352) note that choice experiments which do not explicitly include a "non-purchase" alternative produce market share and not true demand models.

None of these research papers have explicitly considered the problem of introducing a new product concept with differing levels of a set of product attributes into a product class of existing products competing on both price and non-price attributes. The solution to such a problem is of managerial interest because managers need to know how to best position the attribute levels of a new product concept given present product positions and potenal competitive reactions, often price reactions. For example, as reported by Ingrassia (1980), Sony's market share was consistently eroded by the advent of slightly modified foreign and domestic TV products which engaged in intensive price discounting, to which Sony was eventually forced to respond. If an approach were available to managers of new or existing products that could provide information about the likely competitive consequences of various attribute/price configurations in competition with current positions and possible repositionings of existing products, this would constitute a useful extension of previous work.

Such an approach also has the potential to contribute to our empirical understanding of firms' strategic positioning policies as well as the market's response to such policies. The practical relevance of the approach is to provide information to management to anticipate the likely consequences of positioning policies of their own and of their competitors. Additionally, the information provided about positioning consequences for new and existing products in the face of competition provides an important extension to existing conJoint techniques.

The need for such techniques and for empirical research in this area is well-documented in the series of papers presented at the pricing conference at the University of Rochester (Gould and Sen, 1984): for example, reviews by Rao (pp. 39-60) and Nagle (pp. 3-26) clearly indicate the current limitations of applying theoretical economic models to real managerial problems; while Markham (pp. 257-263) indicates the value of empirical research on strategic pricing problems to enrich the axiomatic base of economic models. The approach proposed in this paper, therefore, has the potential to contribute to practical problem solution, theory testing and empirical understanding. The emphasis in this paper, however, is on practical problem solving, although suggestions for useful extensions of theoretical and empirical interest are discussed in The Discussion and Conclusions section.

The purpose of this paper, therefore, is to describe and illustrate an extension to the strategic pricing model of Mahajan, Green and Goldberg (1982) which permits the evaluation of the market potential of new product concepts competing with a set of existing products In addition we provide two methodological extensions for conjoint choice problems:

1. An extension of the Mahajan, Green and Goldberg (1982) method which permits existing products to vary on strategic dimensions other than price. This latter extension permits examination of the potential consequences of reformulations and repositionings.

2. An extension of the Louviere and Hensher (1983) approach for creating multiple levels of numerical variables that explicitly allows for tests of non-linearities.

The proposed approach is particularly well suited to address strategic problems in product classes in which the properties (attributes) of the existing brands are relatively fixed in the short run, as for example, agricultural chemical formulations or ethical drugs. The original formulations may have been discovered accidentally, or may have benefitted from positioning research that suggested certain attribute configurations that would appeal to particular segments. Thus, major marketing strategies for these products involve (inter alia) communication of benefits, positionings and pricing policies. For the sake of example we assume that pricing policy is of major interest to management, an assumption shared by Mahajan, Green and Goldberg (1982) in their approach.

Such problems arise frequently in agricultural chemical marketing and ethical drug marketing because of the relatively permanent nature of the product attributes and the long lead times to introduction dictated by research, development and testing, and U.S.D.A. approval policies. Although agricultural chemicals can be reformulated, existing formulations often are fixed for the near term: hence, estimates of the likely market potential of new product concepts or repositionings of existing products can be of significant strategic value to management faced with a considerable time and monetary commitment to reformulating an existing product or introducing a new formulation.

Existing conjoint judgment techniques are ill-suited to this type of strategic problem because a) there is no explicit incorporation of competitive actions/reactions, b) judgments such as ratings or rankings are not choices, and assumptions must be made to transform such data into choice data, c) the number of judgments required of customers to duplicate choice information that can be easily obtained from a few, well-designed choice sets is often considerable (e.g., in the empirical study reported later, a minimum of 40 conjoint profiles would be needed to develop a choice simulation to duplicate the information obtained from 18 choice sets).

In contrast to this relatively complicated approach that requires a number of untested and untestable assumptions about choice in order to derive forecasts, the present approach is much simpler. In particular, choices are directly observed, not simulated and all relevant products and product concepts compete for customer choice simultaneously. rhus, the data needed to forecast the likely changes in customer choices in response to competitive actions are obtained directly from respondents and used to develop a statistical choice motel. The choice model can then be tested for statistical adequacy using observed choices, unlike the conjoint judgment approach that can only be assessed in terms of ability to predict to some additional (hold out) choice data collected in the study.

This paper outlines an approach to competitive choice problems, and illustrates it with an application to an existing product class of agricultural insecticides. We avoid mention of the type and brands of insecticide and the study region to protect the identity of the organization who sponsored the empirical research. It is important to note that the approach proposed in this paper has application to a wide range of high involvement products in addition to agricultural chemicals.

PROPOSED RESEARCH APPROACH

The effect on choice behavior of introducing various new product configurations into an existing, competitive market can be examined by developing a conjoint choice experiment. This paper develops the basis for a conjoint experiment that (1) accommodates a large number of different levels of price (or any other quantitative variable which is monotonically related to the response or can be prescaled to be monotonically ordered if nominal), and (2) permits simultaneous consideration of the effects of the prices of existing products in competition with a series of new product concepts or profiles. Although the application to a pricing problem is the primary focus, the approach generalizes to any non-price attributes of interest.

The proposed approach represents an extension of the Louviere and Woodworth (1983) choice experiments based on factorial designs to include "split-plot" and block designs (See, e.g., Federer 1975a, 1975b, Cochran and Cox 1957). The idea is to use two (or more) different (fractional) factorial designs to vary both the prices of existing products, and the attribute levels of new product concepts (profiles). These two (or more) designs are then combined into two (or more) "plots" or blocks using conventional procedures associated with these types of designs. The empirical example we use to illustrate the approach is based on the use of "split-plot" designs, although a balanced, incomplete block design could have been used. We concentrate on "split-plots" because they are so easy to construct, and because they satisfy the necessary conditions of alternative independence for estimating Multinomial Logit Choice (MNL) Models.

The "plots" are created by ordering the treatments in each of the two designs (e.g., 1. existing product prices, and 2. new product concepts) separately such that the rank order correlation between the order of treatments in one design with those of a second design is minimized. [If there were n such designs to be merged, the rank order correlation of the orderings of al N(n-1)12 pairs would need to be minimized.] The MNL model assumes non-correlated, i.e., independent, marginal utilities, so minimizing the rank order correlation of two different sets of rank orders corresponds to minimizing the correlation between the attributes of the separate marginals. Because both designs have m(=1,2,...,m) treatments, the ordered pairs determine the choice sets to be used (the merger of the two separate designs).

The specific procedure we propose is: (1) Create separate (fractional) factorial designs with the same number of treatments, e.g., a) to examine pricing policies for existing products, and b) to create new product concepts by varying the key decision attributes of the product class. (2) Develop two sets of rank orderings whose rank order correlation is as close as possible to zero for them treatments. (3) Then, treat the ordered pairs as choice sets, consisting of a pair of treatments from each design. For example, if the first pair of orders is (6, 16), the first choice set should pair the 6th treatment from the pricing design with the 16th treatment of the attribute or concept testing design.

If the marginal relationship of each numerically valued attribute can be assumed to be monotonic with respect to the criterion variable (e.g., "utility") then a fairly large number of levels of this particular attribute can be investigated using a procedure suggested by Louviere and Hensher (1983). In particular, most monotone relationships can be inferred from (at least) a three level factor because most such curves have only one bend. [We recognize that S- and reverse S-shaped curves would not satisfy this condition.] Thus, an extension of the Louviere and Hensher (1983) approach which used factors with two levels to describe price effects can be accomplished by treating each existing product of competitive interest as a price factor with three levels. The main advantage of this approach is to generate a design which varies more than two or three distinct levels of numerical attributes, while retaining the statistical power to estimate nonlinear (but monotonic) marginal relationships relying upon regression rather than ANOVA procedures.

This approach requires that the analyst divide the range of prices that contains the possible variation for the study period of interest into three categories of equal width: e.g., "high", "medium" and "low". One then chooses a (fractional) factorial design to vary product prices which is some version of a 3n plan. Each "high" level of price in the 3n design plan is randomly assigned a particular numerical value of price from a range of prices categorized as "high"; similarly, each "medium" and "low" level of price in the design plan would be determined by randomly assigning price values from the range of prices assigned to the "medium" and "low" price categories. A variation of this would be to assign price values to each price category ("low", "medium", "high") according to a latin square ordering of these levels (e.g. (1,2,3),(1,3,2),(2,1,3),(2,3,1),(3,1,2),(3,2,1) in which each price factor would receive one of the six latin square orderings selected at random. The latin square would determine the order of the levels within each price category.

The use of both the procedure for creating additional levels and the "split plot" approach for merging compatible designs is illustrated in the empirical study reported in the next section.

Empirical Illustration: Farmer Choices Among Alternative Crop Insecticides

As part of a larger study of farmers' use of, knowledge about and perceptions of a variety of crop insecticide products, a choice experiment was designed and administered according to the ideas developed in the previous section. The project was underwritten by a grant to the University of Iowa from a major chemical company, so we will reveal only as much detail as necessary to under stand the experiment, the data analysis and the interpretation of the results. The research project was concerned with investigating the effect of introducing new product concepts into an existing crop insecticide market of a particular type in which existing products compete on price because positions are relative fixed.

DETAILS OF THE STUDY DESIGN

Relevant product attributes were determined from interviews with chemical dealers, farmers, and chemical company officials. The following product attributes were selected for analysis: 1) Price per acre at recommended levels of application; 2) Efficacy against seed attacking, plant attacking or both kinds of insects; 3) The number of weeks of protection provided (duration of effectiveness); 4) Whether the odor is described as unpleasant, offensive or irritating to nostrils; 5) The degree of toxicity expressed as a "caution", "warning" or "danger" on the label; 6) Whether the product is formulated as a liquid or granular compound for Preemergent Banded application (applied in bands prior to plant emergence); 7) Whether the product is formulated as a granular compound for Preemergent In-furrow application (applied in the furrow at the time of planting); and 8) Whether the product is formulated as a liquid or granular compound for Postemergent Banded application (applied in bands after emergence).

These attributes were varied in an orthogonal main effects fraction of a 2x3 factorial that consisted of 18 treatments (conjoint profiles, of new product concepts). This plan was selected from a 6x3 fractional factorial design cataloged in (Chacko 1980) and modified for this problem. Each of the 18 treatments, therefore, represents a new product concept or "position" in the marketplace.

Seven products competed in the product market of interest at the time of this study; we will refer to them as products A-G. Local farm chemical dealers provided mean price per acre estimates at manufacturers' recommended rates of application. These per acre prices were used to determine the pricing levels of the existing products, as well as the pricing levels of the new product profiles as follows:

Each of the seven existing products was treated as a three level factor, the levels of which were prices; three price categories ("high", "medium" and "low") were used to divide the mean per acre price +/-20% into equal thirds. Each price category was given three equally spaced levels ("high" was +10%, +15%, +20%; "medium" was -5%, the mean, +5%; and "low" was -10%, -15%, -20%). The design mentioned earlier (Chacko 1980) was used to develop a main effects fraction of a 37 factorial to vary the price-levels.

This design insures that the marginals of each existing product are statistically independent of one another. In order to insure that the marginals of the pricing design and the marginals of the new product concept design are independent, we use a "split-plot" (Fedderer 1975a,b; Cochran and Cox 1957) procedure to create choice sets that represent a treatment from the pricing design (one profile of the prices of all existing products) paired with a treatment from the new product concept design (a description of a new product and its price).

Because there are nine levels of price for each existing product and the new product concepts, each of the nine levels occurs twice in the main effects plans. The nine levels of price were randomly assigned within each of the three "high", "medium" and "low" price categories separately for each product (other assignment procedures could be used such as Latin Square orderings). The range of price levels for the new product concepts was determined by taking the lowest and highest price levels in the existing product pricing design; this range was divided into equal thirds, nine levels were created and these nine levels were then randomly assigned exactly as was done for the existing products.

The "split-plot" procedure used to create choice sets relies on the creation of two minimally correlated vectors of ranks (the numbers 1-18). The ranks index the treatments in each design; because the treatments in factorials are ordered systematically, minimizing the rank order correlation of the two sets of treatments should make the two sets of marginals approximately statistically independent. Numerical experiments and previous experience with this procedure suggest it achieves this objective. Nonetheless, it would be wise to check the statistical properties of such designs before proceeding to implementation because no mathematical proof yet exists regarding their properties.

Each pair of minimally correlated ranks is used to create a single choice set by associating one treatment from the existing product pricing design with a second treatment from the new product concept design. For example, if an ordered pair is (8,15), the corresponding choice set pairs the 8th treatment in the pricing design with the 15th treatment in the new product concept design. The 18 ordered pairs of ranks therefore generate 18 different choice sets that are shown to subjects in the empirical example described immediately below.

Data Collection and Subjects

The choice design was placed in a survey booklet together with other sections that surveyed demographics, perceptual positioning and insecticide use and purchase. A list of farmers (owners/operators) was obtained from the A.S.C.S. offices in the target state of interest for each of 10 randomly selected counties. In each county 150 surveys were mailed to randomly selected names based on the A.S.C.S. lists. Surveying was conducted during the height of spring planting, which fact, together with a large (but unknown) proportion of non-farmers on the list, resulted in a return rate of 190 surveys. A raffle incentive was used, giving respondents a chance to win either a $50, $30 or $20 cash prize in a drawing. 135 of these surveys had complete choice data, and form the basis for the illustrative analysis. While this appears to be a very low return rate, it is consistent with normal unsolicited mail survey return rates of 20%-30% because of the large proportion of non-farmers. [Despite the low return rate, our estimates of the market shares for 1983 and 1984 are well within the statistical error limits of those independently supplied to us by the company sponsoring the research. Thus, there appears to be negligible bias due to nonresponse, at least as far as share estimates are concerned. Our demographic profiles for the farmers were also consistent with the sponsoring organization's expectations, lending additional support to the respresentativeness of the sample.]

The respondent was required to assume that the per acre prices for products A-G were as listed and that a "New" product was also available, with characteristics and price as described. The respondent was asked to examine each set of products and to decide whether they would have purchased any of those listed for their insecticide needs in 1984 had the products been available, and if so, to indicate which one, or to indicate that they would not have purchased any of the products. Instructions emphasized that the A-G products (listed by actual Brand Name) were the only products currently available in their area, so they would have to purchase one of these products or the "New" product, or do without. Each respondent therefore made a single choice in the manner described in each of the 18 choice sets created by the "Split-Plot" design.

Analysis and Results

The discrete choices made by the respondents were aggregated to absolute frequencies for analysis by Generalized Least Squares (G.L.S.) regression. As explained in Nakanishi and Cooper (1982) and Louviere and Woodworth (1983), weighted least squares regression will produce asymptotically efficient estimates of the parameters of the Multinomial Logit Choice Model. We assume that the MNL model is a reasonable model to approximate the choice data. The MNL model may-be expressed as:

where p(a/A) is the probability of choosing the a-th product given a set of competing products, A, of which a is a member,

U(a),U(j) are the mean levels of utility associated with products a and j, respectively, and

exp is the symbol for exponentiation (i.e., e to the 'x' power).

The mean utility levels correspond to the marginal probabilities of choosing each alternative. These marginals can be parameterized as follows:

where U(x) is the utility of the x-th product,

X

_{k}is a design matrix of levels of attributes, or non-linear transformations of attribute levels, or cross-products of attribute levels, and bkis a vector of regression-like parameters associated with each separate vector in the design matrix.

Equation (2) expresses the mean level of utility for each product as a linear-in-the-parameters and additive function of the vectors in the design matrix.

Interest centers on parameterizing the U(x)s, which is accomplished by creating alternative specific attribute vectors and dummy variables for the denominators of equation (1) as explained in Louviere and Woodworth (1983). In the present case each of the seven products (A-G) has a brand-specific parameter (intercept), and a linear and a quadratic price term; the "New" product has a brand weight coefficient, linear and quadratic terms for price, and dummy variables for (n-l) of the levels of each of the product attributes. The "No Purchase" alternative has a utility value of exactly zero. These parameters were estimated from the choice data via a G.L.S. regression (see Table 1, which also lists the mean per acre price levels used for each product as well as the levels of the "New" product attributes).

Let us describe the results for the "New" product attributes: all numbers at the bottom of Table 1 are relative utilities. All had significant effects, although efficacy against insects, duration of effectiveness and price played very major roles in the choice of a "New" product, and odor and toxity effects were minor, as can be seen by the differences in the utility values of the levels of each attribute. Thus, efficacy against insects and duration of effectiveness had the largest non-price effects. Although not obvious from the top of Table 1, price had the largest single effect with a utility at low of .67 and at high of -.67. All price effects were approximately linear for this product market for the range of prices examined

The MNL model predicts that all cross-price effects are proportional to the shifts in utility values of the various products. This prediction can be tested by including the cross-price effects in a second G.L.S. regression analysis. These results are given in Table 2; they indicate that there are a number of significant cross-price effects (only the significant effects at the .10 alpha level are listed). Thus, the proportionality hypothesis must be rejected; there are cross-price effects that are less than or more than the effects predicted by the simple MNL model. Such violations of the MNL model can tell us about 'Who competes with whom", and which products the "New" product will most effect. For example, the "New" product most affects products A, D, F and G, all of which are either low share or cheap. So, it affects the market leaders less than these products. The model fits significantly better than the simple model; the F value for the 19 additional parameters is 4.2(19,96), which is significant well beyond conventional alpha levels. There is therefore no question that the simple MNL hypothesis must be rejected for these consumers.

Farmers were asked to estimate the per acre price of each product; these data were used with the estimates in Table 1 to forecast the 1984 market shares for each product. Shares observed in another section of the mail survey were compared to shares predicted by the derived choice model using the farmers' mean estimated selling prices per acre for each currently available product. Predicted and observed values are graphed in Figure 1; products are not labelled so as to preserve anonymity. As can be noted, the choice model predicts the observed shares well: all predictions lie within the error limits at the alpha=.05 level. This is especially encouraging in view of the fact that both the sample and model estimated shares have error. While this does not necessarily mean that the choice model is externally valid, it does bolster confidence in its use as a predictive model and as a vehicle for drawing strategic inferences for management.

RESULTS OF CHOICE ANALYSIS FOR SIMPLE MODEL

PREDICTED AND OBSERVED MARKET SHARES

COMPARISON OF MODEL COEFFICIENT ESTIMATES

DISCUSSION AND CONCLUSIONS

This paper described an approach to studying competitive pricing strategy in an existing product market into which new product concepts with varying attribute levels are introduced. This approach extends the previous work of Mahajan, Green and Goldberg (1982) to include more levels of price and competition from a new product. The design approach proposed, when combined with the MNL choice model, permits an analyst to draw strategic inferences about the likely market share consequences of pricing strategies of existing products, as well as the potential shares which can be realized by various positionings of a new product. The proposed approach was illustrated with a strategic choice study of crop insecticides. Model results were meaningful, statistically significant and predictive of actual observed market shares.

Several extensions to the proposed approach are possible. As discussed in Green (1974), the fractional designs within each "plot" can be chosen so as to permit one to estimate various interactions of interest. For example, it will normally be sufficient to estimate only the linear x linear component of each two-way interaction in order to test the null hypothesis of no interaction effects because the majority of the variance in the interaction terms usually will be in that component, even if other components are significant. This is especially true for models in which all marginal effects can be assumed to be monotonic with the criterion; and, of course, this should be the case with price.

An extension to the present study can be developed by imbedding the products that compete on price in a 2n design as described in Louviere and Woodworth (1983). This 2n design can be used to place combinations of products in subsets, each of which could have a (potentially) different pricing design. The use of these subsets of designs permits the analyst to simultaneously examine both the effect of entry and exit (presence/absence) and pricing strategy. In this way the analyst can make inferences about which products will gain share at a rate greater (or less) than in proportion to their average utility levels when competing with various other products. The analyst can also make inferences about the way in which pricing strategy might be expected to interact with the product effects, (See, e.g., Batsell 1980; Batsell and Polking 19841.

Another extension involves the new product concepts: the interactions of the attributes of interest could be examined by creating one or more designs which permit them to be estimated independently. The effects of multiple products being introduced could be examined by creating additional "plots" using minimally correlated multiples of orders, or by imbedding the products in a second 2n design to create different choice surveys. In any case, the "split plot" approach allows one to examine a wide variety of realistic competitive choice problems from which strategic inferences can be drawn according to the nature of the design(s) employed. One could also use block design concepts to develop design strategies for studying these kinds of choice problems.

A major advantage to the strategic choice experiments described in this paper is that they are a step closer to simulating the competitive effects of real markets, while retaining many of the advantages of the traditional conjoint analysis approach. Their appeal is the ability to extend choice analyses to non-Luce type models which avoid the IIA (independence from irrelevant alternatives) and constant cross-elasticity assumptions (See, e.g. Batsell 1980; Batsell and Polking 1984). Allowing for the inclusion of certain types of interactions provides the statistical ability to test for violations of MNL assumptions and to estimate statistical models which describe the violations if appropriate. Yet another advantage is that the estimation can be accomplished using G.L.S. regression approaches with widely available statistical software. This should allow progress to be made in the development and testing of choice models which more closely approximate real behavior in response to competitive strategies and tactics.

REFERENCES

Amemiya, T. (1981), "Qualitative Response Models: A Survey," Journal of Economic Literature, 19(4), 1483-1536.

Batsell, R.R. (1980), "A Market Share Model Which Simultaneously Captures the Effects of Utility and Substitutability," Working Paper No. 80-007, Dept. of Marketing, University of Pennsylvania, Philadelphia.

Batsell, R.R. and J.C. Polking (1984), "A Generalized Model of Market Share," Working Paper No. 48, Jesse H. Jones Graduate School of Administration, Rice University, Houston, Texas.

Chacko, A. (1980), Some Investigations on Fractional Factorials and Weighing Designs, Ph.D. Thesis, University of Delhi, Department of Statistics, Delhi, India.

Cochran, W.G. and G.M. Cox (1957), Experimental Designs, 2nd Edition, New York, John Wiley.

Federer, W.T. (1975a), "The Misunderstood Split Plot," In R.P. Gupta (ed.), Applied Statistics, Amsterdam: North Holland Publishing Co., 9-39.

Federer, W.I. (1975b), "Sampling Structures for Split Plot and Split Block Designs," Mimeo No. BU-551-M, Biometrics Unit, Cornell University, Ithaca, N.Y. (March).

Gould, J.P. and S.K. Sen (1934), ;?ricing Strategy: Proceedings of a Conference, September 24-25, 1382, 'The Journal of Business, 57(1), part 2 (January), S1-S266.

Green, P.E. (1374), "On the Design of Choice Experiments Involving Multifactor Alternatives,' Journal of Consumer Research, 1(Sept), 61-68.

Hensher, D.A. and Johnson, W. (1931), "Applied Discrete-Choice Modeling," New York: John Wiley.

Ingrassia, P. (1980), "In a Color-TV Market .Roiled by Price ,Jars, Sony Takes a Pounding," In Tootelian, D.E.; Gaedeke, R.X. and L.A. Thompson, Marketing Management: Cases and Readings, Santa Monica, CA, Goodyear Publishing Co., 413-415.

Jones, D.F. (1975), "A Survey Technique to Measure Demand Under Various Pricing Strategies," Journal of Marketing, 39(3), 75-77.

Louviere, J.J. and G.G. Woodworth (1983). "Design and Analysis of Simulated Consumer Choice or Allocation Experiments: An Approach based on Aggregate Data,' Journal of Marketing Research, 20(Nov.), 353-357.

Louviere, J.J. and D.A. Hensher (1383), Using Discrete Choice Models with Experimental Design Data to Forecast Consumer Demand for a Unique Cultural Event," Journal of Consumer Research, 10(Dec.), 348-301.

Mahajan, V.; Green, P.Z. and S.M. Goldberg (1982). "A Conjoint Model for Measuring Self- and Cross-Price/Demand Relationships," Journal of Marketing Research, 19(Aug.), 334-362.

Markham, J.W. (1934), 'Discussion," Journal of Business, 57(1), January, S257-S263.

McFadden, D. (1974), "The Measurement of Urban Travel Demand," Journal of Public Economics, 3(3), 303-328.

Nagle, T. (1,;34). "Economic Foundations 'or Pricing, In Gould, J.P. and S.';. Sen (Eds.),'Pricing Strategy: Proceedings of a Conference, September 24-25, 1982," Journal of Business, 57 (1), pt. 2, January, 1934, 3-26.

Nakanishi, M. and T .G. Cooper (1982), "Simplified Estimation Procedures or MCI Models,' Marketing Science,1(3), 316-322.

Rao, V.P.. (1984), ;'¦ricing Research in Marketing: The State of the Art," Journal of Business, 57(1), January, 539-560.

Theil, S. (1371), Principles of Econometrics, New York: John Wiley.

----------------------------------------

Tweet
window.twttr = (function (d, s, id) { var js, fjs = d.getElementsByTagName(s)[0], t = window.twttr || {}; if (d.getElementById(id)) return; js = d.createElement(s); js.id = id; js.src = "https://platform.twitter.com/widgets.js"; fjs.parentNode.insertBefore(js, fjs); t._e = []; t.ready = function (f) { t._e.push(f); }; return t; } (document, "script", "twitter-wjs"));