A Range Model of Overall Evaluation: Extending the Ideal Point Model


Elizabeth Cowley and John R. Rossiter (2001) ,"A Range Model of Overall Evaluation: Extending the Ideal Point Model", in E - European Advances in Consumer Research Volume 5, eds. Andrea Groeppel-Klien and Frank-Rudolf Esch, Provo, UT : Association for Consumer Research, Pages: 174-179.

European Advances in Consumer Research Volume 5, 2001      Pages 174-179


Elizabeth Cowley, University of New South Wales, Australia

John R. Rossiter, University of Wollongong, Australia

[This research was funded by an Australian Research Council Small Grant RMC2332. Correspondence concerning this article should be addressed to Elizabeth Cowley, School of Marketing, John Goodsell Building, University of New South Wales, Sydney NSW 2052, Australia. Electronic mail may be sent via the internet to e.cowley@unsw.edu.au]

A multiattribute range model is proposed. The range model assumes that consumers represent a brand’s level of attribute delivery as a range, which is compared to a range of the desired level of the attribute, and weighted by a range of importance of the attribute. This model allows for the possibility of uncertainty in the perception of a brand belief, a "latitude of acceptance" (or tolerance) for the desired level of an attribute, and contextual variability in the perceived importance of an attribute.

The model was tested with an experiment. Two hundred fifteen undergraduate students were given taste samples of an unfamiliar brand of vegetable juice. One third of the students received factual information about one of the attributes of the juice, which was intended to change their belief about the attribute level. Another third of the students received normative information in the form of other students’ evaluation of the attribute, which was intended to change their belief about the attribute level and the confidence with which they hold the belief. A final third of the students were given unrelated information. The results demonstrated that the range model better predicted students’ overall evaluation of the juice than did the conventional ideal point model, particularly in the normative information condition.

Brand attitude is a critical determinant of brand choice (Kraft, Granbois & Summers 1973), and is said to be "the pillar on which sales and profit fortunes of a giant corporation rest" (Aaker & Myers, 1987, p. 160). Though its importance is undeniable, researchers in behavioural decision theory have provided dozens of examples of the apparent instability of brand attitudes (see Payne, Bettman & Johnson 1993 for a review). There is a great deal of controversy over how to approach specifying the construct to capture its instability over contexts. It is proposed here that each of the components of attitude in a multiattribute framework would be more accurately represented as a range rather than a point estimate.

Our model extends the conventional ideal point model by including ranges around each of the components to capture a consumer’s uncertainty when estimating attribute levels of a brand, a latitude of acceptance for desired levels of an attribute, and uncertainty in stating the importance of an attribute. The two models, the ideal point model and the range model, are tested with data collected in an experiment to investigate which specification captures the changes in the estimation of one or more of the components caused by the post-consumption word-of-mouth.


If product judgments are considered as an overall evaluation of a brand in a multiattribute framework, they are a function of the strength of the beliefs that a brand possesses certain attributes weighted by the evaluations of those attributes (Fishbein 1963). Ahtola (1975) extended Fishbein’s multiattribute attitude model in his Vector Model, which sums the probabilities that a brand has specific levels of an attribute multiplied by the evaluations of those specific levels. Ahtola asked individuals to estimate probabilities for a number of levels of each attribute, which results in a vector or a distribution-like representation of brand beliefs.

Another version of the multiattribute model used in the marketing literature, the ideal point model (Green & Srinivasan 1978), incorporates: (1) brand beliefs B the perceived level a brand has of a particular attribute, (2) attribute level desirability B the desirable level of a particular attribute, and (3) attribute importance. The ideal point model assumes that the consumer has an "ideal point" or a preferred level of each attribute on a continuum of attribute levels. By comparing the perceived level of a particular attribute, or a brand belief, with the desired level of the attribute, consumers can evaluate brand performance with respect to their preference for each attribute. The effect of the evaluation on brand attitude is a function of that attribute’s importance to the consumer.

The ideal point model has been used in perceptual mapping (Johnson 1988) to create shares of preference between brands available in the marketplace which are useful for purposes of segmentation (Feick 1998; Johnson 1995). Some critical limitations of the current form of the model will be discussed in the next sections. An extension of the model to include ranges is designed to resolve these shortcomings.


Brand Belief

Uncertainty in establishing brand beliefs

Multiattribute attitude models typically used in marketing research, such as the ideal point model, are constrained by the assumption that consumers are fully aware of the amount of each attribute a brand possesses (Meyer 1981). Brand attribute beliefs are most often measured by asking the individual to choose a rating scale category that describes the likelihood that a brand has an attribute, with seven categories of likelihood ranging from "very likely" to "very unlikely." The problem with this type of scale is that the amount of uncertainty in the judgment is not captured. Consumers are not able to communicate that they are very certain (judgment is concentrated in one category of the rating scale), or that they are very uncertain (judgment is spread over adjacent categories), or that the uncertainty is asymmetrical (judgment is not equally spread above and below the most probable category).

Ahtola (1975), in his Vector Model of preferences, enabled consumers to distribute poker chips over the rating categories, allowing them to communicate the degree of uncertainty in their estimates, and, if it was skewed, the direction of their uncertainty. The respondents, however, were still limited to the fixed categories composing the rating scale. In our range model, we allow individuals to express their brand beliefs as ranges from a minimum level (Bijkmin) to a maximum (Bijkmax) indicating a "confidence interval" around the point estimate of the brand belief (Bijk) (see Figure 1).

Conditions under which uncertainty might arise

We use two sources of information when forming a brand belief: our perception of the physical reality, and what others say (Van Avermaet 1996). When we estimate Bijk with our "own perception of reality" information only, uncertainty may arise because of a lack of confidence in our ability to accurately make an assessment. The uncertainty in brand beliefs is exaggerated for those less knowledgeable (Biswas & Sherrell 1993) or unfamiliar (Estes & Hosseini 1988) in the domain. When using information from the environment that constitutes "others’ perception of reality," uncertainty may arise because of a lack of credibility or trustworthiness of the information source (see Woodruff 1972). In both of these cases the range around the estimate of the level of an attribute increases (Cowley & Rossiter 2000), reflecting an increase in uncertainty. When the information from the environment is consistent with "own perception," then the range of uncertainty decreases (Cowley & Rossiter 2000), reflecting the boost in confidence that occurs when our judgments are legitimized.

The situation becomes more complicated when there is a discrepancy between "own perception" and information from the environment. Three outcomes could result from the contradiction. First, the point estimate of the attribute level could be altered to be more consistent with the information from the environment. This might be likely if the consumer learns a new fact about the brand that causes them to update their belief by changing their point estimate. Second, the range around the point estimate could increase because information from the environment calls into question the basis of the point estimate. Third, a combination of an alteration of the point estimate and a change in the confidence with which the belief is held could occur. This might be the case if the consumer is provided information about "everyone else’s opinion". In the process of comparing "own evaluation" to "others’ evaluation", "own evaluation" may be altered to be more consistent with the presumed majority evaluation of others (Festinger 1954; Schachter & Singer 1962).

Consider the following scenarios. You are having dinner with five friends. Dinner is served, the wine has been breathing. One of your friends pours the wine, you take a sip, you think the wine is quite light, but before you can comment, you notice that the label describes the wine as a heavy, full-bodied wine. In this case, you might change your point estimate of its heaviness. In the second case, you have always thought this particular wine was quite heavy because a wine expert reported it as such, but one of your friends says during dinner that the expert is not at all credible. In the final case, imagine that after you had decided that the wine was quite light, your friend said "Well, it’s quite heavy," and everyone else at the table concurred, then, your perception of reality is in direct conflict with everyone else’s perception. In this case, you would be fairly confident that the wine, if anything, is not lighter than your original assessment, but you may be unsure about whether it is actually heavier. Your point estimate might change, but also the range would be asymmetrically skewed toward the comment.

The ideal point model would detect any change in the point estimate based on what is perceived to be a fact, but would not detect changes in confidence based on changes in the range around the estimate. In our range model, both changes in brand beliefs and changes in the confidence with which beliefs are held are captured.

Desired Level of an Attribute

A range of acceptance around the desired level

Economic theory is based on the assumption that consumers have an underlying preference structure that guides them in their decisions. This assumption allows consumers to make economically rational judgments using these relatively stable preferences. Behavioral decision theorists have called this assumption into question by demonstrating that both the task and the context impact preferences because preferences, typically, are constructed during their elicitation (Lichtenstein & Slovic 1971; Tversky, Sattath & Slovic 1998). One explanation is that when estimating the desired level of an attribute, Eij, the estimate is actually a range around the point estimate that can be conceptualized as a "latitude of acceptance" (Coombs 1964; Hovland, Harvey & Sherif 1957). Within the range the consumer may not receive the exact ideal level of attribute, yet the level would not be considered undesirable. Outside of the range, below Eijmin or above Eijmax, the level of attribute would be considered undesirable. In our range model the consumer is allowed to specify a range of acceptable attribute levels between Eijmin and Eijmax, indicating a tolerance in preference.

Conditions under which the range might change.

Information from another consumer may influence the desired level of attribute or the acceptable range around attribute if the comment provides a context that alters the outcome of a specific level of the attribute. Consider the following scenarios. Imagine that while you are drinking a beverage, your friend makes a comment about salt. The comment might describe the attribute positively by suggesting that natural salt is part of a healthy diet, or negatively by suggesting that all forms of salt are not healthy. If the comment is consistent with your previous estimate of the desired salt level, then there may be a reduction in the range around your ideally desired level, reflecting a reduction in your tolerance for levels other than your ideal level. Conversely, if the comment is inconsistent with the consumer’s previous estimate of the desired salt level, the range may shift in the direction of the comment, reflecting an increase in tolerance for attribute levels in the direction of the comment. In our model we allow consumers to represent their desired level as a "latitude of acceptance" around Eij, which extends on either side of a previously established point estimate.

Attribute Importance

Uncertainty in Attribute Importance.

An individual’s assessment of the importance of a particular attribute (Impij) has been manipulated by the context (Huber, Payne & Puto 1982; Simonson & Tversky1992), and with the frame (Fischoff 1983; Thaler 1985). Additionally, consumers’ assessment of Impij has been shown to change with accumulation of experience in a product category (Hoeffler & Ariely 1999). Market researchers using decompositional procedures believe that individuals may not be accurate in their assessment of the importance of each individual attribute (Green 1984) which is supported by more general findings revealing inaccuracies in the reporting of attribute importance (Shepard 1964). We believe that the inaccuracy may be the result of constraining the consumer to a point estimate instead of a range of importance. Although consumer researchers have provided importance information in the form of a distribution (Kahn & Meyer 1991), our model captures a range estimate indicating the consideration of contextual variation for Impij.


Winkler (1966; 1967) pioneered the range method as a way of estimating Bayesian prior distributions. It was first used in marketing by Woodruff (1972), who used 19 fixed rating categories (half-points on a 1 to 10 scale) to measure beliefs only. Since then, the only marketing study we could find that employs the notion of the individual’s belief variance is by the marketing consultant William T. Moran (1985), who may have arrived at the notion independently as the earlier work by Woodruff was not cited. A related method, the grain-scale method, has been used recently in decision making to test judgmental estimation models (Yaniv & Foster 1996). In that study, respondents were allowed to choose one interval from one of six scales varying in graininess, or interval size, from 290 years to 2.5 years. Respondents could indicate greater confidence by selecting an interval from a finer scale.



We incorporate a range around each of the components of the ideal point model to allow for a confidence interval around brand beliefs, a latitude of acceptance around preference and contextual variation for the importance of an attribute. We use the ranges to estimate the degree of utility or satisfaction with a brand by measuring the distance between (or degree of overlap of) the range around the desired level (Eijmin to Eikmax) and the range around the brand belief (Bijkmin to Bijkmax) for each attribute. If the two ranges overlap, the utility is positive because the perceived level of the attribute offered by a brand is within the range of desired levels of the brand. If the ranges do not overlap the utility is negative because the consumer believes that the brand offers a level of an attribute that is not within the range of levels acceptable to that consumer. The greater the distance between ranges, the greater the disutility. It is critical to keep the sign of the difference, hence the inclusion of sign in the equation. For instance, if the consumer indicates that they believe the level i of attribute j is between 40-60 on a scale of 100. And that same consumer would ideally like the level to be between 70-90. The utility would be B10. If on the other hand, the ideal point was between 40-60, the utility would be positive.

We use both the point estimate of importance and the range around the point estimate to represent the importance of each attribute. If the subject reports that the importance of the attribute ranges dramatically with the context (ie. reports a large range), then the weighting of the rating is reduced. If the subject believes that the importance does not vary with the context, then their ability to identify the importance is improved and the weighting increases. For instance, if the consumer says low sugar content is always important to them 90/100 with a very small rang 85-95, then the utility would be multiplied by an importance factor of 9. Conversely, if the consumer indicated that the range was between 10-100 depending on the context, the importance factor would only be 1. (See Figure 1)


The reactions of others are often incorporated in the decision of appropriate behavior for self (Festinger 1954; Schachter & Singer 1962) as has been illustrated in the scenarios in previous sections. In the process of comparing "own evaluation" to "others’ evaluation", "own evaluation" may be altered to be more consistent ith others (Festinger 1954). In the context of product evaluation, it is now well documented that the opinion of others heard during the consumption of a product can affect the evaluation of the product (Bone 1995; Burnkrant & Cousineau 1975; Cohen & Golden 1972; Venkatesan 1966).

It is proposed here that the range model will better explain consumers’ overall evaluations, particularly when the opinion of others serves to alter the range around the estimate of brand belief, attribute desired level, or attribute importance. As a first step toward testing the explanatory power of the model, the empirical work here includes a manipulation of the information concerning a brand belief presented in the post-consumption environment. The study includes three levels of information: factual, normative and unrelated (as a control condition). We expect a change in the point estimate when factual information is introduced post-consumption, a change in point estimate should be explained by both the range model and the ideal point model. We expect a change in both the point estimate and the symmetry of the range in the normative condition. A comment suggesting that most people think the product has a lot of one attribute will result in an asymmetry in the range. The asymmetry will be captured by the specification of the range model, but not by the ideal point model.



Two hundred fifteen undergraduate students enrolled in an introductory marketing course at a large Australian university received course credit for participation in the study.

Product Category

Vegetable juice was chosen as the product category because it is a product that is purchased by university students. The brand was Campbell’s V-8, an unfamiliar brand. [Pre-testing revealed that although many of the students had heard of V-8 juice, very few had tried it recently. In the sample used for the results reported here, 79% reported they had not tried it before, and 18% reported they rarely drank the brand. This may be surprising for readers in North America where the brand is heavily supported with promotional spending. In Australia, Campbell=s does not support the brand with advertising or point-of-sale material.]


There were three conditions in the study. In the factual condition participants were exposed to a fact about the level of salt in the juice immediately after consumption and just prior to reporting their evaluation of the juice. In the normative condition participants were informed of the evaluations of the level of salt in the vegetable juice of the majority of other participants. In the control condition participants heard a comment that was unrelated to the juice.








Students were randomly assigned to the comment condition. Students were told that during the cracker taste test they must drink some of the juice before, in between, and after tasting each brand. Direct experience, as in a taste test, enables consumers to form what should be for them a highly valid evaluation of the product with a high degree of certainty (Fazio & Zanna 1983; Smith & Swinyard 1981). Immediately after consumption of the juice, the study administrator told the participants in the factual condition that "the juice was chosen because it has a high salt content which helps clear the palate." Subjects in the normative condition were told that "your fellow students in past sessions thought the juice was very salty." Subjects assigned to the control condition were told that "the crackers brands are both popular in Europe".

Post-consumption ratings were gathered for attribute importance, attribute level desirability, and brand beliefs for 4 attributes (the scales are described in the next section) for both brands of cracker. Participants were then asked to evaluate the juice on 4 attributes (the scales are described in the next section). Participants then provided responses on unrelated tasks, were debriefed and thanked for their participation.

Dependent Measures

The importance ratings were made for "sweetness," "salt content," "thickness" and "tomato content" [The four attributes were determined in a preliminary study to be the most important for student evaluations of vegetable juice.] on 100mm continuous scales with the following instructions (the scale is exemplified in Figure 2): "Please use the scale below to indicate how important the attributes of vegetable juice are to you. It is often difficult for people to indicate exactly how important any particular attribute is to them. Please identify a point on the line that represents the approximate importance of the attribute (mark it with an X). Draw a vertical line to indicate the maximum importance you would give to the attribute. Draw another vertical line to indicate the minimum importance you would give to the attribute. Then please shade the area in between, creating a range of importance around the X. The X does not need to be in the center of the range."

The desirable levels of the attributes were indicated for the four attributes on a second set of 100mm scales (the scale is exemplified in Figure 3) with the judgment described as follows: "Please use the scale below to indicate the level (or how much) you like of each of the attributes of vegetable juice. It is often difficult for people to indicate exactly" The rest of the instructions, asking for he point estimate and the range, were as above.

The attribute level beliefs for V-8 were rated for the four attributes on a third set of 100mm scales (the scale is exemplified in Figure 4) with the judgment described as follows: "Please use the scale below to indicate the level (or how much) the V-8 brand of vegetable juice has of each attribute. It is often difficult for people to indicate exactly" The rest of the instructions, asking for the point estimate and the range, were as above. Participants also provided an overall evaluation of the juice on a 100mm continuous scale anchored with "dislike very much" and "like very much."




To test whether the range measure contributes to the explanation of the overall evaluations of consumers, the data were used to estimate the fit of the range model versus the ideal point model. The results are shown in Table 1. The adjusted R-squared statistic indicates that the range model better explains the overall evaluation of consumers, than does the ideal point model. As expected, the range model is particularly sensitive to the changes in overall evaluation when a normative statement is made altering both the point estimate and the range around the estimate.

The Akaike’s Information Criterion (AIC) is used to consider investigate whether the attributes measured contribute to the overall evaluation. In both cases the lowest AIC which indicates a better fit with a lower number, occurs when all components of all 4 attributes are included in the models (range model AIC = 1298, ideal point model AIC = 1313).

To look more closely at the results of the manipulation, an ANOVA run on the change in the level of salt belief in the juice revealed a significant effect for the word-of-mouth factor (F(2, 214) = 16.1, p < 0.0001). As expected, the point estimate is significantly higher in both the factual and normative condition compared to the control condition (factual = 67.4, normative = 66.5, control = 51.9).

The symmetry in the range for the level of salt belief varies between conditions. In the control and the normative condition the ratio of area above the point estimate compared to below the point estimate should be close to 1, indicating that no systematic asymmetries are present in the ranges. In the normative condition the ratio should be significantly larger than 1, indicating that the range is larger above the estimate in the direction of "more salt". This pattern of results is expected because word-of-mouth from unknown others may serve to alter the consumer’s confidence in the upper ranges of salt content only, "maybe there is more salt, and now I’m pretty sure there isn’t less". With a new piece of factual information the consumer is likely to reconsider their belief without incorporating asymmetry in the range. The asymmetry was found for the normative condition in the data. The Word-of-mouth factor in an ANOVA of the ratio of the range is significant (F(2, 214) = 9.81, p < 0.0001), where the ratios for the factual and control conditions were 0.92 and 1.21, respectively, with neither different than 1. In the normative condition the ratio is 2.05, which is significantly different than 1 (t = -3.61, p < 0.001). This asymmetry explains why the range model predicts better in the normative condition. Explaining the results of this condition is particularly important because many of the studies revealing an effect for word-of-mouth on evaluations have used social judgment theory to explain the effects found in their results (Burnkrant & Cousineau 1975; Cohen & Golden 1972; Pincus & Waters 1977; Venkaesan 1966).

This study provides initial support for the idea that our beliefs, desires and values are better represented as ranges than points on a continuum. Of course, the study represents only one small manipulation of a brand belief. Future research could incorporate manipulations of the desired level of an attribute or the importance of the attribute, as well as different combinations of discrepancy between information in the post-consumption environment and "own perception" of attribute level, desired level, or importance of an attribute.


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Elizabeth Cowley, University of New South Wales, Australia
John R. Rossiter, University of Wollongong, Australia


E - European Advances in Consumer Research Volume 5 | 2001

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