The Effects of Normalization on the Multi-Attribute Attitude Model

Citation:

James L. Ginter (1974) ,"The Effects of Normalization on the Multi-Attribute Attitude Model", in NA - Advances in Consumer Research Volume 01, eds. Scott Ward and Peter Wright, Ann Abor, MI : Association for Consumer Research, Pages: 302-309.

Advances in Consumer Research Volume 1, 1974    Pages 302-309

THE EFFECTS OF NORMALIZATION ON THE MULTI-ATTRIBUTE ATTITUDE MODEL

James L. Ginter, Ohio State University

[The research reported in this paper was funded through a grant from the American Association of Advertising Agencies to Prof. Frank M. Bass. Data analysis was supported by the College of Administrative Science, Ohio State University. The author is indebted to Kenneth E. Miller for his assistance in data processing.]

[Assistant Professor of Marketing, College of Administrative Science, The Ohio State University.]

INTRODUCTION

The multi-attribute attitude model has been the subject of much discussion and debate. Pessemier and Wilkie (1972) indicate that the researchers who have worked with the model have used it in various forms without an investigation of the basic issues underlying these different forms One such issue is that of normalization of the raw data before they are used in the calculation of attitude scores. This paper is an investigation of (1) the normalization issue, (2) the various forms of the model created by normalization, and (3) the relative performance of these alternative forms of the model.

BACKGROUND AND HYPOTHESES

The Model

The basic form of the attitude model as it has been used in marketing is:

EQUATION

where

i = specific product attribute

j = brand

k = subject

Ajk = attitude of subject k toward brand j

Iik = importance of attribute i as perceived by subject k

Bijk = the amount of attribute i which subject k believes a brand j has

The resultant attitude score is a measure of affect and it is based upon beliefs and importance weights indicated by the subjects. These values are usually measured through the use of semantic differential scales.

Normalization

Individuals who indicate brand locations or attribute importances on a semantic differential scale may give different responses for two reasons. (1) They may not have similar feelings about the object being measured. (2) They may interpret the scale differently, and there will therefore be level differences in their responses.

Normalization of semantic differential responses eliminates the level differences in responses by transforming the absolute responses concerning objects to the relative responses for these objects.

        Normalized Response = Raw Response

                                    Total of all Raw Responses

The benefit of normalization in studies using data from more than one subject or more than one measurement of the same subject is developed in the following discussion.

Alternative Forms of the Model

Both the belief data and the attribute importance data are collected through the use of semantic differential scales. Alternative forms of the model can be developed from the various combinations of raw and normalized data. Bass and Wilkie (1973) note that various forms of the attitude model have usually been compared on the basis of their correlation with brand preference. This basis of comparison will be also used here, but the specific measure of preference as discussed in a later section is somewhat unique.

Normalized Importance Weights

The first form of the model to be considered uses normalized importance weights and the raw beliefs.

EQUATION

Each belief is weighted by the importance of that attribute relative to all other attributes rather than the indicated absolute value of the importance. Level effects in the importance data are eliminated since two observations in which importance responses were equal for all attributes but at two different levels would result in the same attitude scores. The assumption that the importance scale was interpreted in the same way for all observations is therefore eliminated. The correlation between attitude and preference across observation (either across subjects or over time) should be greater than that achieved through using raw data since attitude scores will not depend upon the interpretation of the importance scale. The following null hypothesis was tested.

H1: The IN form of the model does not perform better than the model using raw data in correlation across observations.

The importance normalization will have no effect on the attitude-preference correlation within one observation. The attitude scores from each observation are multiplied by a scale factor by this transformation, and the correlation would therefore not be affected.

EQUATION

Normalized Beliefs

Another form of the model uses normalized values of the believed locations of the brands on each attribute. The use of relative locations of the brands on each attribute eliminates the level effects present in the belief scores.

EQUATION

In an analysis done across observations the attitude scores would be affected by the level difference on the belief scales. The attitude preference correlation should therefore be greater with the BN model. The following null hypothesis was tested.

H2: The BN form of the model does not perform better than the model using raw data in correlation across observations.

The normalization of beliefs on an attribute by attribute basis will also affect the within observation correlation analysis.

EQUATION

The normalization of beliefs does not change the attitude score toward all brands by a scale factor. In other words, a unit difference on an attribute on which the brands vary greatly is weighted less than a unit difference on an attribute on which the brands vary little. The attitude scores toward the brands will be changed within each observation, and the within-observation correlation will therefore be altered.

Normalized Beliefs and Importances

The normalized importance weights and beliefs as discussed previously can be used jointly in yet another form of the model. For each observation this form of the model differs from the BN model by a scale constant, so it will differ from the raw data model in the same manner as the BN model.

EQUATION

In an analysis across observations, however, the INBN model will eliminate the level effects of both the importance and the belief variables. Therefore, this form of the model should perform better than either the raw data model, the IN model, or the BN model. The following null hypothesis was tested.

H3: The INBN form of the model does not perform better than the raw data model, the IN model, or the BN model in correlation across observations.

Normalized Attitude Scores

The final form of the model to be considered does not use normalized importance or belief data, but the attitude scores are normalized within each observation.

EQUATION

The AN model therefore differs from the raw data model by a constant scale factor for each observation. Within observation correlation analysis will not be altered by this transformation.

The AN model eliminates level effects in the attitude scores, so results of analysis across observations will be different. This form of the model eliminates level effects in the importance and belief responses as well as the interaction of these level effects. This form of the model should provide highest correlation between attitude and preference in analysis across observations. The following hypothesis was tested.

H4: The AN form of the model does not perform better than the raw data model or the INBN model in correlation across observations.

Prediction of Choice

The previous discussion considered comparison of alternative forms of the model on the basis of correlation between attitude and preference. Correlation analysis is not relevant to prediction of choice, however. Also, choice of responses on all questions, and the following analyses were done on only these subjects.

The analysis consisted of a correlation of attitude and preference across all subjects for the five brands. This was performed separately for each of the time periods to avoid variation across time. The correlation results of the raw data model and the four alternative normalized forms of the model are shown in Table 1.

TABLE 1

ATTITUDE VS. PREFERENCE CORRELATION

The hypotheses concerning the relative performance of different forms of the model were tested by testing the null hypothesis

H0: u1 - u2 = 0

on the basis of the differences

di = X1i - X2i   for   i = 1, ...., 8

The means and standard deviations of these differences are shown in Table 2.

TABLE 2

COMPARISON OF ALTERNATIVE MODELS

prediction is necessarily a within-observation analysis. This is true because the attitude scores of all brands are calculated for an observation and the brand with the most favorable attitude score is predicted to be chosen. The only forms of the model discussed which could alter a within-observation analysis utilized normalized belief data (BN and INBN). The normalization of beliefs may affect the relative attitude scores of the brands, but in order to affect prediction of choice it would have to change the brand with the most favorable attitude score. Therefore, normalization would change accuracy of choice prediction only in rare instances.

METHODOLOGY

Data

The data were collected in a laboratory experiment conducted with 453 housewives in Lafayette, Indiana. Each subject attended a two-hour session each week for four consecutive weeks. Attitude and preference measures were taken at the beginning and end of each session, and subjects were exposed to advertising for some of the brands during the sessions to stimulate change.

Five brands of household cleaning product were used for the data in this analysis. The following attributes were used for the importance and belief measures.

Stain removing power

Whitening power

Sudsiness

Mildness to skin

Mildness to clothes

Pollution control

For a detailed description of the experiment, see Winter and Ginter (1971).

Preference Measurement

The level of preference for each of the alternative brands was measured by the use of the dollar-metric procedure, Pessemier et al (1971). This measurement method uses graded paired preference measurements for all possible pairs of brands and results in an interval affective scale for each subject. For each pair, the subject indicated the preferred brand and the amount (in dollars) the current price of this preferred brand could increase before preference would switch to the other brand.

The five brands are located on an interval scale by applying a least-squares fit criterion to the subject's original paired preference judgments. The units on this scale are dollars because of the nature of the original dollar-metric responses. This measure of preference seems better suited for correlation analysis of attitude and preference than rank order measures because of its interval nature.

Results

Attitude and preference measurements were made at the beginning and end of each of the four sessions the subjects attended, so there were eight observations on each of the 453 subjects. 140 of these subjects had a complete set.

The comparison of the IN model and the raw data model (R) shows that the IN model produced correlation coefficients significantly greater than those of the raw data model. H1 was therefore rejected. The comparison of the BN model and the raw data model produced similar results; H2 was also rejected.

H3 was tested by comparing the INBN model with the raw data model, the IN model, and the BN model. The INBN model performed significantly better in all three cases; HR was therefore rejected.

H4 was tested by comparing the AN model with the raw data model and with the INBN model. The AN model performed significantly better in both comparisons; H4 was rejected.

CONCLUSIONS

The results of these analyses show that normalization of data used in the multi-attribute attitude model increases the correlation of attitude and preference in analyses done across observations. Although normalization of either of the variables increases the predictive power of the model, normalization of both variables increases the prediction even further. The best form of the model, however, utilizes normalization of the attitude scores across brands rather than normalization of the input variables.

These conclusions are based entirely upon the level of the correlation coefficient between attitude and preference in cross-sectional analysis. They support the idea that elimination of the assumptions of homogeneous interpretation and response level to the semantic differential scales improves the model's predictive power. This analysis does not address the issue of the relative contribution to the model of the attributes when they are in either raw or normalized form. Bass and Wilkie (1973) have shown that normalization improves the model in this respect, also.

Researchers have frequently done cross-sectional analyses with the raw data form of the model. This research indicates that the implicit assumptions of this model form are such that a prior transformation of the data improves the model's predictive power significantly.

REFERENCES

Bass, Frank M. and William L. Wilkie. A Comparative Analysis of Attitudinal Predictions of Brand Preference. Journal of Marketing Research, 1973, 10, 262-269.

Pessemier, E. A., Philip Burger, Richard Teach, and Douglas Tigert. Using Laboratory Brand Preference Scales to Predict Consumer Brand Choice. Management Science, 1971, 17, B371-B385.

Pessemier, E. A., and William L. Wilkie. Multi-Attribute Choice Theory--A Review and Analysis. Institute Paper No. 372, Krannert Graduate School, Purdue University, 1972.

Winter, Frederick W., Jr., and James L. Ginter. An Experiment in Inducing and Measuring Changes in Brand Attitudes. In Fred C. Allvine (ed.), Proceedings, American Marketing Association, 1971, 441-445.

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