# Scaling of Cross-National Survey Data

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James B. Wiley and Gordon G. Bechtel (1985) ,"Scaling of Cross-National Survey Data", in NA - Advances in Consumer Research Volume 12, eds. Elizabeth C. Hirschman and Moris B. Holbrook, Provo, UT : Association for Consumer Research, Pages: 215-219.

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http://acrwebsite.org/volumes/6387/volumes/v12/NA-12

As the significance of international marketing grows and data becomes available, marketers and consumer researchers increasingly will deal with cross-national analyses. Much of the data will be in the nature of subjective social indicators which are reported in aggregated form. This paper illustrates a model based approach for analyzing data of this type. The approach is illustrated using "happiness" evaluations of married, never married, and divorced respondents in five prominent members of the European Economic Community.

1. INTRODUCTION

Kotler notes two changes in the social context of marketing that result in information needs that are quite different from the past:

The first trend is the shift from local to national and international marketing. The concept of the national and international firm means that company decision makers must make their key decisions on the basis of secondhand information, since they are far removed from the scene where their products are sold. The second is the transition from buyer needs to buyer wants. As the society becomes more affluent, its members' survival needs are increasingly satisfied. Buying becomes a highly expressive personal act, and sellers must depend on systematic research to understand the overt and latent wants of buyers. (Marketing Management: Analysis, Planning, and Control, 5th ed., p. 602.. emphasis added)

There are four consequences of the above trends that are particularly relevant to this research:

1. Information will be collected from different countries and cultures. In many cases, the language of the respondents will differ from market to market.

2. The information will increasingly relate to "subjective" variables: attitudes, satisfaction, social norms, and the like.

3. Information pertinent to the above issues is not likely to be generated internally to the firm . On the contrary, information increasingly will be sample data taken from secondary sources (e.g., Anderson and Engleden, 1977) or generated by a primary research project (e.g., Douglas, 1976).

4. The information will be reported and analyzed in aggregate form, especially in the case of subscription and government sources.

The importance of aggregate analysis has recently been stressed by Epstein (1980), who echoes Katona's (1978) call for a macropsychology using aggregation over subjects, stimuli, occasions, and measures. Katona has illustrated the power of aggregation in bringing into focus the relationship between attitude, as measured by the well-known Index of Consumer Sentiment, and behavior in the form of discretionary consumption.

The objective of this paper is to illustrate how cross-national responses to a prototypical subjective attribute ("happiness") may be analyzed using a model-based scaling procedure developed and refined by Bechtel (1981), Bechtel and Wiley (1983) and Wiley and Bechtel (1983). A response model related to the Rasch model of latent trait theory (Rasch, 1966) is posited-The model's closely related to Andrich's (1978) reformulation of the Rasch model for attitude rating data. The approach differs from the Andrich formulation in that successive-internal scaling theory (Guilford, 1958) is used.

It is possible in general applications using this approach to simultaneously scale stimuli, subpopulations, and category boundaries on several attribute continua tapped by a questionnaire. Examples of continua that may be analyzed include: purchasing intentions; preferences; satisfaction with and importance of stimuli attributes: or social norms, satisfaction with one's personal situation; and happiness. In this present paper, the analysis of a single subjective response item is illustrated . The item concerns ' s overall happiness with "the way things are these days." Respondents are stratified by marital status and data from five prominent, linguistically distinct members of the European Economic Community are used: France, United Kingdom, West Germany, Netherlands, and Denmark.

2. CROSS NATIONAL ANALYSIS OF MARTIAL STATUS AND HAPPINESS

Table 1 presents endorsement proportions for "happiness" and number of respondents in each of the five countries. It is evident that the Dannes (Den.) and the Dutch (Neth.) make greater use of the "very happy" category than do the French, British (U.K.) and West Germans (W. G. ): while the latter three countries make greater use of the middle category than do the British and French. The unweighted average percents over martial status in the respective countries are W.G. (67.3%), Neth. (61.3%), Den. (56.3%), France (52.3%, and U.K. (50.7%).

HAPPINESS BY MARTIAL STATUS IN FIVE EUROPEAN COUNTRIES

The data are drawn from Veenhoven (1983) who emphasizes the impact of marital status on well-being (or lack of it). The linkage is fairly consistent across industrialized nations:

at the bottom the divorced, then the widowed, next, at a distance, the never married, and the married at the top (Veenhoven, 1983, p. 50).

Veenhoven's interpretation is based on an analysis in which the data are grouped into discrete response categories. In many instances a traditional analysis of this type of data will leave the resulting proportions in the form of unwieldy sets of percentages. At the other extreme, investigators may assign successive integers (e.g., 1,2,3,4,5) to ordered response categories and assume an interval level of measurement. In a sense this amounts to measurement by fiat.

The present paper avoids the two traditional approaches by adopting a stochastic response model appropriate for proportions generated by ordered, survey rating scales. A principle advantage of this model based approach is that the measurement procedure, being theory based, is vulnerable to goodness-of-fit tests. One may have more confidence in the validity of market measures stemming from a successfully tested model.

The reanalysis of the data presented in the present paper supports the "happiness" order suggested by Veenhoven. A key feature of the reanalysis, however, is that differences between languages in the response formats are modeled and a formulation is provided for parsing the responses of possible linguistic influences.

2.1 Response Format Theory

Figure 1 shows how the response format may be conceptualized as successive, ordered intervals on a latent "happiness" continuum. The first panel contrasts a hypothetical distribution of married individuals with a corresponding distribution for widowed individuals. This distribution for marrieds is centered toward the happy end of the continuum, at a11, while the distribution for widowed individuals is centered at the "unhappy" end of the latent continuum, at a31. However, some widowed individuals are happier than some married individuals.

RESPONSE TO CATEGORY BOUNDARIES

Following successive interval scaling theory, the three categories on the happiness continuum are defined by two, ordered category boundaries. Panel (b) of Figure 1 indicates that the respondents may differ in the intensity they assign to boundary values and, hence, the boundary values may themselves be distributed in the subpopulations. Married individuals whose happiness is at A on the latent continuum will respond "very happy" if they place the boundary at B since the level of happiness exceeds the intensity of the boundary in this case. They will respond "happy" if they replace the boundary at C, since the intensity of the boundary dominates their level of happiness.

2.2 The Response Model

Accumulating to the right, the probability of responding "above" a threshold on the latent continuum may be written as:

which may be inverted as

l_{ijk} = ln (p_{ijk} / (1-p_{ijk})). (1)

The latter function is called the logit of p_{ijk} (the "true" probability of an "above k" response) and represents the logarithm (to the base e) of the "true" odds of an "above k" to a "below k" response. This logistic response model also appears in Rasch latent trait theory although the subscripting and interpretation of the parameters in the formulation below differs from that of the Rasch model (Rasch, 1966a and b). (In actual practice, of course, p_{ijk} is estimated by P_{ijk}, the observed sample proportion responding "above k" and estimation is based on the corresponding observed logit l_{ijk}.)

In order to highlight the similarity with the Rasch motel, l_{ijk}, the "true" logit, may be decomposed as:

l_{ijk} = a_{ij} - t_{k(j)}, (2)

where

a_{ij} = a fixed (population) value of marital status i in country j (analogous to ability of the individual in the Rasch model).

t_{k(j)} = a fixed (subpopulation) value of boundary k in martial status i (analogous to the difficulty of the item in the Rasch model).

Then

The implication of Equation 3 is that as a_{ij} moves from "below" (less than) t_{k(j)} to "above" (more than) t_{k(j)} agreement probability increases and disagreement decreases.

Figure 2 shows the monotonic relationship between the probability of an above boundary k response, p_{ijk}, and happiness. The two characteristic curves are each logistic functions that capture the hypothesized monotonic increase of p_{ijk} as a_{ij} moves from right to left for fixed t_{k(j)}. When a_{ij} = t_{k(j)} then p_{ijk} = .50. A fixed a_{ij} such as a_{11} in Figure 2, divides the unit probability ordinate into three proportions, namely the respective probabilities of a "very happy," "happy," and "not too happy" responses.

CHARACTERISTIC RESPONSE CURVES FOR BOUNDARIES

Model (3) may be further simplified by hypothesizing that the a.. may be linearly decomposed into separate marital status and country components as

l_{ijk} = b_{i} - (t_{k(j)} + d_{j}) (4)

where b_{i} is the effect of status i, regardless of country, and d_{i} is the effect of country (or language), regardless of marital status. Both boundary values t_{k(j)} and d_{j} are specific to country.

The position of the country specific parameter d_{j} is subject to at least three sets of influence

First, there may be differences in the 'objective' conditions. Not all domains lend themselves to being judged by anything resembling common objective standards, but areas such as housing, education, income, and medical care are probably easier to agree upon than overall 'subjective' measures as life satisfaction and happiness. Second, even if the objective conditions were identical, it is entirely possible that [different cultures] might not perceive them in exactly the same way. Cultural expectations differ and in turn affect perceptions. Third, given identical perceptions about the various areas of life satisfaction, there may be culturally influenced biases in how particular individuals reveal or report their feelings (Osteroot, et. al., 1982, 134-135).

Equation (4) is structured to emphasize the latter interpretation of the country specific parameter d., i.e., as a country specific shift of the country specific boundary values. That is, one interpretation of the greater endorsement of happier categories by the Dutch vis-a-vis the French is that the boundaries of the response format are taken to be further to the right by the Dutch than by the French. Note that the relative width of the middle category is greater for the Dutch reflecting the greater use of the middle category in Holland. Reason for such a shift and differential width of middle categories across nations might be attributable to language differences or to generalized, country specific predispositions to respond favorably or unfavorably.

2.3 Distribution assumptions at micro level.

It is evident from Figure 1 that there are two latent random variables controlling the response to a format, i.e.,

a_{ij} = b_{i} - d_{j} + e_{ij} (5a)

t_{k(j)} = t_{k(j)} + e_{j} (5b)

In (5a) the b_{i} and d_{j} are population constants of (4), while e_{ij} and e_{j} and hence a_{ij} and t_{k(j)} are randomly distributed over individuals.

If it is assumed that in the population of individuals the two random variates e_{ij} and e_{jk} (corresponding to the density distributions of figure 1) are independently identically distributed (i i.d,) with the double exponential distribution density function, then by a proof due to Maddala (1983, pp. 59-61), the population probability that an individual of marital status i from country j will respond above k is given by

P_{r} (a_{ij} > t_{k(j)}) = [1 + exp {-a_{ij} - t_{k(j)}}]^{-1} (6)

The observed log odds or logit of (4)l_{ijk} is given by

l_{ijk} = b_{i} - (t_{k(j)} + d_{j}) + h_{ijk} (7)

which corresponds to the (4) with b_{i}, d_{j}, and t_{k(j)} estimating b_{i}, d_{j} and t_{k(j)} respectively. The residual term h_{ijk} contains the pooled (ij), (ik), and (ijk) interaction.

3. RESULTS

Table 2 presents the parameter estimates for Equation (7). Estimates for a formulation corresponding the "Rasch-like" Equation (2) also are provided as a basis of comparison. The OLS estimators and their sum-of-squares are presented in the Appendix.

PARAMETER ESTIMATES UNDER (EQ. 2) AND (EQ. 7)

The greater width of the middle category in West Germany, Netherlands, and Denmark vis-a-vis France and the United Kingdom reflect the greater utilization of the middle category in the former countries. The country specific parameters are greatest for the Danes (-.915) with Netherlands (-.344), U.K. (.153), France (.500) and W.G. (.623) following the order listed. The order of the parameters reflects the consistently greater use of the "very happy" category by the Danes, regardless of marital status, compared to other nationalities. Conversely, the W.G. values reflects the in frequent use of the "very happy" category by the West Germans.

The marital status parameters are precisely in the order suggested by Veenhoven (1983) with the married are the happiest, followed by the never married, and the widowed.

Table 3 presents the ANOVA Table for the data. Both country and marital status effects are highly significant. The effect "country" accounts for about 62% of the remaining sum-of-squares after the effect of "boundary" is removed. The effect "marital status" accounts for about 31% of the sum-of-squares, excluding "boundary" sum-of-squares.

ANOVA TABLE

4. CONCLUSIONS

The model proposed in this paper presents a first step toward modeling the influence of language in cross-national surveys. In the present case, a single question item, taken as a linguistic entity, is decomposed into language specific parameters. Our analysis of this item is illustrative of analyses which may be carried in other subjective indicator areas, such as quality of life (Reynolds and Barksdale, 1978), life style (Wells, 1979), and consumer sentiment (Katona, 1979). For example, the five items constituting the classic Index of Consumer Sentiment are in service throughout the European Economic Community. A fruitful application for the proposed model might involve similar linguist analysis for the several components of this international consumer instrument.

REFERENCES

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Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561-573.

Bechtel, G.G. (1981). Measuring subjective social indicators. Journal of Economic Psychology, 1, 165-181.

Bechtel, G.G., and J.B. Wiley (1983). Probalistic measurement of attributes: a logit analysis by generalized least squares. Marketing Science, 2, 463-489.

Douglas, S.P. (1976). "Cross-National Comparisons and Consumer Stereotypes: A case study of working and non-working wives in the U.S. and France. Journal of Consumer Research, 3, 12-20.

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Maddala, G.S. (1983). Limited-Dependent and Qualitative Variables in Econometrics, New York: McGraw-Hill Book Co., Inc.

Osteroot, N., D. Shin, and W. Snyder (1982). "Quality of Life Perceptions in Two Cultures" Social Indicators Research 11, 113-138.

Rasch, G. (1966a). An individualistic approach to item analysis. In P.F. Lazarsfeld & N.W. Henry (eds.), Readings in mathematical social science. Chicago: Science Research Associates, 89-108.

Rasch, G. (1966b). An item analysis which takes individual differences into account. British Journal of Mathematical and Statistical Psychology, 1949-1957.

Reynolds, F.D. and H.C. Barksdale (1978). Marketing and the Quality of Life. Chicago: American Marketing Association.

Veenhoven, R. The growing impact of marriage. Social Indicators Research, 1983, 12, 49-63.

Wells, W.D., (1979). Life Style and Psychographics, Chicago: American Marketing Association.

Wiley, J.B. and G.G. Bechtel. "Theory Based Monitoring of Social Constructs." Advances in Consumer Research vol. x, Bagozzi, R.P. and A.M. Tybout (ed) Associations for Consumer Research, 1983, 257-162.

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