# Measurement Approaches For Consumer Behavior Constructs: a Multidimensional Perspective

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Jagdip Singh (1988) ,"Measurement Approaches For Consumer Behavior Constructs: a Multidimensional Perspective", in NA - Advances in Consumer Research Volume 15, eds. Micheal J. Houston, Provo, UT : Association for Consumer Research, Pages: 487-492.

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http://acrwebsite.org/volumes/6851/volumes/v15/NA-15

Measurement issues are becoming increasingly important to consumer researchers. Concepts such as measurement error and reliability are incorporated in much of the research conducted today. Relatively less attention, however, has been directed toward understanding the diverse number of measurement approaches available. More importantly, discussions of which measurement approaches are appropriate under which conditions have received less attention. We propose an elementary taxonomy for categorizing the various measurement approaches. This taxonomy is based on considering the properties of the three dimensions of measurement elements: construct, operationalization, and indicants. The taxonomy is shown to be useful in deciding the suitability of different approaches. Several examples from marketing are provided. Implications for future research are also discussed.

INTRODUCTION

Consumer researchers often work with "constructs" as the basic units of research. That is, much effort is directed in building, investigating and modifying theories which specify relationships between two or more constructs., Most such constructs are "latent", i.e., can only be measured indirectly by (usually) multiple indicators. Dillon et al. (1983, p. 209) observe that, "the use of multiple indicators to reflect inherently abstract constructs not subject to direct measurement is perhaps the most significant advance in social science research in the last decade." Within this context, the role of measurement as the link between observed indicators and the latent construct is unequivocally regarded as "the most difficult and crucial to scientific enterprises." (Greer 1969; p. 160).

Recognition of measurement's role is increasing within the marketing discipline in general (Ray 1979; Bagozzi 1982; Churchill and Peter 1984), and consumer behavior in particular (Dillon et al. 1983; Fornell 1983; Bagozzi 1983). This is evidenced by the widespread adoption of measurement concepts (e.g., reliability) in published articles. In most cases, however, this adoption is limited to linear factor analysis--either exploratory or confirmatoryCbased investigation of measurement properties. Yet in a recent review of the literature, Lewis (1986) noted that the last twenty years of measurement research have led to about fifty different "models" for understanding the "elusive" relationship between the latent construct and the observed responses.

The purpose of this paper is to explore some of the preceding models. More specifically, the underlying motivation of this research is twofold. First, to highlight some measurement approaches that heretofore have remained underutilized in consumer research. Second, to provide an elementary taxonomy of the different measurement models. In particular, the suggested taxonomy is based on a multidimensional perspective of measurement. This perspective derives from considering the characteristics of the three elementary units of measurement: construct, operationalization, and indicants. Although the proposed taxonomy is not rigorous in a strict sense, it helps to identify the fundamental differences in the various approaches. Such identification can be useful to researchers in applying appropriate measurement models, and thus in better characterizing the latent construct measured by fallible indicators. Several examples from consumer behavior are provided. Implications for future researchers are also discussed. However, we first attempt to delineate the scope of measurement for the purposes of this paper.

DELINEATING THE SCOPE OF MEASUREMENT

Researchers sometimes employ different perspectives in examining measurement issues. Because u e adopted perspective represents a framework within which various issues would be evaluated, it is important that researchers clearly identify the perspective they utilize. This section addresses this prescription. More specifically, we discuss the perspective (and its characteristics) employed in this research to examine the multi-dimensional measurement approaches.

Bagozzi (1983) suggests three broad perspectives for examining measurement issues. These perspectives can be viewed as understanding measurement properties of constructs resulting from examining (1) other constructs, (2) instrumentation, and (3) observations. The first focuses on the affect of "other" constructs such as omitted variables, method variation (e.g., response sets) and predictor constructs (e.g., those suggested by theory). Such other constructs can potentially influence the measurement properties (e.g., reliability, validity) of _ the focal construct. The second perspective attempts to understand the effect of theoretical "laws" underlying the instrumentation used to obtain responses such as data collection, recording, and responding systems (Bagozzi 1983). The third perspective constitutes understanding the relationship between observations and the theoretical construct as the basis for characterizing its measurement properties. Several different theoretical frameworks (e.g., true-score model, and latent trait theory) are available to understand the preceding relationship.

The present research utilizes Bagozzi's (1983) third perspective to analyze the various measurement approaches. This choice was guided by several factors. First, this perspective has evidenced a phenomenal growth in the areas of psychology and educational research over the last twenty years. In fact, Lewis's (1986) observation regarding the development of fifty different models pertains to this perspective. Second, most of this advancement is not reflected in current marketing or consumer behavior research. This is evidenced by the sole dependence on the true-score model for understanding the relationship between the observations and the focal construct (see Dillon et al. 1983; and Fornell and Bookstein; 1982 for exception). Thus it is not unlikely that most researchers are not aware of the potential of many other measurement approaches and its impact on consumer research. Third, there is little discussion within the marketing discipline regarding the systematic errors introduced by the selection of any one approach (e.g., true-score model) under this perspective. In contrast, several studies have attempted to address the implications of the other two perspectives (Kumar and Dillon 1987; Fornell 1983; Anderson and Gerbing 1982; Phillips 1982). By highlighting and categorizing various approaches for the third perspective, it is hoped that consumer researchers would be more alert to the possibilities and the limitations inherent in the multiple ways of understanding the relationship between the observations and the latent construct.

THE MULTIDIMENSIONAL FRAMEWORK

The proposed multidimensional framework for categorizing the various measurement approaches is displayed in the Table. This framework is a 2X2X2 table, which in turn is composed of two level characteristics each for the latent construct, indicators, and operationalization. We discuss these characteristics below.

Latent Construct

Two possibilities for the nature of the latent construct are considered: categorical or continuous. A continuous latent construct is operative when the underlying unobservable trait is expected to be a random variable such that the objects (e.g., consumers) could possess any bounded or unbounded value of this variable. An example of this type of trait is the attitude toward the brand. Irrespective of the specific measurement utilized, different consumers inherently possess different attitude toward the focal brand. The set of possible attitude values in the population could theoretically range from positive to negative infinity.

THE MULTIDIMENSIONAL FRAMEWORK FOR CATEGORIZING MEASUREMENT APPROACHES

In contrast, categorical latent construct is applicable when the underlying trait is conceptualized as consisting of a bounded number of distinct classes. Consider, for example, the involvement construct. Several researchers have discussed involvement from a conceptual standpoint as consisting of two broad classes: High, and Low (Engel and Blackwell 1982). In fact, different models of consumer behavior are proposed for each of the two conditions of involvement (Petty, Cacioppo and Schumann 1983). Clearly, while the measures for the involvement construct are often continuous (e.g., Zaichowsky 1985), the underlying latent construct is conceptualized as categorical. Another empirical example of this conceptualization is provided in a study of residence satisfaction by Dillon et al. (1983). Although "satisfaction" is generally regarded as a continuous trait, these researchers posit that the underlying trait--residence satisfaction--has four distinct (but latent) classes; namely extremely satisfied, moderately satisfied, indifferent, and dissatisfied (p. 212). More specifically, it is hypothesized that all objects (e.g., people) can be categorized into one of four classes based on their perceptions of residence satisfaction. Within each class, objects have homogeneous satisfaction level but not so across classes. Further, in this study the latent (class) trait was measured by three observable items. The family life cycle construct is yet another example of a latent concept with nine distinct classes as proposed by Wells and Gubar (1966). In general, the number of classes can be any finite, positive integer.

Operationalization

Reflexive and formative are the two types of operationalizations considered in the proposed framework. A formative operationalization is defined when the latent construct is conceived as explanatory combination of its indicators (Fornell and Bookstein 1982). The Computerized Status Index (CSI) is an example of such an operational definition for the measurement of social class (Coleman 1983). In this -particular index, the latent construct social class is posited as a combination (i.e., sum) of several object characteristics; namely education, occupation, area of residence, and total family income.

When the observed indicators are conceived as being "caused" by the underlying latent construct, a reflexive operationalization is operative (Fornell and Bookstein 1982; Bagozzi and Fornell 1982). Bagozzi (1982) provides an example of the reflexive operational definition. He defines the latent construct, affect toward the act of giving blood, as measured by responses to five semantic differential items. Further, two additional assumptions are implicitly incorporated: (1) the covariation among the five items arises only due to (or is caused by) the underlying latent construct, and (2) the covariation represents a measure of the affect toward the act. Another recent example of the reflexive operationalization is the market maven construct (Feick and Price 1987). The market maven concept attempts to characterize individuals on the basis of their general marketplace expertise, such as information about many kinds of products, places to shop, and other facets of markets. Six items are proposed as a tenable operationalization of the market maven construct. It is shown that the covariation among the six items is due to a single underlying factor, which may be characterized as the market maven construct (Feick and Price 1987). In this sense, an individual's response to the six items is conceived as being caused by the individual's level of general marketplace expertise.

Indicants

The third dimension of the proposed framework represents the property of the indicants used to measure the latent construct. Two possibilities are considered: categorical, and continuous indicators. These possibilities stem from the nature of numbers assigned to the scale used in the particular operationalization. More specifically, numbers that conform to an interval or ratio scale are generally regarded as a continuous indicators (Churchill 1983). An example of continuous indicator is the use of a dollar amount scale to measure respondent's income. Such a scale has a natural zero ($0.0), and the difference between any two dollar amounts have ratio property. Another example of a similar indicator is the use of sales amount as a measure of salesperson's performance.

In contrast, categorical indicators are obtained when the assigned numbers are from a set of bounded, discrete integers. When these integers possess interval characteristics, they are continuous type indicators. Often consumer researchers obtain responses with category codes corresponding to such phrases as (1) strongly agree, (2) agree somewhat, (3) neither agree nor disagree, (4) disagree somewhat, and (5) strongly disagree, or some other variation of this. general theme. There is some debate if indicators of this type have ordinal versus interval properties. From a statistical standpoint, it is difficult to defend that such numbers have equal interval between adjacent values. Thus Dillon et al., (1983) contend that such measures have only ordinal properties. In this sense, these indicators are categorical.

CATEGORIZING THE VARIOUS MEASUREMENT APPROACHES

The proposed multidimensional framework results in eight cells into which the different measurement approaches can be categorized. The table also depicts some typical approaches that have been classified into one of eight cells using the three dimensions. The purpose of this section is not to categorize an exhaustive list of measurement approaches. Instead, the objective is to show how the framework can be used to classify any given approach, and to expose consumer researchers to the range of possible methods.

Approaches for Continuous Latent Construct and Reflexive operationalization (Cells 5 and 7)

Judging by the published articles, it would appear that most consumer researchers operate within cell-7 of the proposed taxonomy. This cell is characterized by the assumptions of continuous latent construct, reflexive operationalization, and continuous indicators. The true wore model (Zeller and Carmines 1980) or the classical test theory (Lord and Novick 1968) represent two approaches for understanding measurement properties of constructs under the preceding assumptions. The true score model in turn involves three different models for representing data: (a) the congeneric measure, (b) the tau-equivalent measure, and (c) the parallel measure models. However, these models are properly nested in each other, with the congeneric model as the most general, and the parallel model as the most restrictive (Joreskog 1971). Joreskog (1971) has also demonstrated that common factor analysis and LISREL represent two techniques to implement the true score models. Both techniques produce underlying factors that are continuous. In addition, these factors represent the shared covariation among a set of continuous indicators. Finally, responses to indicators are seen as "caused" by the underlying factor. Because the aforementioned features are consistent with the characteristics of cell-7, these techniques are classified into this cell. Similar reasons apply for the true score model and the classical test theory (see Lord and Novick 1968 for a detailed discussion).

Note, however, that there are some important differences between the factor analysis or LISREL model and the true score models. In particular, the former techniques can also implement models that are even more general than the congeneric true score model. For instance, true score model allows for only random measurement error in observables, whereas factor analysis models unique as well as random error in each indicator. Also, true score model assumes error terms to be uncorrelated while LISREL allows the possibility of estimating correlated error terms.

While factor analysis and LISREL are two techniques, the true score model and the classical test theory are overall theoretical frameworks to understand measurement properties of constructs when the assumptions of cell-7 are met. One could argue that assumptions of reflexive operationalization and continuous latent construct need to be evaluated from a rather philosophical standpoint. In contrast, the assumption of continuous indicators is statistical in nature. Rating scales (e.g., Likert) generally do not meet this assumption (Dillon et al., 1983; Stevens 1966). In a recent analysis of this issue, Borgatta and Bohrnstedt (1981) argue that while most rating scales have more than ordinal properties, they may not be truly interval. In practice, however, much research using such scales operates with methods and techniques categorized in cell-7. Thus an implicit (though often technically incorrect) assumption is made that rating scales yield interval data.

However, it is not necessary to make the preceding implicit assumption. When indicators are categorical (e.g., rating scale), approaches of cell-5 are applicable. In this situation, the Latent Trait Theory represents a theoretical framework for determining measurement characteristics of constructs. This theory has been discussed fully by Lord (1980) and Hulin, Drasgow and Parsons (1983). Although these researchers specifically discuss the relevance of this framework to social science constructs (e.g., attitude), applications of Latent Trait theory in marketing are conspicuous by their absence.

In a recent article, Thissen and Steinberg (1986) have reviewed the different models available to implement Latent Trait Theory. Such models are often referred to as Item Response models, since a specific -item response function is utilized to relate the observed response and the latent trait. Applications of such models in psychology are growing (see for instance special issue of Applied Psychological Measurement, 1982). Because the item response models appear to be especially appropriate for rating scales, marketing researchers must examine these models carefully.

Approaches for Continuous Latent Construct and Formative operationalization (Cells 6 and 8)

The notion of formative operationalizations, and the recognition that some latent constructs in marketing may have such operational definitions is relatively new to marketing (Fornell and Bookstein 1982). In addition, theoretical frameworks for understanding measurement properties under these conditions are relatively less formalized (as compared to Classical Test theory). Although not specifically developed for measures of cell 6, the Guttman scaling model appears to be appropriate for several reasons (Guttman 1950). In particular, Guttman models assume a continuous latent construct, indicators that are of the Yes/No type (i.e., categorical), and a compositional rule (i.e., summate) for determining the underlying trait. Several examples of such measures are available in consumer research. For instance, in a recent study Bearden and Teel (1983) used a Guttman model for characterizing the measurement of consumer complaint behavior construct. For this construct, five indicants were used to obtain a yes or no response based on whether an individual engaged in that particular complaint behavior or not. Finally, the sum of yes responses was used as the measure for the latent construct.

Bagozzi (1983a) argues that the principal components methodology (as opposed to common factor analysis) is suitable when the measures are continuous and the underlying latent trait is assumed to be a linear combination of observables. Because a linear combination of continuous measures is also continuous, the principal components technique appears to be appropriate for cell-8 measures. Several constructs in consumer behavior appear to conform to cell-8 conditions. For instance, in a recent study Beatty and Smith (1987), p. 89) defined the latent construct, total external search (for information) as "a linear combination of four sub-indices:" media search, retailer search, interpersonal search and neutral search. Although these researchers do not utilize principal components to obtain the compositional rule for defining the latent construct, this technique is clearly applicable in such situations. Note, however, that by placing principal components in cell-8, and common factor analysis in cell-7, we are also highlighting key differences in these techniques (see also Bagozzi 1983a).

Wold (1980) and his associates have developed more advanced techniques for handling continuous indicators of formative operationalizations. Such techniques are termed Partial Least Squares (PLS), and they also fall into cell-8 of the proposed framework. Although it is suspected that several marketing constructs may be categorized as cell-8 measures (e.g., social class), applications of PLS in marketing are scarce. Fornell and Bookstein (1982) provide a rare example of the use of PLS to examine the "marketing concentration" construct, and its effects. A formative operationalization of four indicants for this construct is utilized. The four indicants are different measures of concentration ratios from the Census of Manufacturers'. Thus these indicants are continuous and possess ratio property. These characteristics of the marketing concentration construct make it suitable for cell-8 methods, and PLS is the appropriate technique.

Approaches for Categorical Latent Construct (Cells 1 thru 4)

While the use of continuous latent construct is ubiquitous in consumer research, conceptualization of a categorical latent construct is relatively much less popular. As the Table suggests, when the operationalization is formative, and the indicants are continuous, the measurement process reduces to definitional characteristics (cell-4). That is, in this situation the proper conceptualization of the construct should also include formal rules that define how a combination of indicants ought to be grouped into two or more latent classes. Cell-4 methods, therefore, cannot be easily evaluated empirically for their "goodness" of measurement (e.g., reliability).

In contrast, when the indicants are categorical and the operationalization is reflexive, a well developed theoretical framework is available to researchers for the assessment of measurement (cell-1). This framework is often referred to as the Latent Class theory. Goodman (1975) and Clogg (1979) have presented several models that implement this theory. Applications of such models in consumer research are growing. Dillon et al. (1983) provide an example of such models to the measurement of residence satisfaction. The latent construct, as indicated earlier, is hypothesized to constitute four distinct classes. Three categorical indicants with four levels each are employed. Finally, a reflexive operationalization is assumed since the residence satisfaction is posited to be reflected in satisfaction with the house, the landlord, and the neighborhood.

Our review of the literature did not reveal any frameworks especially suitable for cells 2 and 3. From a taxonomical standpoint, these cells are "empty cells" (Hunt 1983). However, measures of cell-2 share several characteristics with cell-4 measures. Importantly, both measures are conceptualized as formative operationalizations of categorical latent constructs. The differences lie in the type of indicants (continuous/ categorical). As noted above, however, in practice researchers often do not draw clear distinctions between the quality of indicants used. Nevertheless a definitional rule for defining the latent construct is appropriate for cell-2 measures. Clearly this definitional rule ought to be conceptually different than the one used for cell-4 measures. Because such differences are often not articulated, frameworks of cell-2 have tended to be no different than cell-4 techniques.

In contrast, while cell-3 measures share some features with cell-l, the techniques of cell-1 are generally not applicable to cell-3. In particular, latent class models traditionally were not developed to handle continuous observables. Other techniques (e.g., Guttman scaling) also do not conceptualize measures as defined by cell-3. In published research, however, several examples that treat the measures and the construct in accordance with cell-3 can be found. In almost all cases elementary definitional operations are performed. Consider for example a recent attempt to operationalize the involvement construct (Zaichkowsky 1985). A 20 item measure is proposed. Responses are obtained on a seven point semantic differential scale. Responses are assumed to possess interval scale properties. The underlying construct, involvement, is defined in a two-step process. First, responses to the twenty items are factor analyzed to show that the covariation among items is due to a single latent construct. Although Zaichkowsky (1985) does not explicitly suggest a reflexive operationalization, the preceding operation for defining the latent construct appears to imply such an operationalization. Second, the items are then combined using an equally weighted, linear combination rule. The obtained at summed, score is then compared as being above or below a specified value (89.55). This rule results in classifying respondents into a high or low involvement class, implying a categorical latent construct. Thus, this measure appears to be operating under cell-3 conditions.

The preceding discussion clearly highlights the lack of standard procedures for addressing cell-3 and cell-2 measures. Future researchers may wish to address these issues. In addition, it also underscores the need for explicitly articulating the measurement properties of indicants, constructs and operationalizations utilized in a particular study. Because method (i.e., techniques) and measure properties are interdependent (e.g., as in Table), this articulation would insure the use of consistent methods and measures.

DISCUSSIONS AND IMPLICATIONS

The purpose of this study has been to closely examine measurement approaches that attempt to understand the relationship between observed responses and the latent construct they purport to measure. Toward this end, a multidimensional schema is proposed that can potentially classify the various measurement approaches into one of eight cells. This schema serves several objectives: (1) it affords a taxonomy of measurement frameworks; (2) it exposes consumer researchers to the breadth of methods and frameworks available; (3) it helps researchers decide which method(s) is appropriate under a given set of assumptions; (4) it highlights the fact that most consumer research is limited to methods which belong to only one cell (7) of the taxonomy. Implications of these statements are discussed below.

Although measurement issues are beginning to receive increased attention, previous research has not attempted to develop a taxonomy of different approaches. The present research has posited a multidimensional schema which addresses the preceding gap in consumer research. In addition, the proposed schema utilizes elementary units of measurement--construct, operationalization, and indicants--and their properties. These units have received considerable attention from consumer researchers (Bagozzi 1983; Fornell and Bookstein 1982). Thus by bringing together well examined units into a taxonomical framework, the resulting classification is expected to be both relevant and useful to consumer researchers

Using the proposed taxonomical framework, the present study has attempted to categorize some typical measurement approaches. While many of these approaches have been independently introduced in the JCR (e.g., Latent class models), studies that utilize the different measurement approaches have been less forthcoming. A case in point is the analysis of the last two issues (December and March) of JCR. Of all the empirical studies reported, all but one study had employed the true-score model (i.e., alpha reliability) and/or factor analysis for examining measurement characteristics. Earlier issues of JCR also depict a similar disproportionate use of cell-7 methods and models. Several implications stem from this analysis.

First, it is probable that consumer researchers are not aware of the range of measurement approaches available, and more importantly how these approaches differ from each other. The proposed framework lays out the different approaches in a way that highlights the differences between them. For instance, the Latent Trait theory (cell-5) is different from the true-score model (cell-7) in the assumptions about the indicants (categorical/continuous). By highlighting the differences, it is hoped that consumer researchers would be better equipped to understand the various measurement methods.

Second, the disproportionate use of cell-7 methods and models by itself is not a cause for alarm If indeed the data meet the assumptions of these methods, the use of cell-7 measurement approaches ought to be advocated. In most cases, however, the data do not satisfy the true-score model assumptions. In particular, rating scales yield categorical data. For such data, our taxonomy suggests that the Latent Trait theory (cell-5) based methods are more appropriate. Unfortunately, such methods have not been explored by consumer researchers. Thus the effects resulting from the use of cell-7 methods for cell-5 data cannot be assessed. Two possibilities exist. Either the measurement characteristics of constructs, in general, are sensitive to such substitution of methods, or the affects can be practically ignored. More definitive statements can be made when these possibilities are examined empirically. Future researchers may wish to address these issues. Finally, the proposed taxonomy may be useful to future researchers in their selection of the appropriate measurement approach. Although the proposed schema should be regarded as a first step toward developing a comprehensive taxonomy, it can potentially afford guidelines in choosing measurement approaches. Once the properties of the three elementary measurement units is identified in a given research design, the taxonomy narrows down the choice considerably. Such guidelines would advocate the use of measurement frameworks that are appropriate, not just convenient. Because good measurement is necessary (though not sufficient) for affording a valid test of our theories, the use of appropriate approach is central to progress in consumer research. We offer our taxonomy for this purpose.

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