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The marketplace has been defined by the interaction between consumers and brands, which has been recognized by the majority of marketing literatures with the exception of the measurement literature. Measurement researchers in marketing have been continuously working on improving the quality of measurement of marketing constructs by applying psychometric theories from the early Classical Test Theory to later generations such as Generalizability Theory and Item Response Theory. But only main effects (normally consumers, sometimes brands) have been focused on, and interactions between them are either ignored or treated as measurement error. This is surprising, given the voluminous literature in other areas of marketing (e.g., marketing segmentation, customer lifetime value, and customer relationship management) that build their entire frameworks on the interpretation and usage of this interaction. In the current research, we propose a new Many Faceted Item Response Theory model to fill this gap in measurement literature. Two sets of indexes describe consumers (and brands); individual main effects (and brand main effects) and brand-specific individual effects (or individual-specific brand effects). Soft drink brand equity data were used for the empirical examination.

In marketing, there are many important multidimensional constructs, such as service quality, market orientation, and consumer-based brand equity (CBBE). Survey methods and multidimensional scales are used to measure these constructs. But the survey responses collected for these constructs are also dual-faceted. Except for consumers, the other facet (such as services, firms or brands) is involved too. Assessment of multidimensional marketing scales (such as SERVQUAL and MARKOR) has relied on confirmatory factor analysis (CFA) and structural equation modeling (SEM), which may not give accurate and unbiased evidence about the estimates and dimensionality across both facets. The authors introduce a hierarchical extension of many facet item response theory (MFIRT) to empirically investigate the causal relationships between a construct and its dimensions for scales that generate dual-faceted data. CBBE data for soft drink brands are used in an empirical study, which demonstrates the method and finds CBBE best modeled as formative from its dimensions along the consumer facet.