From Psychometrics to Marketing Science: The “Distance” is Not as Far as You Think!

Eric T. Bradlow

Published Online: January 20, 2026

Abstract

While every discipline has its own terminology, jargon, mathematical models and commonly used inferential methods, Marketing’s focus on latent constructs (e.g., choice utility) as an underpinning of consumer behavior makes its “distance” to other fields, especially psychometrics (and its measurement of latent ability) very small. In this reflection/thought piece, I will discuss how as a Bayesian Statistician and Psychometrician I hope to methodologically and meaningfully contribute to Marketing Science and note (to scholars within and outside of marketing) how we are much less discipline specific than you might think.

1. Introduction

One (of many) research paradigms within quantitative marketing science is to mathematically model manifest variables (i.e., observed dependent variables) as a function of latent constructs. In fact, the equivalence between latent variable random utility models and choice models (i.e., choice utility, McFadden 1974) as an economically rational utility maximizing framework underpins much of the empirical and theoretical work in our field. In parallel, in the field of mathematical psychology, item response theory (IRT, Lord et al. 1968) models dominate the purported relationship between educational manifest variables (e.g., test item scores) and latent (test-taking) ability. The premise of this article is that whether you call it “latent choice utility” or “latent test ability”, underlying consumer propensity to buy or underlying examinee strength, product characteristics or test item features, cross-person choice heterogeneity or heterogenous abilities, within-person latent states (e.g., modeled via an HMM, Netzer et al. 2008) or time-varying ability (Bradlow et al. 1998), these models of behavior are remarkably similar. In addition, and what I hope to expand on here, is that the open research questions are remarkably similar and these two fields can and should borrow from each other conceptually, methodologically and in practice because the “distance” between them is quite small.

2. Equivalence between Random-Utility and IRT Models

Marketing “utilized” random utility models (MRUMs, typically) propose a structure where the utility assigned to person $i$ for product $j$, $U_{ij}\left(M\right)$, $M$ for Marketing, is an additive function of a deterministic component and an IID random error term, ${\epsilon }_{ij}$, given by:

where ${\beta }_i$ is a person-specific heterogeneous slope vector, and $X_{ij}$ is a set of characteristics for the $j$-th product and person $i$. Note, in many cases $X_{ij}=X_j$ to the degree that the characteristics are common (objective) to all respondents.

We compare and contrast this marketing/economics random utility model with a commonly used psychometrics-IRT model, $P$ for Psychometrics (PRUMs), known as the two-parameter logistic model (2PL, Birnbaum 1968) which specifies that:

where the ability of test-taker $i$ is ${\theta }_i$, $a_j$ (constrained to be $>0$) and $b_j$ are item-level parameters representing the slope (correlation) between ability and getting an item correct (called a discrimination parameter) and one representing the item’s difficulty, and ${\epsilon }_{ij}$ is an IID error term. When $a_j=1$, this is the simplified IRT model known as the Rasch model (Rasch 1960) which is equivalent to a generalized linear model for utility with dummy variables for the respondent $i$ and item $j$ in the corresponding design matrix $X_{ij}$. Simply put, the equivalence between these two models is evident and accomplished by recasting $a_j({\theta }_i-b_j)={\beta }_i{X}_{ij}$ where ${\beta }_i=a_j{\theta }_i$ and $X_{ij}=a_j{b}_j$, a commonly known reparameterization of IRT models as a logistic regression. Once one recognizes this equivalence, purchasing an item when $U_{ij}\left(M\right)>0$ is no different than a test-taker getting an item right when $U_{ij}\left(P\right)>0$. Thus, the educational testing problem of designing and selecting items with high discrimination ($a_j$) can be seen as similar to selecting product features ($X_j$) that help drive and discriminate choice.

We discuss next another important conceptual similarity between Marketing and Psychometrics-based utility models, the distance they imply between the consumer’s utility and a corresponding threshold.

3. It’s All About the Distance

While the mathematics of (binary) DV random utility models is straightforward, subjects purchase (get an item correct) when $U\left(M\right)$ (or $U\left(P\right)$) is greater than $0$, another illustrative and graphical way of representing these models is on a line where consumer $i$’s location for item $j$ is $U_{ij}$ and there is a threshold (in the binary DV case) normalized to $0$.

Figure 1. A Graphical Depiction of a Random Utility Model with Threshold

Notes. Things that drive $U_{ij}$ farther to the right from $0$ increase $D_{ij}\left(M\right)$ and hence the likelihood of purchase/correct. Similarly, things that further separate ${\theta }_i$ from $b_j$ (e.g., training that improves respondent $i$’s ability level, or clarification/help that lowers the difficulty of item $j$) raise $D_{ij}\left(P\right)$ and hence the probability correct.

From Figure 1, we can see the following:

1. For $U_{ij}\left(M\right)$, when test-taker $i$ is more able than item $j$ is difficult (i.e., ${\theta }_i$ > $b_j$) then the deterministic component of utility $=a_j({\theta }_i-b_j)>0$ and since the corresponding probability of correct given ${\epsilon }_{ij}$ is symmetric around $0$, $p_{ij}$ is greater than $0.5$.
2. As the distance between ${\theta }_i$ and $b_j$ increases (i.e., $D_{ij}\left(P\right)$ increases) then $p_{ij}$ increases. Similarly, as the distance between $U_{ij}$ and $0$ increases, $p_{ij}$ increases.

What this suggests, as per the dual-meaning title of this research thought piece, distance matters. In fact, many probabilistic models (race models of behavior in psychology (Merkle and Van Zandt 2006); random utility models in marketing; IRT models in educational testing) are purely distance models where the latent locations are what need to be estimated.

4. Past and Future Research Directions

The similarities between these two disciplines go far beyond just recognizing the isomorphism between their mathematical forms. As I discuss next, the extensions and challenges that each discipline has tackled, and the future challenges, appear (to me) to be almost identical. Two that I describe below are heterogeneity and functional form (different decision rules used across respondents).

A common challenge in MRUMs is how to handle cross-person heterogeneity which can come in many forms. The most widely addressed is for parameters (Rossi et al. 1996) reflecting that individuals put different weights on various aspects of $X_{ij}$. Its counterpart in PRUMs, while researched, has been much less so and usually comes of the form where the item parameters, $a_j$ and $b_j$ are modeled as examinee-specific, or context specific adding a subscript $i$ in the former case and $c\left(j\right)$, context, in the latter case. Issues having to do with the flexibility/form of the heterogeneity distribution, while addressed in both fields (e.g., using a mixture prior) have been addressed (Kamakura and Russell 1989) but the use of Bayesian non-parametrics with Dirichlet Process Priors (Ferguson 1973) is clearly more advanced in MRUMs due to the larger data sets, increased granularity and frequency, and (likely) the form of population-distribution needed.

Other forms of “well-studied” heterogeneity include within-person implying the propensities change over time for a given individual that could reflect state switching (HMMs), non-stationarity (reflecting both exogenous changes over time and those that are more structural and “caused” by firm action), and reference/context effects that include topics like state-dependence (which are commonly believed to exist in choice models, Dubé et al. 2010), but attempted to be designed away or modeled (Bradlow et al. 1999) in educational tests where items are meant to be conditionally independent.

Lastly, both MRUMs and PRUMs want to understand both descriptors of heterogeneity and actions (firm in the MRUM case and test design/educator in the PRUM case) that can optimize some objective function (sales, test-scores, learning, etc.). This is commonly accomplished in MRUMs via hierarchical models where:

with $Z_i$ being individual-specific covariates (commonly acquired via survey or transaction data), and $(\lambda ,\Sigma )$ being slopes and a covariance matrix describing the population distribution. The important thing to note is that both MRUMs and PRUMs consider heterogeneity fundamental to the statistical models employed and necessary for downstream firm optimization.

Another area of research that is common in both cases, and one that is less researched than parameter heterogeneity, is allowing for alternative decision models that aren’t linear and compensatory that "${\beta }_i{X}_{ij}$" models are. A number of MRUM papers (Gilbride and Allenby 2004; Hauser et al. 2010) have addressed conjunctive rules (A and B are both needed to buy), disjunctive rules (A or B), and combinations thereof. In the educational testing domain, especially in the area of skill development as well as when considering tree-based models of competency (Komboz et al. 2016), there is also a long history of models that are more complex in their structure.

Lastly, there is a need for future research on a significant number of topics related to RUMs. These include a growing need for RUMs that can jointly model data of multi-modalities (e.g., surveys and transactions, multiple-choice items and essays, responses and response times) simultaneously which given cookie tracking and other technologies is becoming more prevalent, models where coefficients are non-stationary and dependent on firm action (e.g., the firm drops price and the consumer becomes more price-sensitive; i.e., their “state” changes), and models that consider context-dependent utilities where the context may be very high dimensional (e.g., based on a consumer’s very rich test responses, response times or analogously a consumer’s clickstream history in a given session).

5. Concluding Thoughts

While the goal of this research note was to try and draw similarities between two disparate literatures, another reason for writing it was a reflection on my own career and a path, of sorts, for others. As methodologists, we should all be looking for problems where the methods, models, open challenges, solutions, etc. stay the same but the jargon is simply different. For me, whether it’s building latent variable IRT models or latent variable models to understand marketing outcomes of interest, the distance between these two fields is small. Hopefully, this will lead PhD students today to study more math psychology and psychometrics as investing in these measurement tools will lead to broad training in random utility modeling in marketing.

Eric T. Bradlow ([email protected]) is the K.P. Chao Professor, Professor of Marketing, Statistics and Data Science, Economics and Education, Chairperson Wharton Marketing Department and Vice Dean of AI and Analytics at the Wharton School of the University of Pennsylvania. He served as Editor-in-Chief of Marketing Science from 2008-2010.