An empirical analysis of shopping basket similarities across consumers

ABSTRACT

What makes shopping baskets similar or different across consumers and how much of shopping basket similarities is explained by similarities in observable characteristics, especially when a typical basket includes a few hundred products as a result of the consumer’s purchase decisions over tens of thousands of products? I attempt to answer these questions by expressing the entirety of households’ baskets as a vector of expenditure shares on various grocery products and computing pairwise cosine similarities. I find households’ shopping baskets vary greatly, with similarities in the demographic profiles and where they shop explaining only about 13%-16% of their similarities. The similarity in where households shop has the largest explanatory power, orders of magnitude larger than similarities in demographic profiles such as income and race. It underlines the importance of similarities in the products offered to households in explaining similarities in the products they ultimately purchase.

KEYWORDS:

• Grocery baskets
• cosine similarities
• product availability
• scanner data

JEL CLASSIFICATION:

• D12
• L81

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ If each group of people with the same characteristic includes 30 people instead and 20 out of 30 in each group make choices the same within the group but different between two groups, then more pairs with the same characteristic make the same choices than pairs with different characteristics.

² There are of course studies that consider consumer shopping baskets as a whole. For example, Kalyanam, Lenk, and Rhee (2017) studies the relationship between shopping channel choices by shoppers of multi-channel retailers and their basket compositions, and Martin et al. (2020) examines shopping basket size patterns across retail types in relation to retailer performance using the same data as mine. As can be seen from these examples, the questions and focuses of those papers are very different from this paper’s.

³ Source: https://www.statista.com/statistics/754815.

⁴ I do not consider a shopping basket similarity measure for which a cosine similarity is not computed category by category, but instead for all UPCs (or brands) at once, characterizing each household’s shopping basket with a vector of expenditure shares on all UPCs (or brands) across categories. The reason is that this would require working with vectors with a length of ${\sum }_c{N}^c$ (about 326,000 for UPCs and 57,000 for brands) 13.9 million times, which is prohibitively computationally, especially memory-wise, expensive.

⁵ A random permutation that preserves the original correlation structure can be obtained by, for example, if there are 5 households and thus 10 pairs, drawing a random rearrangement of five indices that determines a swapping rule. For example, a rearrangement of (2, 5, 1, 3, 4) leads to a swapping rule of (1$\to$2, 2$\to$5, 3$\to$1, 4$\to$3, 5$\to$4) so that $y_{1,2}$ is swapped by $y_{2,5}$ and $y_{2,5}$ is swapped by $y_{5,4}$. In this paper, each empirical sampling distribution is obtained from a QAP with 2,000 random permutations.

⁶ The QAP t-statistics of Sim_Chains are 85.55, 83.16, and 100.70 in model (1), (2), and (3), respectively. The next largest values of the t-statistics are 31.49 and 31.00 for S_State in model (1) and (2), followed by 16.02 for S_HheadMarriedCpl in (1) and 11.50 for D_FmlHeadEduc in (2). As for model (3), the second largest value is 16.72 for S_MlHeadAge.

⁷ Some notable mergers and acquisitions during the period of interest include BI-LO’s merger with Winn-Dixie Stores in 2012, Kroger’s acquisition of Harris Teeter in 2013, and the second-largest supermarket chain Albertsons’ acquisition of Safeway Inc in 2015.

Additional information

Funding

This work was supported by Humanities & Social Science Research Promotion of Pusan National University, 2021.