Evaluation of Gross sales Shift in Retail with Causal Influence: A Case Research at Carrefour

Disclosure: I work at Carrefour. The views expressed on this article are my very own. The info and examples introduced are printed with my employer’s permission and don’t include any confidential info.

A retailer’s assortment is a whole and diverse vary of merchandise offered to clients. It’s topic to evolve based mostly on numerous components reminiscent of: financial circumstances, shopper tendencies, profitability, high quality or compliance points, renewal of some product ranges, inventory ranges, seasonal adjustments, and so on.

When a product is not obtainable on the shop cabinets, a few of its gross sales might shift to different merchandise. For a significant meals retailer like Carrefour, it’s essential to estimate this gross sales shift precisely to handle the chance of loss resulting from product unavailability and approximate the loss resulting from it.

This measurement serves as an indicator of the implications of the unavailability of a product. Moreover, it steadily builds a worthwhile historical past of gross sales shift affect estimates.

But, estimating gross sales shifts is complicated. Buyer conduct — influenced by hard-to-predict emotional components — seasonality of sure merchandise, or introduction of recent merchandise can all have an effect on gross sales shifts. As well as, many merchandise develop into unavailable throughout all shops concurrently, making it not possible to determine a management inhabitants.

The Causal Influence artificial management method, developed by a Google crew, matches the particularities of our evaluation framework. It permits us to isolate the impact of product unavailability on gross sales from influencing components, and is appropriate for each quasi-experimental and observational research. Primarily based on Bayesian structural time-series fashions, Causal Influence performs a counterfactual evaluation, calculating the impact on gross sales because the distinction between the gross sales noticed after a product turns into unavailable and, by way of an artificial management, the gross sales that might have been noticed had the product remained obtainable.

This text presents our Causal Influence method for estimating the gross sales shift impact following product unavailability, in addition to a heuristic for choosing management group time sequence.

As a consequence of confidentiality issues, the quantitative values on the graphs have been redacted. Notice that every block represents one month alongside the x-axis, and the y-axis represents a variable amount, which could be fairly massive.

I) Specifying the Use Case

Product unavailability happens in two fundamental types:

• Full unavailability: the product is not obtainable within the nationwide assortment, affecting all shops.
• Partial unavailability: the product is not obtainable from some — however not all — shops. It stays obtainable in others.

We take into account {that a} dependable gross sales shift affect estimate ought to precisely assess each misplaced gross sales and portion of gross sales transferred to different merchandise. But, figuring out the precise worth of those portions is not possible, making this problem complicated.

Our research analyzes instances of full product unavailability as these instances are essentially the most vital when it comes to gross sales affect.

Please additionally be aware that causal inference isn’t a predictive framework for future occasions: it identifies causal hyperlinks up to now slightly than forecasting future occasions.

II) Why did we select Google’s Causal Influence mannequin?

Causal approaches goal to grasp causal relationships between variables, explaining how one impacts one other by isolating the impact we try to investigate from all different present results.

Amongst these instruments, Causal Influence is a user-friendly library, and it operates inside a totally Bayesian framework, permitting prior info integration whereas offering inherent credibility intervals in its outcomes. Its predictions symbolize anticipated outcomes had the intervention not occurred, expressed as distribution capabilities slightly than single values.

Causal Influence generates predictions by combining endogenous parts, reminiscent of seasonality and native stage, with user-chosen exterior time sequence (covariates). These covariates have to be unaffected by the intervention and will seize tendencies or components that might affect the principle time sequence. We are going to talk about covariate choice later.

Fig. 1: A simplified instance of Causal Influence in motion. The highest graph exhibits two time sequence: the orange line represents precise noticed knowledge, whereas the blue line is the mannequin’s prediction, created utilizing covariates and endogenous parts. Every block represents a month. This prediction estimates what would have occurred if the occasion of curiosity (marked by the vertical dashed line) had not occurred. The blue shaded space signifies the prediction’s uncertainty. The second graph shows the point-by-point distinction between the prediction and the noticed knowledge, and the underside graph exhibits the cumulative affect.

III) Managing Outliers and Anomalies in knowledge

To make sure correct evaluation, we addressed gross sales knowledge anomalies by following two key steps:

• We excluded time sequence with destructive gross sales or a lot of zero gross sales from the evaluation.
• For time sequence with occasional zero gross sales, we changed these values with the typical of the previous and following weeks’ gross sales.

IV) Mannequin Design

The selection of covariates considerably influences counterfactual prediction accuracy. These time sequence should seize tendencies or exterior components more likely to affect the goal time sequence with out being affected by the intervention.

As well as, it’s essential to contemplate the scale of the estimated gross sales shift impact relative to the time sequence being studied: if the intervention is predicted to have an effect on the goal sequence by only some %, the sequence is probably not applicable, as small results are tough to tell apart from random noise (particularly because the library designers have proven that results lower than 1% are tough to show as being linked to the intervention). Due to this fact, we analyzed gross sales shift solely when the theoretical most gross sales shift price exceeds 5% of gross sales in its sub-family. We calculated this as S/(1-S), the place S represents the proportion of turnover the product generated in its sub-family earlier than turning into unavailable.

Given these preliminary issues, we designed our Causal Influence mannequin as follows:

Goal

Because the goal time sequence, we chosen the sum of gross sales for the product’s sub-family, excluding the product that turned unavailable.

Covariates

We first excluded the next kinds of time sequence:

• Merchandise from the identical sub-family because the discontinued product, to forestall any affect from its unavailability.
• Merchandise from totally different households than the discontinued product, since covariates ought to stay business-relevant.
• Time sequence that confirmed correlation however not co-integration with the goal sequence, to keep away from spurious relationships.

Utilizing these filters, we chosen 60 covariates:

• 20 covariates have been chosen based mostly on their highest co-integration with the goal sequence throughout the yr earlier than intervention.
• 40 further covariates have been chosen from the highest 200 co-integrated sequence, based mostly on their strongest correlation with the goal sequence throughout the yr earlier than intervention.

Notice that these numbers (20, 40, and 60) are guidelines of thumb derived from our earlier mannequin matches.

This empirical method combines time sequence that seize each long-term tendencies (by way of co-integration) and short-term variations (by way of correlation). We intentionally selected a lot of covariates as a result of Causal Influence employs a “spike and slab” methodology, which robotically reduces the affect of much less vital sequence by assigning them near-zero regression coefficients, whereas giving higher weight to essential ones.

V) Mannequin Validation

To validate our covariate choice technique, we drew closely on the method utilized by the Causal Influence designers. We performed a research of partial product unavailability as follows:

1. We examined instances the place merchandise turned partially unavailable and carried out an preliminary typical statistical evaluation utilizing difference-in-differences.
2. We utilized Causal Influence utilizing, as covariates, a management inhabitants that consisted of the product’s sub-family gross sales (excluding the unavailable product) in shops the place the product remained obtainable. These covariates supplied one of the best obtainable counterfactual since these shops have been unaffected by the intervention.
3. Lastly, we utilized Causal Influence with no management inhabitants, as an alternative utilizing our choice course of based mostly on co-integration and correlation as outlined within the Mannequin Design part.

Constant estimates throughout a number of stories (spanning totally different merchandise, portions, and classes) would exhibit that we will reliably apply this method on a broader scale.

Moreover we developed two metrics to judge the artificial management’s high quality: a health measure and a predictive functionality measure.

• The health measure, scored between 0 and 1, assesses how properly the artificial management fashions the goal over the pre-intervention interval.
• The predictive functionality measure is a type of backtesting that evaluates the artificial management’s high quality throughout a simulated false intervention up to now.

A Sensible Validation Instance

To validate the method described above with a sensible instance, we analyzed a case the place a yogurt pack turned unavailable in sure shops. We established remedy and management teams by matching every retailer the place the product turned unavailable with the same retailer that also had the product, based mostly on standards reminiscent of gross sales efficiency, buyer traits, and geographic location.

The theoretical most gross sales shift price for this product was 9.5%, and our earlier analyses confirmed very excessive gross sales shift charges within the dairy product household. Consequently, we anticipated to acquire an estimate near the theoretical most price.

Following our three-step validation methodology, we obtained these outcomes:

1. The difference-in-differences evaluation estimated the causal impact at 8.7% with 98.7% chance.
2. As proven in Determine 2 (beneath), the Causal Influence evaluation utilizing a management inhabitants estimated a causal impact of 9.0%, with a confidence interval of [3.7%, 14.4%] and 99.9% chance. We will additionally see that whereas the mannequin successfully tracks the time sequence fluctuations, it does present some minor deviations.

 Fig. 2: Causal impact estimation for the dairy product model after product unavailability, utilizing a management inhabitants to assemble the artificial management.

As well as, when utilizing covariates chosen based mostly on co-integration and correlation as an alternative of a management inhabitants, the Causal Influence evaluation estimated a causal impact of 8.5%, with a confidence interval of [2.4%, 15.1%] and 99.9% chance as proven in Determine 3 (beneath). Once more, the mannequin successfully tracks the time sequence fluctuations, but exhibiting some minor deviations.

 Fig. 3: Causal impact estimation for the dairy product model after product unavailability, utilizing proxies (solely knowledge from shops within the remedy inhabitants to represent the artificial management).

Here’s a abstract of the estimates obtained throughout the three totally different evaluation strategies:

It exhibits that the estimates stay constant in magnitude, whether or not utilizing a management inhabitants or not, thus validating our choice course of for covariates when no management inhabitants is accessible.

VI) Full unavailability: A rice pack not obtainable

We examined a nationwide case the place a pack of rice model turned unavailable. We restrained our evaluation to the next few months after the product turned unavailable to keep away from capturing unrelated results which may emerge over an extended interval. The theoretical most gross sales shift price for the product was 31.2%. We utilized the covariate choice methodology described earlier to estimate the potential gross sales shift impact.

Fig. 4: Causal impact estimation after the pack of rice model turned unavailable, utilizing proxies (solely knowledge from shops within the remedy inhabitants to represent the artificial management).

As proven in Determine 4, the artificial management fashions the goal very properly over the interval earlier than the intervention. The prediction precisely captures seasonal tendencies after the intervention. The credibility interval may be very slender across the estimate.

We obtained a statistically vital estimate at 22% enhance in turnover attributable to the product unavailability over the next months, with over 99.9% chance. This amount represents roughly 70% of the pack of rice complete gross sales earlier than the product turned unavailable, implying that 30% of the pack of rice gross sales didn’t shift.

VII) Utilization suggestions and expertise report

Causal Influence is a sturdy and user-friendly software for causal inferences. But after vital time spent specifying the mannequin and bettering its accuracy, we encountered challenges in fine-tuning it to acquire an industrializable answer.

• The primary level we wish to spotlight is the significance of the “rubbish in, rubbish out” precept, which is especially related when utilizing Causal Influence. Whatever the covariates used, Causal Influence will at all times produce a consequence, typically with very excessive chance, even in instances the place outcomes are unrealistic, or not possible.
• Time sequence chosen solely based mostly on the co-integration criterion typically overshadow others in mannequin function significance, which may drastically scale back the estimation accuracy when adjustment isn’t well-controlled.
• The choice of 20 sequence for co-integration and 40 for correlation is an empirical rule of thumb. Whereas efficient typically we encountered, it may gain advantage from additional refinement.

Conclusion

On this article we proposed a causal method to estimate the gross sales shift impact when a product turns into unavailable, utilizing Causal Influence. We outlined a technique for choosing analyzable merchandise, and covariates.

Though this method is purposeful and strong typically, it has limitations and areas for enchancment. Some are structural, whereas others require spending extra time on mannequin adjustment.

• We examined the methodology on totally different merchandise with promising outcomes, however it isn’t exhaustive. Some very seasonal merchandise or ones with little historic knowledge pose challenges. Moreover, merchandise that turned unavailable in only some shops are uncommon, limiting our means to validate the tactic on a lot of numerous instances.
• One other structural limitation is the mannequin’s requirement for post-hoc evaluation: the software doesn’t enable gross sales shift impact prediction earlier than a product turns into unavailable. Having the ability to take action would significantly profit enterprise groups. Work is underway to method gross sales shift prediction utilizing bayesian structural time sequence forecasting.
• The gross sales shift impact evaluation ignores margin impacts: the product that turned unavailable might have a better unit margin than the merchandise to which its gross sales shifted. The industrial conclusions to be drawn may then differ, however evaluation at a sub-family stage precludes this stage of element.
• Lastly we may discover various artificial controls, reminiscent of Augmented SC, Strong SC, Penalized SC, and even different causal approaches such because the two-way fastened impact mannequin.