Questions & explanations
1. How do you interpret a hazard ratio of 1.5 for 'number of logins'?
A hazard ratio above 1 means increased risk. So a hazard ratio of 1.5 for number of logins means that each time a customer logs in more often, the risk of churning increases by 50%? Actually careful: hazard ratio of 1.5 means the hazard (instant risk) is 1.5 times higher for each one-unit increase in logins. But wait, usually more logins should reduce churn. So if hazard ratio is 1.5, it suggests more logins are associated with higher churn. That could be surprising. The correct interpretation: for each additional login (per unit), the churn risk multiplies by 1.5, meaning a 50% increase. But if the factor is continuous, it's per unit increase. So negative factors like low engagement might have hazard >1. Typically, a hazard ratio <1 means protective. So we need to phrase carefully. Let's say: A hazard ratio of 1.5 means that for each one-unit increase in the variable, the hazard (risk of churn) is 1.5 times higher. So a customer who logs in once more per month has 50% higher churn risk. But that would mean logging in hurts, which is unlikely. In practice, we expect hazard ratio less
2. An e-commerce site finds that 80% of visitors view a product page, 20% add to cart, and 5% complete purchase. Calculate the conversion rate for each step and explain where the biggest loss happens.
From product view to cart: 20% out of 80% (but we need per step rate: from view to cart = 20/80 = 25%). Actually, better: step 1: view to add-to-cart rate = 20% (since 20% of all visitors add to cart, but if we consider only those who viewed, it's 20/80 = 25%? Let's keep simple: overall, 80% view, so out of viewers, 20%/80% = 25% cart, but the question expects? I'll rephrase. More straightforward: of 100 visitors, 80 view a product, 20 add to cart, 5 buy. So rate from view to add = 20/80 = 25%. From add to buy = 5/20 = 25%. The biggest absolute drop is from view to add (80 to 20), but the drop in rate (25% to 25% is same). However, the biggest loss in numbers: 60 visitors leave between view and add. So the store should improve the product page to encourage more adds.
3. How does a hierarchical model share information between users?
A hierarchical model has a top-level distribution that represents the population of all users. Each user's individual parameters are drawn from this population distribution. So if one user shows a strong preference for books, that information affects the population distribution slightly, which in turn influences estimates for other users. This sharing happens through the statistical model: the population parameters are estimated from all users' data, and individual estimates are pulled toward the population mean. The amount of sharing depends on how much data each user has; users with little data are pulled more toward the average. This is how information flows between users in a hierarchical model.
4. Compare matrix factorization with collaborative filtering.
Collaborative filtering, especially user-user or item-item, works directly with user or item similarities. Matrix factorization is a more advanced method that learns hidden features. Traditional collaborative filtering can struggle with sparse data and is hard to scale to very large datasets. Matrix factorization handles sparsity better because it compresses the data into dense vectors. It also tends to give more accurate predictions because it captures underlying patterns. However, matrix factorization is more complex to implement and requires tuning. Both are types of collaborative filtering in a broad sense, but matrix factorization is the modern standard in many recommendation systems.
5. What is the role of latent factors in matrix factorization?
Latent factors are the hidden characteristics discovered by the algorithm that explain why users like certain items. They are not predefined but are learned from the data. For movies, a factor could represent genre, director style, or even subtle aspects like mood. For users, each factor measures how much they care about that characteristic. The role of these factors is to compress the rating behavior into a small number of dimensions. This allows the model to generalize from observed ratings to unobserved ones. The more factors you use, the more detailed the model, but too many can lead to overfitting. Choosing the right number of factors is important for good performance.
6. Why might simple regression give wrong results when endogeneity is present?
Simple regression assumes that the explanatory variable is not correlated with the error term. When endogeneity exists, this assumption is violated, and the estimated coefficient is biased and inconsistent. For example, regressing customer lifetime value on satisfaction might show a positive relationship, but if happier customers are also wealthier (unobserved), the regression mixes the true effect with the wealth effect. The coefficient might be too high or even the wrong sign. This can lead to bad business decisions, like investing in satisfaction programs that don't truly increase value. IV methods correct this bias by using instruments that isolate the causal part.
7. How is online retail in an emerging market different from in a developed market?
In a developed market, most people already shop online, so growth is slower. Retailers focus on improving service and loyalty. In an emerging market, many people are shopping online for the first time, so growth is fast. Payment methods differ: developed markets use credit cards and digital wallets, while emerging markets often use cash on delivery or mobile money. Logistics in developed markets have fast, reliable delivery, but in emerging markets, delivery can be slow and unreliable. Customer trust is also lower in emerging markets, so retailers need to build it with clear policies. Finally, product prices in emerging markets are often lower to match local incomes.
8. What is the cold start problem in collaborative filtering?
The cold start problem is when a collaborative filtering system cannot make good recommendations for new users or new items because it lacks data. A new user has no history, so the system cannot find similar users or items. A new item has no user interactions, so it cannot be compared to other items. This is a major weakness of pure collaborative filtering. Solutions include combining with content-based filtering, asking new users for initial preferences, or using popularity-based recommendations. For new items, you can use their attributes to find similarities until they accumulate user ratings. Without such strategies, the system fails to personalize for newcomers.
9. How does RD differ from comparing customers just above and below the threshold without regression?
Simply comparing average outcomes of customers just above and below the threshold disregards the relationship between the assignment variable and the outcome. For example, if higher scores are linked to higher engagement even without the treatment, the raw comparison may overstate the effect. RD uses regression to model this relationship, so the estimated jump at the cutoff is adjusted for the general trend. Without regression, the comparison might also be biased by differences in the variable itself. RD also allows using data farther from the cutoff to improve precision, while simple comparison only uses a narrow band. This makes RD more accurate and powerful.
10. A company has two customer segments: frequent buyers and occasional buyers. How does CLV differ between them and how can the company use this difference for customer experience?
Frequent buyers have a higher CLV because they purchase more often and maybe spend more per visit. Occasional buyers have a lower CLV. The company can give different experiences to each segment. For high-CLV frequent buyers, they can offer a premium support phone line or free shipping. For low-CLV occasional buyers, they can send automated reminders or discounts to encourage more visits. This way the company spends more resources on customers who bring more money, while still trying to improve the experience for others. The goal is to make all customers feel valued but in a cost-effective way. Segmenting by CLV helps personalize communication and services.
11. How do you check if propensity score matching worked well?
After matching, you check the balance of features between treated and untreated groups. For each feature (e.g., age, spending), you compare the means or proportions. Ideally, after matching, these differences are small (standardized difference below 0.1). You can also plot the distribution of propensity scores – before matching, they differ; after, they should overlap. Another check is a love plot showing standardized differences before and after. If balance is poor, you may need to use a different matching method (like caliper matching) or include interactions in the propensity model. Good balance supports that the matching removed observable confounders.
12. How does emotional engagement differ from satisfaction in customer experience?
Satisfaction is a judgment about whether the product or service met expectations. Emotional engagement is about the customer's feelings during the experience. Two customers can both be satisfied but have different emotions: one feels happy and excited, the other feels relieved but neutral. Emotional engagement predicts future behavior better because emotions drive decisions. For example, a satisfied but uninterested customer may leave for a competitor, while an emotionally engaged customer will stay. Companies measure emotions to see if they create a bond, not just a transaction. Emotional metrics help design experiences that feel personal and memorable.