How to cold call firms? An application of multi-armed bandit optimization in corporate web surveys

We conduct an adaptive experiment using Thompson Sampling instead of an experimental setup with static group composition. The main advantage of using a reinforcement learning algorithm is that insights about treatment effects are continuously exploited while the experiment is conducted, optimizing output (survey starting rates) already during the exploitation phase of the (sequential) experiment. In addition, such research design allows us to compare a larger number of treatments than in previously conducted experiments that consider a maximum of 16 different invitation letters (Kaplowitz et al., 2011).

Our research design varies five key elements of a survey invitation letter. Specifically, we consider (1) the personalization of invitation letters, (2) emphasizing the authority and status of the sender, (3) survey link placement, (4) stressing compliance with data protection, and (5) using a distinct request style by offering potential survey respondents the opportunity to share their opinion or pleading for help. We implement each of these factors in two different ways, resulting in a full-factorial experiment with a total of 32 (2^5) treatments.

2022-08-29

2023-01-20

survey starting rate

survey starting rate is used for determining dynamic group sizes

- survey linking agreement,
- panel retention rate,
- response behavior to sensitive survey questions

Randomization is conducted via random allocation of subjects into 32 different treatment groups. Yet, group sizes might differ during the course of the experiment. Within the first four weeks of the survey period, allocation to all groups happens with the same frequency.

Following this burn-in-phase, each week the bandit algorithm evaluates realized treatment effects and dynamically determines group sizes. In doing so, the bandit algorithm prioritizes relatively strong treatments versus relatively weak ones, while still testing the latter. Weights for allocation (size of the treatment groups) are calculated according to the formula stated in the section “Sampling design” of the research proposal. In sum, subjects are allocated to treatment groups at random, however the probability of receiving a specific treatment is updated weekly and is equivalent to the weights calculated by the Thompson Sampling algorithm.

Randomization done by a computer with equal probability for each of 32 invitation letters in the burn-in-phase.

To determine treatment group sizes after the burn-in-phase of the experiment, we use Thompson Sampling. Each week, the algorithm updates prior beliefs about success probabilities using the hitherto realized sample and calculates sampling weights for each treatment group that will be applied for the next week of invitations that will be sent.

The algorithm
i) uses independent prior beliefs over the success probability for each treatment,
ii) updates the distribution using Bayes' rule (considering the number of successes and trials),
iii) determines the treatment with the highest success probability, and updates the expected success distribution.

See research proposal for more detailed information.

Firm

No

No clusters

Approximately 1,250,000 invitation letters will be sent, of which we expect approx. 1,000,000 to be received, 300,000 to be opened, 30,000 to start the survey, 13,500 to finish the survey, and 8,100 to be willing to receive a follow-up survey

During burn-in-phase: approximately 6,250 per invitation letter of which a starting rate can be observed for 1,500.

Sample sizes are adaptively determined after start of Thompson sampling (see section "Intervention").