Curve Fitting for Survey Response Rates

The Field Time Estimator forecasts when your study will finish. This tool tells you why it's slowing down and whether intervention will help.

Every panel-based study has a response rate that decays over time. The responsive segment completes early, the less engaged segment trickles in later, and eventually you're pulling from the long tail of people who rarely take surveys. The decay rate varies by audience, incentive level, panel quality, and survey length, but the shape of the curve is always the same: exponential decline.

What the model does

Input your daily completion counts. The tool fits an exponential decay curve using least-squares regression and calculates the half-life of your response rate, meaning the number of days until your daily completions drop by 50%. A half-life of 3 days means fast decay; you'll burn through your responsive sample quickly. A half-life of 8 days means slower, steadier performance.

The shortfall detection is the actionable part. The model projects your total completions at current trajectory and compares it to your target. If the projection shows you'll fall short, it estimates the gap and flags it. That's your signal to release more sample, send a reminder wave, or increase the incentive.

I've used this approach to catch shortfalls 4-5 days before they would have become obvious from just eyeballing the daily numbers. Those extra days of lead time are worth a lot when you're trying to hold a delivery date.

Tech stack

React 18.2 + Babel CDN. Exponential regression using linearized least-squares (log-transform the completion data, fit a line, back-transform). Half-life = ln(2)/k where k is the decay constant. Shortfall projection integrates the fitted curve from current day to infinity and compares the asymptotic total to the target.