Background: Studies examining how sentiment on social media varies depending on timing and location appear to produce inconsistent results, making it hard to design systems that use sentiment to detect localized events for public health applications. Objective: The aim of this study was to measure how common timing and location confounders explain variation in sentiment on Twitter. Methods: Using a dataset of 16.54 million English-language tweets from 100 cities posted between July 13 and November 30, 2017, we estimated the positive and negative sentiment for each of the cities using a dictionary-based sentiment analysis and constructed models to explain the differences in sentiment using time of day, day of week, weather, city, and interaction type (conversations or broadcasting) as factors and found that all factors were independently associated with sentiment. Results: In the full multivariable model of positive (Pearson r in test data 0.236; 95\% CI 0.231-0.241) and negative (Pearson r in test data 0.306; 95\% CI 0.301-0.310) sentiment, the city and time of day explained more of the variance than weather and day of week. Models that account for these confounders produce a different distribution and ranking of important events compared with models that do not account for these confounders. Conclusions: In public health applications that aim to detect localized events by aggregating sentiment across populations of Twitter users, it is worthwhile accounting for baseline differences before looking for unexpected changes.