Learning from Convenience Samples: A Case Study on Fine-Tuning LLMs for Survey Non-response in the German Longitudinal Election Study

Survey researchers face two key challenges: the rising costs of probability samples and missing data (e.g., non-response or attrition), which can undermine inference and increase the use of convenience samples. Recent work explores using large language models (LLMs) to simulate respondents via persona-based prompts, often without labeled data. We study a more practical setting where partial survey responses exist: we fine-tune LLMs on available data to impute self-reported vote choice under both random and systematic nonresponse, using the German Longitudinal Election Study. We compare zero-shot prompting and supervised fine-tuning against tabular classifiers (e.g., CatBoost) and test how different convenience samples (e.g., students) used for fine-tuning affect generalization. Our results show that when data are missing completely at random, fine-tuned LLMs match tabular classifiers but outperform zero-shot approaches. When only biased convenience samples are available, fine-tuning small (3B to 8B) open-source LLMs can recover both individual-level predictions and population-level distributions more accurately than zero-shot and often better than tabular methods. This suggests fine-tuned LLMs offer a promising strategy for researchers working with non-probability samples or systematic missing-ness, and may enable new survey designs requiring only easily accessible subpopulations.