# Predicting Missing Values in Survey Data Using Prompt Engineering for Addressing Item Non-Response
## 3 Methods
### Our Methods
#### 3.3.2 Column Selection  
The Column Selection process is designed to identify the most relevant question-answer pairs from the dataset \(D\) that can provide valuable context in answering the target question \(q_{t_{q}}\) for the target respondent \(\mathbf{r}_{t_{r}}\). This step addresses the limitations of the Naive Prompt approach by selectively utilizing the most relevant information. The procedure consists of the following steps:  
1. Prompting for Related Questions for Enhanced Retrieval: To identify the most relevant questions to the target question \(q_{t_{q}}\), we prompt the LLM to produce alternative phrasings, expansions, or related inquiries that capture different aspects of \(q_{t_{q}}\). Specifically, we use GPT-4 Turbo to generate a set of candidate questions \(\mathcal{Q}_{c}=\{q_{c_{1}},\cdots,q_{c_{m}}\}\) that are semantically related to \(q_{t_{q}}\). This approach allows us to uncover relevant questions that may not be directly similar in wording but are conceptually related, thereby enriching the pool of potential context for the LLM to use in prediction. By using these generated related questions as queries for retrieval, we can capture information that might be missed by using the target question directly, as discussed in Section 3.2. 2. Embedding with Dense Retriever: Once the candidate questions \(\mathcal{Q}_{c}\) are generated, each candidate question \(q_{c_{i}}\in\mathcal{Q}_{c}\) and each actual question \(q_{j}\in Q\) are embedded using a dense retriever model. Specifically, the retriever maps each actual question to an embedding \(e(q_{c})\) by taking the [CLS] token of the last hidden representation over the tokens in \(q_{c}\). At query time, the same encoder is applied to the candidate question \(q_{c_{i}}\) to obtain a candidate question embedding \(e(q_{c_{i}})\). This embedding process converts the textual content of the questions into dense vector representations that capture their semantic meaning, enabling more accurate similarity calculations. 3. Retrieving Similar Questions: After embedding the candidate questions \(\mathcal{Q}_{c}\) and the actual questions \(Q\) using a dense retriever model, we calculate the cosine similarity between the embedded vectors \(e(q_{c_{i}})\) and \(e(q_{j})\). For each candidate question \(q_{c_{i}}\), we select the question \(q_{r_{i}}\in Q\) with the highest cosine similarity: \[q_{r_{i}}=\operatorname*{argmax}_{q_{j}\in Q}\cos(e(q_{c_{i}}),e(q_{j}))\] (4) This process yields a set of retrieved questions \(Q_{r}=\{q_{r_{1}},\cdots,q_{r_{n}}\}\), where each \(q_{r_{i}}\), selected through Equation (4), is the most similar question to the corresponding candidate question \(q_{c_{i}}\). To ensure that the selected question in \(Q_{r}\) does not overlap, each question \(q_{r_{i}}\) must be unique. If a question \(q_{j}\) has already been selected for another candidate, it is excluded from the pool of options for subsequent selections, and the next most similar question is selected. This process ensures that all questions in \(Q_{r}\) are distinct. 4. Final Selection of Question-Answer Pairs: From the set of retrieved question-answer pairs \((q_{r},r_{ir})\), we select the top-k pairs that exhibit the highest relevance to the target question \(q_{t_{q}}\). The relevance is determined by the order of the \(\mathcal{Q}_{c}\), which is predetermined by the GPT-4 model per target question. This ensures that the selected pairs provide the most informative context, thereby enabling the LLM to generate more accurate predictions. Additionally, the few-shot respondents selected through the Row Selection process (Section 3.3.1) also undergo the same process of extracting relevant question-answer pairs, ensuring that both row and column selections are optimally aligned to support the LLM's decision-making process.