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Jerker Denrell (Behavioural Science Group) & Adam Sanborn (Department of Psychology) - Date(s) - 17 November 2016

Implicit corrections for missing feedback: Imputation vs. statistical models

In many real-life settings feedback is only available for cases decision makers accept. How do people learn from such selective feedback? There are two approaches in statistics for this kind of missing data: imputing the missing values, and using a statistical model of the task. Elwin et al. (2007) provided evidence that people rely on a type of imputation called ‘constructivist coding’, i.e., people code rejected cases, for which no feedback is available, as failures. It is not intuitively obvious whether relying on this kind of internally generated feedback is sensible or leads to bias in an exemplar model. To examine this, we formally analyze the impact of constructivist coding on the performance of exemplar learning algorithms. Our analysis shows that constructivist coding is an adaptive strategy: it maximizes the total reward. The reason is that constructivist coding compensates for the failure of exemplar algorithms to take selection-bias into account. In two experiments we then test whether participants impute missing values through constructivist coding, or use a statistical model of the task to correct for selection bias. These experiments have a simple setup: a financial advisor is predicting the amount an investment will return, but the advisor’s predictions are noisy and have an unknown bias. Participants decide on each trial whether to invest, receiving feedback only if they do so. We find that about half of participants use an exemplar model; a large majority of these participants use constructivist coding, some of whom internally generate values that are very close to optimal. The other half of participants correct for selective feedback with a sensible task-specific strategy, the majority of whom correct for bias using a Bayesian model of the task.