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The primary concern of reducing Type II error in modeling is to avoid false negatives and ensure that significant findings are identified. A Type II error occurs when a test fails to reject a false null hypothesis, meaning that the model does not detect an effect or difference when one actually exists. By focusing on reducing this type of error, researchers aim to enhance the model's ability to identify true relationships or significant factors within their data, thus improving the reliability of results and decision-making based on those results.

In the context of the options provided, maintaining high precision in estimates, increasing the complexity of the model, or minimizing the number of variables used do not directly address the concern of failing to detect significant results. High precision is more related to the accuracy of the estimates rather than the detection ability of a model. Increasing complexity could sometimes lead to overfitting, which might actually increase the risk of Type II errors in practical applications. Minimizing variables might improve model interpretability but does not necessarily contribute to reducing Type II errors. Thus, the correct choice emphasizes the importance of identifying true effects to ensure meaningful and actionable insights.