Скачать или смотреть Unraveling the Mystery of Unknown Input Values in R Functions: How to Solve for mdes and power

Learn how to effectively tackle optimization challenges in R by solving for unknown input values like `mdes` and `power`, using well-defined methods for clarity and accuracy.
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Unraveling the Mystery of Unknown Input Values in R Functions: How to Solve for mdes and power

When working with R functions for statistical analysis and optimization, you might encounter certain scenarios where you need to determine unknown input values based on various parameters. A common question arises when trying to solve for mdes (minimum detectable effect size) when all other inputs are known, or even for both mdes and power. In this guide, we’ll explore how to tackle these issues effectively.

The Problem: Solving for Unknown Values in R

It’s typical in statistical computations to define functions that take several input values. In our case, there's an R function, named foo, which calculates various statistical metrics based on its input parameters. However, the values of mdes and possibly power need to be calculated rather than directly provided.

Here's a brief overview of the function definition:

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The challenge arises in figuring out how to effectively calculate mdes (or both mdes and power) when the other parameters are known.

Solution Approach for Finding mdes

Step 1: Define a Function of One Variable

The first step in solving for mdes is to create a new function that retains the essence of the original but isolates mdes as the variable of interest. We can achieve this by using the following code:

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In this snippet, p0 captures the default output of the function foo when it is run with its default mdes value of 0.25. The fn1 function calculates the sum of squared differences between the output of foo(mdes = x) and p0. This set-up is crucial for the optimization task.

Step 2: Optimize to Find the Minimum

Next, we use the optimize() function in R to find the minimum of fn1. A minimum value of 0 corresponds to the correct mdes input since it suggests that the difference between the actual function output and the expected output (stored in p0) is negligible.

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The output will give you access to both the minimum mdes found and the corresponding value of the objective function:

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The result shows that the optimized value is approximately 0.25, matching the input we were looking for.

Solving for Two Variables: mdes and power

Finding values for both mdes and power is inherently more complex due to the multi-dimensional aspect of the problem. The function could have multiple local minima, making it challenging to pinpoint the global minimum. In this case, the optim() function is recommended, which allows for more flexibility in optimization tasks:

Step 1: Setting Up optim()

To use optim(), you need to define a function that encapsulates both mdes and power. This would require carefully chosen starting points to guide the search towards potential solutions.

Step 2: Running optim()

Here’s a concise example for running the optimization:

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Selecting appropriate initial values for mdes and power is crucial to ensure convergence to the correct solution.

Conclusion

Dealing with unknown inputs in R functions can definitely be challenging, especially when faced with complex statistical functions. By defining a clear approach—isolating the variable of interest through functions and effectively using optimization techniques—you can derive the necessary values for mdes and power. Now you have a structured method for tackling similar challenges with your R programming projects.

With this guide, you should feel more equipped to approach function optimization in R and extract meaningful insights from your dat