Bootstrapping confidence intervals

Having bootstrapped the distribution of the female-effect coefficient in the last exercise, you can now use it to estimate a confidence interval. It will allow you to make the following assessment about your data: "Given the uncertainty from imputation, we are 95% sure that the female-effect on earnings is between a and b", where a and b are the lower and upper bounds of the interval.

In the last exercise, you have run bootstrapping with R = 50 replicates. In most applications, however, this is not enough. In this exercise, you can use boot_results that were prepared for you using 1000 replicates. First, you will look at the bootstrapped distribution to see if it looks normal. If so, you can then rely on the normal distribution to calculate the confidence interval.

This exercise is part of the course

Handling Missing Data with Imputations in R

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Plot and print boot_results
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Handling Missing Data with Imputations in R

AdvancedSkill Level

4.7+

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In this chapter, you’ll find out why missing data can be a risk when analyzing a dataset. You’ll be introduced to the three missing data mechanisms and learn how to recognize them using statistical tests and visualization tools.

Exercise 1: Missing data: what can go wrong Exercise 2: Linear regression with incomplete data Exercise 3: Analyzing regression output Exercise 4: Comparing models Exercise 5: Missing data mechanisms Exercise 6: Recognizing missing data mechanisms Exercise 7: t-test for MAR: data preparation Exercise 8: t-test for MAR: interpretation Exercise 9: Visualizing missing data patterns Exercise 10: Aggregation plot Exercise 11: Spine plot Exercise 12: Mosaic plot

Get to know the taxonomy of imputation methods and learn three donor-based techniques: mean, hot-deck, and k-Nearest-Neighbors imputation. You’ll look under the hood to see how these methods work, before learning how to apply them to a real-world tropical weather dataset. Along the way, you’ll also learn useful tricks that you can use to make them work even better for your problems.

Exercise 1: Mean imputation Exercise 2: Smelling the danger of mean imputation Exercise 3: Mean-imputing the temperature Exercise 4: Assessing imputation quality with margin plot Exercise 5: Hot-deck imputation Exercise 6: Vanilla hot-deck Exercise 7: Hot-deck tricks & tips I: imputing within domains Exercise 8: Hot-deck tricks & tips II: sorting by correlated variables Exercise 9: k-Nearest-Neighbors imputation Exercise 10: Choosing the number of neighbors Exercise 11: kNN tricks & tips I: weighting donors Exercise 12: kNN tricks & tips II: sorting variables

It’s time to learn how to use statistical and machine learning models, such as linear regression, logistic regression, and random forests, to impute missing data. In this chapter, you’ll look into how the models make their predictions and use this knowledge to draw the imputed values from conditional distributions. This is important as it ensures your imputations are more varied and plausible, making them more similar to the true data.

Exercise 1: Model-based imputation approach Exercise 2: Linear regression imputation Exercise 3: Initializing missing values & iterating over variables Exercise 4: Detecting convergence Exercise 5: Replicating data variability Exercise 6: Logistic regression imputation Exercise 7: Drawing from conditional distribution Exercise 8: Model-based imputation with multiple variable types Exercise 9: Tree-based imputation Exercise 10: Imputing with random forests Exercise 11: Variable-wise imputation errors Exercise 12: Speed-accuracy trade-off

Imputed values are not set in stone. They are just estimates and estimates come with some uncertainty. In this final chapter, you’ll discover how bootstrapping and chained equation using the mice package can be used to incorporate imputation uncertainty into your models and analyses to make them more reliable and robust.

Exercise 1: Multiple imputation by bootstrapping Exercise 2: Wrapping imputation & modeling in a function Exercise 3: Running the bootstrap Exercise 4: Bootstrapping confidence intervals

Current Exercise

Exercise 5: Multiple imputation by chained equations Exercise 6: The mice flow: mice - with - pool Exercise 7: Choosing default models Exercise 8: Using predictor matrix Exercise 9: Putting it all together Exercise 10: Analyzing missing data patterns Exercise 11: Imputing and inspecting outcomes Exercise 12: Inference with imputed data Exercise 13: Final remarks