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Bayesian estimation offers a flexible alternative to modeling techniques where the inferences depend on p-values. In this course, you’ll learn how to estimate linear regression models using Bayesian methods and the rstanarm package. You’ll be introduced to prior distributions, posterior predictive model checking, and model comparisons within the Bayesian framework. You’ll also learn how to use your estimated model to make predictions for new data.
Introduction to Bayesian Linear ModelsFree
A review of frequentist regression using lm(), an introduction to Bayesian regression using stan_glm(), and a comparison of the respective outputs.Non-Bayesian Linear Regression50 xpExploring the data100 xpFitting a frequentist linear regression100 xpBayesian Linear Regression50 xpFitting a Bayesian linear regression100 xpConvergence criteria50 xpAssessing model convergence50 xpComparing frequentist and Bayesian methods50 xpDifference between frequentists and Bayesians50 xpCreating credible intervals100 xp
Modifying a Bayesian Model
Learn how to modify your Bayesian model including changing the number and length of chains, changing prior distributions, and adding predictors.What's in a Bayesian Model?50 xpAltering chains100 xpDo I have enough iterations?50 xpPrior distributions50 xpDetermine Prior Distributions100 xpCalculate Adjusted Scales100 xpUnadjusted Priors100 xpUser Specified Priors50 xpChanging Priors100 xpSpecifying informative priors100 xpConsequences of informative priors50 xpAltering the estimation process50 xpAltering the Estimation100 xp
Assessing Model Fit
In this chapter, we'll learn how to determine if our estimated model fits our data and how to compare competing models.Using the R Squared statistic50 xpCalculating Frequentist R-squared100 xpR-squared for a Bayesian Model100 xpPosterior predictive model checks50 xpPredicted score distributions100 xpDistributions for a single observation50 xpModel fit with posterior predictive model checks50 xpR-squared Posterior100 xpPosterior Predictive Testing100 xpBayesian model comparisons50 xpCalculating the LOO estimate100 xpComparing models50 xp
Presenting and Using a Bayesian Regression
In this chapter, we'll learn how to use the estimated model to create visualizations of your model and make predictions for new data.
Psychometrician, ATLAS, University of Kansas
Jake is a Psychometrician at the Center for Accessible Teaching, Learning, and Assessment Systems (ATLAS) and received his PhD in Educational Psychology and Research. His interests are include educational assessment, diagnostic classification modeling, and Bayesian inference. Follow him at @wjakethompson on Twitter or on his blog.
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