1. Bootstrapping Byrne Chapter 12

2. Bootstrapping Quick distinction: – Population distribution – Sample distribution – Sampling distribution

3. Bootstrapping Sampling distribution is approximately normal if: – Underlying population distribution is normal – N > 30 Central Limit Theorem

4. Bootstrapping We can’t really assume the underlying population is normal usually So we are going to use large samples to approximate normality, even if that population is not

5. Bootstrapping Bootstrapping is especially helpful for skewed/kurtotic data – Which Likert scales have a bad tendency to be!

6. Bootstrapping Reminder on why non-normal data is bad: – Chi-square is adversely affected – Also makes your modification indices look like OH YEAH, when it’s actually just an inflated chi-square

7. Bootstrapping Reminder on why non-normal data is bad: – CFI and TLI are decreased – S.E. is underestimated, which makes paths look significant that might not be.

8. Bootstrapping How does it work? – Start with your large sample – Treat it like the population (sort of pretend it’s everyone ever that you wanted to sample). – Take lots of samples from that population with the same N

9. Bootstrapping How does it work? – Repeat! Lots of samples! Usually 500. – Run ML estimation of each of those samples – Average the ML estimates to create a bootstrapped estimate

10. Bootstrapping How does it work? – So you get the highest probability of the estimation, averaged over the many fake samples you’ve taken from this population

11. Bootstrapping Why? – To be able to test if your mean and standard error (or estimates and standard error) are stable if you were to sample the population over and over again – Deal with non-normality

12. Bootstrapping How’s that different than Bayes? – Bayes: starts with a proposed distribution of the data (prior distribution) Remember that can be any type of distribution – Then it takes a random walk around that distribution to come up with estimated samples (MCMC) – Then you get estimates based on the data + that prior

13. Bootstrapping How’s that different than Bayes? – BS: uses your data to estimate lots of samples (with replacement!) – Then averages those samples

14. Bootstrapping Good: – Gives you an idea if the estimates are going to be stable – Tells you how consistent the samples are

15. Bootstrapping Bad: – Really normal data gives you biased estimates – Sample must be representative of the population – Must be sure independence is met

16. Bootstrapping View > analysis properties > bootstrap!

17. What to look at Compare loadings from ML and BS Compare SE from ML and BS SESE = standard error of the standard error – You want these to be very small

18. What to look at Mean is the estimate column to be able to compare – (make sure you compare standardized to standardized and not mix and match with unstandardized)

19. What to look at Bias is the difference between ML and BS – Want small! – SE bias should be small too You can also get BS CIs!

20. Let’s try it! Go back to the one-factor RS model (simple CFA) to test bootstrappping.