1. Interactive graphics Understanding OLS regression Normal approximation to the Binomial distribution

2. General Stats Software example: OLS regression OLS regressionOLS regression example: Poisson regression Poisson regressionPoisson regression as well as specialized software

3. Specialized software Testing: Classical test theoryClassical test theory – ITEMIN Item response theoryItem response theory –BILOG-MG –PARSCALE –MULTILOG –TESTFACT

4. Specialized software Structural equation modeling (SEM) – – –

5. Specialized software Hierarchical linear modeling (HLM) – –

6. Open data

7. Run simple linear regression

8. Analyze  Regression  Linear

9. Enter the DV and IV

10. Check for confidence intervals

11. Age accounts for about 37.9% of the variability in Gesell score The regression model is significant, F(1,19) = 13.202, p =.002 The regression equation: Y’=109.874-1.127X Age is a significant predictor, t(9)=-3.633, p=.002. As age in months at first word increases by 1 month, the Gesell score is estimated to decrease by about 1.127 points (95% CI: -1.776, -.478) Output

12. Enter the data Fit a Poisson loglinear model: log(Y/pop) =  +  1 (Fredericia) +  2 (Horsens) +  3 (Kolding) +  4 (Age) Click to execute

13. City doesn’t seem to be a significant predictor, whereas Age does. G 2 = 46.45, df = 19, p <.01

14. Plot of the observed vs. fitted values-- obviously model not fit

15. Fit another Poisson model: log(Y/pop) =  +  1 (Fredericia) +  2 (Horsens) +  3 (Kolding) +  4 (Age) +  5 (Age) 2 Both (Age) and (Age) 2 are significant predictors.

16. Plot of the observed vs. fitted values: model fits better

17. Fit a third Poisson model (simpler): log(Y/pop) =  +  1 (Fredericia) +  2 (Age) +  3 (Age) 2 All three predictors are significant.

18. Plot of the observed vs. fitted values: much simpler model

19. Item Response Theory Easy item Easy item Hard item Hard item Person Ability Item Difficulty Low ability person: easy item - 50% chance

20. Low ability person: moderately difficult item - 10% chance Item Response Theory Easy item Easy item Hard item Hard item Person Ability Item Difficulty High ability person, moderately difficult item 90% chance

21. -3 -2 -1 0 1 2 3 100% - 50% - 0% - Probability of success Item Item Response Theory Item difficulty/ Person ability