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Interactive graphics Understanding OLS regression

Interactive graphics Understanding OLS regression Normal approximation to the Binomial distribution. General Stats Software. example: OLS regression example: Poisson regression as well as specialized software. Specialized software. Testing: Classical test theory – ITEMIN

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Interactive graphics Understanding OLS regression

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

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

  3. Specialized software Testing: • Classical test theory – ITEMIN • Item 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. Output 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)

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

  13. G2 = 46.45, df = 19, p < .01 City doesn’t seem to be a significant predictor, whereas Age does.

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

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

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

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