Interactive graphics Understanding OLS regression Normal approximation to

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 • Item response theory – – BILOG-MG PARSCALE MULTILOG TESTFACT

Specialized software Structural equation modeling (SEM) – – –

Specialized software Hierarchical linear modeling (HLM) – –

Open data

Run simple linear regression

Analyze Regression Linear

Enter the DV and IV

Check for confidence intervals

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. 127 X 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)

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

G 2 = 46. 45, df = 19, p <. 01 City doesn’t seem to be a significant predictor, whereas Age does.

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

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.

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

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

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

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

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

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