Interactive graphics Understanding OLS regression Normal approximation to the Binomial distribution

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

Specialized software Testing: Classical test theoryClassical test theory – ITEMIN Item response theoryItem 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

Age accounts for about 37.9% of the variability in Gesell score The regression model is significant, F(1,19) = , p =.002 The regression equation: Y’= 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 points (95% CI: , -.478) Output

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

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

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

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

% - 50% - 0% - Probability of success Item Item Response Theory Item difficulty/ Person ability