Interactive graphicsInteractive graphicsUnderstanding OLS regressionUnderstanding OLS regression

Normal approximation to the Normal approximation to the Binomial Binomial distribution distribution

General Stats SoftwareGeneral Stats Software

example: OLS regressionexample: OLS regressionexample: Poisson example: Poisson

regressionregression

as well as specialized softwareas well as specialized software

Specialized softwareSpecialized software

Testing:Testing:• Classical test theoryClassical test theory

–– ITEMINITEMIN• Item response theory Item response theory

– BILOG-MGBILOG-MG– PARSCALEPARSCALE– MULTILOGMULTILOG– TESTFACTTESTFACT

Specialized softwareSpecialized software

Structural equation Structural equation modeling (SEM)modeling (SEM)–

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Specialized softwareSpecialized software

Hierarchical linear Hierarchical linear modeling (HLM) modeling (HLM) –

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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) = 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

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, City doesn’t seem to be a significant predictor, whereas Age does.whereas Age does.

G2 = 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 TheoryItem Response Theory

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Harditem

Harditem

Person Ability

Item Difficulty Low ability person: easy item - 50% chance

Low ability person: moderately difficult item - 10% chance

Item Response TheoryItem Response Theory

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Item Response TheoryItem Response Theory

Item difficulty/ Person ability