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
Easyitem
Easyitem
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
Easyitem
Easyitem
Harditem
Harditem
Person Ability
Item Difficulty High ability person, moderately difficult item90% chance
-3 -2 -1 0 1 2 3
100% -
50% -
0% -
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Item
Item Response TheoryItem Response Theory
Item difficulty/ Person ability