Modeling and Multivariate Methods - SAS

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Contents Introduction to Item Response Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525 Launching the Platform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 528 Item Analysis Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .530 Characteristic Curves. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .530 Information Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 Dual Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 Platform Commands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533 Technical Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
Chapter 22 Scoring Tests Using Item Response Theory 525 Introduction to Item Response Theory Introduction to Item Response Theory Psychological measurement is the process of assigning quantitative values as representations of characteristics of individuals or objects, so-called psychological constructs. Measurement theories consist of the rules by which those quantitative values are assigned. Item response theory (IRT) is a measurement theory. IRT uses a mathematical function to relate an individual’s probability of correctly responding to an item to a trait of that individual. Frequently, this trait is not directly measurable and is therefore called a latent trait. To see how IRT relates traits to probabilities, first examine a test question that follows the Guttman “perfect scale” as shown in Figure 22.1. The horizontal axis represents the amount of the theoretical trait that the examinee has. The vertical axis represents the probability that the examinee will get the item correct. (A missing value for a test question is treated as an incorrect response.) The curve in Figure 22.1 is called an item characteristic curve (ICC). Figure 22.1 Item characteristic curve of a perfect scale item P(Correct Response) 1.0 0.5 b Trait Level This figure shows that a person who has ability less than the value b has a zero percent chance of getting the item correct. A person with trait level higher than b has a 100% chance of getting the item correct. Of course, this is an unrealistic item, but it is illustrative in showing how a trait and a question probability relate to each other. More typical is a curve that allows probabilities that vary from zero to one. A typical curve found empirically is the S-shaped logistic function with a lower asymptote at zero and upper asymptote at one. It is markedly nonlinear. An example curve is shown in Figure 22.2.
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INDIRECT OR CONSEQUENTIAL DAMAGES O
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6 Emphasis Options for Standard Lea
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8 Models with Crossed, Interaction,
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12 Examining the Residuals . . . .
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14 Response Frequencies . . . . . .
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16 19 Analyzing Principal Component
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18 Interpreting the Profiles . . .
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20 Discriminant Analysis . . . . .
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Contents Book Conventions. . . . .
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Contents Launch the Fit Model Platf
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136 Fitting Stepwise Regression Mod
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Contents Example of a Multiple Resp
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158 Fitting Multiple Response Model
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Contents Overview of Generalized Li
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180 Fitting Generalized Linear Mode
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Contents Introduction to Logistic M
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200 Performing Logistic Regression
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Contents Overview of the Screening
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232 Analyzing Screening Designs Cha
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Contents Introduction to the Nonlin
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244 Performing Nonlinear Regression
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Contents Overview of Neural Network
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280 Creating Neural Networks Chapte
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Contents Launching the Platform. .
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296 Modeling Relationships With Gau
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Contents Overview of the Loglinear
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306 Fitting Dispersion Effects with
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Contents Introduction to Partitioni
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318 Recursively Partitioning Data C
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Contents Launch the Platform . . .
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354 Performing Time Series Analysis
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Contents The Categorical Platform .
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386 Performing Categorical Response
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Contents Introduction to Choice Mod
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404 Performing Choice Modeling Chap
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Contents Launch the Multivariate Pl
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444 Correlations and Multivariate T
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Contents Introduction to Clustering
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462 Clustering Data Chapter 18 The
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464 Clustering Data Chapter 18 Hier
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470 Clustering Data Chapter 18 K-Me
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472 Clustering Data Chapter 18 K-Me
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640 References Becker, R.A. and Cle
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642 References Draper, N. and Smith
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646 References Matsumoto, M. and Ni
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648 References Rawlings, J.O. (1988
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650 References Umetrics (1995), Mul
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654 Statistical Details Appendix A
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692 Index Ellipses Transparency 451
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696 Index Customizing 267 Nonlinear
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700 Index Stable 363 Stable Inverti
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702 Index
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Modeling and Multivariate Methods - SAS

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