CTT

Question 1

3 assumptions of CTT

Answer 1

1. measurement is on an interval scale
2. the variance of the observed scores is finite
3. the measurements are repeatedly sampled in a linear, experimentally independent way

Question 2

challenges of CTT

Answer 2

1. The true score does not necessarily correspond to a unidimensional construct score
   > you can still have a high cronbach’s alpha, but this doesnt say anything about the dimensionality of a test, so you don’t know how to interpret the true score from crohnbach’s alpha only
2. Statistics from CTT depend on both the item properties (item difficulty and discrimination) and the properties of the subjects/sample (mean and variance of the true scores)
3. The true score contains irrelevant -but systematic- item specific effects

Question 3

latent variable models’ solutions to CTT problems

Answer 3

1. Latent variable models explicitly model the dimensionality of a test
   > e.g., modeling results will show that the model does not fit data thus dimensions may have to be added/subtracted
2. Latent variable models are falsifiable
   > show when there are no dimensions to data and that only item specific effects are displayed (i.e. latent variable explained variance approaches 0)
3. Item properties and person properties are distinguished in latent variable models (LVMs are not test and sample dependent)
   > test properties are captured in item parameters
   > sample properties are captured in the latent variable
   > this way different tests on the same construct measure the same latent variable
4. Latent variable models explicitly account for item specific error
   > latent variable capture the common variance between items
   > thus item effects are not captured in the LV

Question 4

disadvantages LVMs

Answer 4

1. Require much larger sample sizes
2. Statistically more complex

Question 5

cronbach’s alpha

Answer 5

reliability coefficient

a measure of the proportion of true score variance over the total variance

calculated from a correlation or covariance matrix

lower bound when not essentially tau equivalent

Question 6

cronbach’s alpha assumptions

Answer 6

1. unidimensionality
2. tau equivalence

Question 7

measurement model

Answer 7

describes the relationship between item and construct

contains latent variable parameter and item parameters

Question 8

structural model

Answer 8

describes the relationship between construct and other variables