LCA

Question 1

latent classes

Answer 1

categories of theta

within each class, items are independent (local independence)

Question 2

goal

Answer 2

classify subjects to the latent classes on the basis of observed item scores

Question 3

conditional probabilities

Answer 3

single points, since theta is categorical

Question 4

maximum likelihood

Answer 4

1. expectation maximization algorithm
   E-step:
   > determine expected values of the latent classes given some initial values for the other parameters
   M-step:
   > maximize the likelihood using these expected values to obtain new values for the other parameters
   - iterate between these steps
2. newton-raphson algorithm
   > approximates the log-likelihood function locally, using linear functions to find firections towards the maximum

Question 5

identification

Answer 5

1. scaling the LV
   > the LV has a scale that is defined by the number of categories
2. statistical identification
   > k should not exceed M
   > this can happen if you have too few observed variables in your model
   > k = #cond.probs + #class.probs-1

Question 6

model fit

Answer 6

absolute fit measures
1. expected number of subjects
> overall.prob * N
2. goodness of fit
> pearson X^2, G^2

comparative fit measures
> likelihood ratio, AIC, BIC

Question 7

X2

Answer 7

should decrease as model complexity increases