LCA 2

Question 1

parameter restrictions

Answer 1

1. equality constraints
   > conditional probabilities are equal within classes
2. fixed value constraints
   > conditional probabilities are equal to e.g., .25 wihtin a class (guessing)
3. linear constraints
   > p(correct) of class 1 = 1 - p(correct) of class 2

Question 2

k

Answer 2

classes-1 + #free conditional probabilities

Question 3

classification

Answer 3

posterior probabilities

tells you how likely it is that a person belongs to a certain class

Question 4

LPA identification

Answer 4

scaline the latent variable by fixing the number of classes

Question 5

LPA parameter estimation

Answer 5

ML (EM algorithm)

bayesian estimation

Question 6

calculating values in LPA

Answer 6

multiply the class probability by the distribution for every class and sum these

Question 7

comparing models in LPA

Answer 7

models can be compared in some assumptions are relaxed
> e.g., when relaxing the local independence assumption, the whole covariance matrix will be estimated insead of just the diagonal.

Question 8

differences and similarities between LCA and LPA

Answer 8

The key difference is that in latent profile analysis, the items are continuous, while in a latent class analysis the items are categorical.

The key similarity is that in both type of models, the latent variable is categorical.

Question 9

In a latent profile model, explain how the assumption of local independence is enforced in the model and how this assumption can be relaxed.

Answer 9

In latent profile analysis, local independence is enforced by fixing all the off-diagonal entries of the within-class covariance matrix to 0.

The assumption is relaxed by estimating these within-class covariances