These models are similar to Item Response Theory models but here we use skill-level parameters in order to predict the probability of answer question correctly. Learning Factory Analysis can be expressed as :

$P(\alpha) = \sigma (\theta + \sum_{j \in skills} (\lambda_j N_j - \beta_j))$

The parameters have the following meanings:

1. $\sigma$ - sigmoid function
2. $\theta$ - student ability
3. $\beta_j$ - item difficulty
4. $N_j$ - number of attempts (input)
5. $\lambda_j$ - learning rate for the skill j

There was an assumption that the focus on the student performance will solve knowledge tracing problem in a better manner than having higher sensitivity for the student ability. This lead to a new model which is called Performance Factory Analysis (PFA):

$P(\alpha) = \sigma (\sum_j \alpha_j S_j + \rho_jF_j - \beta_j))$

The parameters can have the following meanings:

1. $\alpha_jS_j$ + $\rho_jF_j$ - student ability
2. $\alpha_j$ - learning rate for the skill j when it is applied successfully
3. $\rho_j$ - learning rate for the skill j when it is applied unsuccessfully

These models require manual labeling of the skills and cannot deal with inherent dependency among skills.