Factor analysis-based knowledge tracing models are similar to Item Response Theory (IRT) models, but they use skill-level parameters to predict the probability of a student answering a question correctly.

Learning Factors Analysis (LFA) can be expressed as: $P(\alpha) = \sigma (\theta + \sum_{j \in skills} (\lambda_j N_j - \beta_j))$

The parameters represent:

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 skill $j$

The assumption that focusing on student performance resolves the knowledge tracing problem better than high sensitivity to student ability led to the Performance Factors Analysis (PFA) model: $P(\alpha) = \sigma (\sum_j (\alpha_j S_j + \rho_j F_j) - \beta_j)$

The parameters represent:

1. $\alpha_j S_j + \rho_j F_j$: student ability
2. $\alpha_j$: learning rate for skill $j$ when applied successfully
3. $\rho_j$: learning rate for skill $j$ when applied unsuccessfully

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