Empirical Results & Intervention

1. Characteristics of the Latent Dropout States

The application of the NDLC-SEM allowed for the separation of two discrete latent states,
$s = 1$ (no intention to quit) and $s = 2$ (intention to quit), based on distinct response patterns across seven continuous affective and cognitive scales.

Intention to Quit ($s = 2$) Profile

Students who transitioned to the latent state $s = 2$ exhibited consistently higher values across all seven affective/cognitive scales.
This profile characterizes students with:

• Higher stress levels
• Stronger fear of failure
• Perceived overinvestment of time
• Pronounced negative affective states (PAN)

These patterns clearly align with an emerging intention to quit.

Persistent Dynamics in $s = 2$

The autoregressive coefficients ($\mathbf{B}_{1is}$) were larger under $s = 2$ than under $s = 1$ (except for the “time investment” scale).
This indicates that students intending to quit display stronger, more self-reinforcing autoregressive patterns, suggesting persistent negative feedback loops in affective and cognitive processes.

Role of Cognitive Skills (IQ)

Baseline cognitive ability ($\eta_{2i}$) showed strong predictive power for within-level scales when students were in state $s = 1$.
Higher IQ scores corresponded to lower stress and more stable motivational states.

To reflect the Rubicon model of action, the return probability from the “intention to quit” state back to “no intention to quit” was constrained:

$$P_{12} \sim \text{unif}(0.0, 0.1)$$

The estimated mean value was:

$$P_{12} = 0.097$$

indicating that individuals rarely and only slowly return to the no-intention state once the quitting intention is formed.

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2. Predictive Factors and the Markov Switching Model

The parameters of the Markov switching model identified critical predictors for the transition from $s = 1$ to $s = 2$.

Primary Predictors ($\gamma_3$)

The transition was primarily driven by:

• Negative Affect (PAN)
• Fear of Failure

Thus, the dynamic affective states and expectation of failure are the key determinants of entering the dropout-intention state.

Cross-Level Effects ($\gamma_4$)

The interaction between baseline cognitive skills (IQ, $\eta_{2i}$) and within-level states ($\mathbf{\eta}_{1i,t-1}$) was negligible ($\gamma_4 \approx 0$).
This shows that while IQ stabilizes affect in $s = 1$, it does not directly prevent the switch to $s = 2$, which is primarily emotion-driven.

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3. Establishing the Intervention Window

The most practically relevant finding was the identification of an intervention window that precedes actual dropout by several weeks.

• Critical State Timing:
  The transition to “intention to quit” ($s = 2$) occurred, on average, at

  $$t = 22.2 \; (\text{SD} = 6.5)$$

  corresponding to approximately the 8th week of the semester.

• Actual Dropout Timing:
  Dropout behavior occurred on average at

  $$t = 45.0 \; (\text{SD} = 11.9)$$

  corresponding to the 16th week.

• Lead Time for Intervention:
  The forecasted state switch occurred about 8 weeks before the actual dropout behavior.

• Intervention Implication:
  The period around $t = 22.2$ represents a critical monitoring point for identifying and supporting at-risk students.

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4. Overall Student Status and Forecasting Extent

At the end of the observation period ($t = 50$):

• 36.1% of students had actually dropped out.
• The model classified 73.8% of students as either having dropped out or belonging to the latent class $s = 2$.
• When the forecast was extended by 5 additional time points, the proportion predicted to develop dropout intentions rose to 40.2%, suggesting a continued increase in risk beyond the observed period.

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5. Robustness and Performance (Simulation Study)

A simulation study was conducted to assess the robustness of the FFBS forecasting procedure across varying conditions of sample size ($N_1$) and number of measurement occasions ($N_t$).

Sensitivity

The model achieved high sensitivity (> 0.91) across all conditions.
This means that individuals who switched states were reliably detected — even for forecasted time points.

Specificity

Specificity was lower in the forecast period, ranging between 0.53–0.70, indicating a slight over-prediction of dropout risk (progressive classification).
However, specificity improved significantly when the sample size increased from $N_1 = 25$ to $N_1 = 50$.

Forecast Precision

Forecast precision was strongly dependent on the number of measurement occasions ($N_t$):

• With $N_t = 50$, the model achieved lower quadratic score values ($\delta_h$), indicating higher precision.
• With $N_t = 25$, forecast variance and uncertainty increased.

Forecast Interval Width

Forecast interval (FI) width increased with longer forecasting horizons, forming a megaphone pattern.
However, increasing both $N_t$ and $N_1$ reduced FI width substantially.

Coverage Rates

The 95% forecast interval coverage was slightly below nominal, at 88–90%.
This deviation is attributed to the model’s tendency to over-classify students into the risk state ($s=2$).

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Summary:
The empirical findings from the SAM study confirm the NDLC-SEM + FFBS framework’s ability to:

• Accurately forecast latent psychological state transitions
• Identify precise intervention windows for dropout prevention
• Achieve robust predictive performance across different sampling and time configurations

Together, these results provide a foundation for data-driven, early-warning systems in higher education, capable of detecting and addressing dropout risk dynamically.