A Simulation Study on Latent Transition Analysis for Examining Profiles and Trajectories in Education: Recommendations for Fit Statistics

Figures & data

Figure 1. Penalty per model parameter that the different fit indices pose on models, depending on sample size.

Table 1. Fit indices were obtained in the study by Flaig et al. (2018).

Number of profiles	Number of parameters	Log-likelihood	AIC	BIC	aBIC	AIC3	CAIC
1	24	−1513	3074	3144	3067	3098	3168
2	25	−1350	2750	2823	2743	2775	2848
3	41	−1278	2638	2758	2627	2679	2799
4	63	−1245	2616	2800	2599	2679	2863
5	91	−1212	2606	2872	2581	2697	2963

Note. The sample size was N = 137. Fit indices are computed based on the number of parameters and log-likelihood values reported by authors.

Figure 2. Four latent profiles are defined by patterns of mean values across three indicator variables.

Figure 3. Simulated transitions between the four profiles across the three measurement points. Note. Thicker lines indicate higher probabilities of transitioning between two profiles between two-time points. The thinnest lines indicate a 5% probability, the thickest line is 95%. Percentages at each time point indicate the resulting percentage of learners showing each profile at the respective measurement point.

Table 2. Overview of simulated scenarios and study conditions within those scenarios.

Standard scenario	Sample sizes	Entropy	Attrition
3 indicator variables, 4 latent profiles	N = 50, 100, 200, 500, 1,000	E = .73, .82, .87	No attrition/10% attrition per wave
Robustness check scenarios	Poor conditions	Moderate conditions	Good conditions
1, 2, or 4-time points, 4 indicator variables, alternative profiles, 3 or 5 latent profiles	N = 200, E = .73, 10% attrition/wave	N = 500, E = .82, 10% attrition/wave	N = 1,000, E = .87, no attrition

Figure 4. Accuracy (proportion of correctly identified models) for the fit indices across all thirty conditions of sample size, entropy, and attrition. Note. A full horizontal line indicates 50% accuracy and dashed lines 33 and 66%.

Figure 5. Propensity to indicate the correct model or under- and overfit for different fit indices across sample sizes. Note. 0-line indicates perfect calibration of the fit index at respective sample size, >0 propensity to overfit, <0 propensity to underfit.

Figure 6. Accuracy of fit indices in the seven robustness check scenarios. Note. A full horizontal line indicates 50% accuracy and dashed lines 33 and 66%.

Table 3. Derived guidelines for fit indices for latent transition analysis.

	Moderate sample (N = 100–200)	Large sample (N = 500–1,000)
Moderate entropy (≤.82)	AIC and aBIC	aBIC and AIC3
High entropy (≥.87)	AIC and aBIC	AIC^a and AIC3

^aUnder attrition, the weight should be shifted more toward the AIC.

Flaig, M., Simonsmeier, B. A., Mayer, A.-K., Rosman, T., Gorges, J., & Schneider, M. (2018). Reprint of “Conceptual change and knowledge integration as learning processes in higher education: A latent transition analysis”. Learning and Individual Differences, 66, 92–104. https://doi.org/10.1016/j.lindif.2018.07.001

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