A logistic regression model was performed to identify the association between factors and AP. This model allowed calculating Odds Ratio (OR) for each variable according to low AP.

The model's predictive quality was evaluated using the goodness-of-fit criteria and area under the curve (AUC) based on sensitivity and specificity. The model was set with 2/3 of the data and the remaining 1/3 for validation.

In the logistic model, the dependent variable Yi (defined as the event that a student has low AP) is calculated according to expression (1):

Where:

Πi: is the probability that student i will experience low academic performance, and it is the value of the dependent variable in case i for the regression coefficients 𝛼 and β.

Expressed as regression, the logistic model can be represented as:

The risk ratio OR indicate the probability that a student has low AP concerning one who has normal AP according to the value assumed by the independent variable 𝑋𝑖. This value constitutes a level of the relative effect of each variable in AP. According to this, the OR can be estimated from the logistic regression model as follows:

For logistic regression, all hypotheses were tested with a significance of 0.05.

We hypothesized that variables associated with sociodemographic, pedagogical, institutional, and past academic performance were included as risk variables and are significantly correlated with AP according to the Saber-Pro test.

Considering the mean score of high-quality accredited universities in Colombia, 46 (59.74%) were in low AP, and the remaining 31 (40.26%) obtained normal AP.

A descriptive analysis is reported from pedagogical (Tables 1 and 2), institutional (Table 3), and sociodemographic factors (Table 4). Statistical differences were tested with low AP according to the Hosmer-Lemeshow methodology, where variables with a p-value < .25 or less are considered significant [33].

Pedagogical variables associated with low AP are if chair professors directed courses (p<.001), older (p=.045), paid less for their work (p=.002), without a master's degree (p=.23), and with low scores in didactics (p=.17). Students with low scores in subjects of quantitative reasoning (QR), English (EN), critical reading (CR), citizen comprehension (CC) and written communication (WC) (p<.001) were associated with low AP (Table 1 and 2). These variables were selected to be included in the multivariate logistic regression model.

Table 1

Source: own

Table 2

*,** and *** indicates statistical differences with .05, .02 y >.01 of significance.

According to institutional factors, variables associated with low AP were student has not had any subsidy (p<.01), has enrolled in few concurrent subjects/semester (p<.01), has obtained low partial (p<.01), and final grades (p<.01). Student who has high repetition rate (p<.01), has been in an advanced semester at the time of presenting Saber-Pro (p=.18) and has had a lower number of subject approval (p<.01) has been associated with low AP (Table 3).

In the sociodemographic factor, the female sex (p=.02) comes from rural and foreign regions (p<.01), enrolled in industrial engineering (p=.02), and being older (p<.01) are variables associated with low AP. Critical remarks suggest high student competencies in CC, WC, CR, and QR acquired during their student trajectory increment AP. According to Saber-Pro, students with poor subject results are likelier to have low AP (Table 4).

Table 3

Institutional factors
Variable	Professor Contract			Test
	Low AP	Normal AP	Sig.	Test
Have a subsidie	53,41%	46.59%	>0.01**	Chi-2
Not have a subsidy	63.60%	36.40%
Concurrent subject/semester (Me ± DAM)	5 ± 1	5 ± 1	0.061	Kruskal-Wallis
Cancelation subject/semester (Me ± DAM)	1 ± 1	1 ± 0	>0.01**	Kruskal-Wallis
Midterm exam scores (Me ± DAM)	3.7 ± 0.7	4 ± 0.6	>0.01**	Kruskal-Wallis
Follow-up score (Me ± DAM)	4.2 ± 0.4	4.2 ± 0.3	>0.01**	Kruskal-Wallis
Final exam score (Me ± DAM)	3.8 ± 0.8	4 ± 0.7	>0.01**	Kruskal-Wallis
Repetition rate (Me ± DAM)	1 ± 0	1 ± 0	0.029**	Kruskal-Wallis
Level or semester	9 ± 1	9 ± 0	0.18	Kruskal-Wallis
Credits per semester (Me ± DAM)	10 ± 3	10 ± 3	0.27	Kruskal-Wallis
Approval credits per semester (Me ± DAM)	9.5 ± 3.5	9 ± 3	0.41	Kruskal-Wallis
Average semester grades (x̄ ± Sd)	4 ± 0.52	4.232 ± 0.47	0.048**	ANOVA
Accumulated average grades (Me ± DAM)	3.8 ± 0.2	3.9 ± 0.1	0.027**	Kruskal-Wallis
Approved subject per semester (Me ± DAM)	4 ±1	5 ± 1	>0.01**	Kruskal-Wallis

*,** and *** indicates statistical differences with .05, .02 y >.01 of significance.

Table 4

Sociodemographics factors
Variable	Professor Contract		Test
	Low AP	Normal AP	Sig.	Test
Female	68.50%	31.50%	0.02	Chi-2
Male	57.80%	42.20%
Public School	59.90%	40.10%	0.47	Chi-2
Private School	63.00%	37.00%
From metropolitan Region	65.70%	34.30%	>0.01	Chi-2
From rural nearest areas	69.30%	30.70%
From colombian foreign regions	100%	0%
From nearest big metropoli - Medellin	31.10%	68.90%
Study environmental engineering	59.20%	40.80%	0.02	Chi-2
Study computer engineering	45.20%	54.80%
Study industrial engineering	78.40%	21.60%
Electronics engineerings	30.90%	69.10%
Age (Me ± DAM)	22 ± 4.45	21 ± 2.97	>0.01	Kruskall-Wallis

*,** and *** indicates statistical differences with .05, .02 y >.01 of significance.

Figs. 1 - 3 show a discriminant analysis for pedagogical, institutional, and sociodemographic factors. This analysis allows us to determine which variables significantly classify between low and average AP. These models also explain 100% of the variance in their first dimension.

Canonical discriminant analysis in pedagogical factors identifies 56.71% of students with low or average (Normal) AP (Fig. 1). Variables that best discriminate against low AP were if the professor had no full-time contract (Prof.Vinculate). This result could be associated with their limited time to accompany students during extracurricular hours. Another variable that favors low AP is the professor's age (Prof.Age): older had more students with low AP. These results suggest that teaching methodologies must be updated to new disciplinary trends that older teachers did not incorporate. Another consideration is that older teachers must be more empathic with their younger students.

Nevertheless, variables that favor average AP in pedagogical factors (Fig.1) are high professor salary, high overall professor qualification, and high grades in pedagogy and didactics. According to students, good grades in a subject associated with writing communication (WC) and quantitative reasoning (QR) favored average AP. These results suggest that competencies of WC and QR acquired during student trajectory could be decisive in improving AP. A high professor's salary could be associated with motivation and responsibility, and students recognize the effort and competence of an excellent professor to give them good qualifications [34].

Canonical discriminant in sociodemographic factors was able to identify 65.34% of students with low AP. According to Fig. 3, students from rural regions, being females, studying industrial engineering and older, are associated with low AP in engineering. These results suggest reviewing industrial engineering curricula, competencies, and teaching support is a strategy to improve AP in this specific program. Finally, older working students, have families, and have less time for their academic activities could be associated with low AP [35].

The canonical discriminant model of institutional factor allows for identifying the 57.48% of students with low and normal (Normal) AP (Fig. 2). In accordance, institutional variables like have not a subsidy, repetition rate, and low accumulated, midterm, final, and follow-up grades are associated with low AP. The number of concurrent subjects and credits enrolled per semester (Credits and Concurrent. Subj) and if they had in a lower semester when students present Saber Pro were associated with low AP. This result suggests that providing economic or subsidy support could be an effective strategy to improve in a meaningful manner AP. Maintaining and promoting subsidies implies they make extraordinary efforts to have a good AP in their student trajectory. In the same way, low AP is also associated with high grades in university. According to Saber Pro, these results suggest that better performance in student trajectory is associated with good AP.

Figure 1 Source: own

Figure 2 Source: own

Based on logistic regression performed as multivariate analysis and Hosmer-Lemeshow criteria using a stepwise methodology, it was possible to select those variables that best explain low AP and risk association Odds Ratio (OR) (Table 5). OR establishes a proportional relationship of the variable with AP; that is, if for females, the adjusted OR (adj.OR) obtained is 1.3, this implies that women present 1.3 times more feasibility of having low AP than men. In consequence, the female will be a risk variable. On the other hand, if the adj.OR is less than 1, the variable could be considered protective.

Figure 3: Source: own

The logistic regression in Table 5 allows correctly classifying 73.56% of students. In addition, this model identifies 82.49% with low and 61.20% of normal AP by cross-validation. According to this, the model performs well in explaining variables affecting AP according to Saber Pro for a cut-off probability of 0.5.

Regarding pedagogical factor, the variable that most affects AP is professor degree: professors with master's and specialization have students with better AP in Saber-Pro (adj.OR 0.59 [ 0.38,0.92]) and (adj.OR 0.63 [0.4,0.99]) respectively, compared with professional (adj. OR 0.56 [0.33,0.95]) and Ph.D. which was the reference category. These results suggest that the investment made by professors and universities in postgraduate training contributes significantly to improve AP.

Logistic regression also presented risk variables considering the institutional factor (Table 4). It was observed that having a subsidy (adj.OR 0.53 [0.43,0.65]), a high ratio of approved credits per semester (adj.OR 0.43 [0.2,0.94]), good grades in subjects related to critical reading at university trajectory (adj.OR 0.43 [0.2,0.94]), good grades in midterm (adj.OR 0.86 [0.77,0.96]) and final exams (adj.OR 0.99 [0.81,0.99]) becomes protectives factor. On the other hand, a student who was at a high level or semester when presenting Saber Pro was considered at risk of low AP (OR 1.51 [0.95, 2.42]).

According to Saber-Pro, this result suggests that good performance in the university training trajectory guarantees average AP. In the sociodemographic factor, males (adj.OR 0.75 [0.59,0.95]) who had been enrolled in computer engineering (adj.OR 0.51 [0.4,0.67]) were considered protective. Older age at the moment of presenting Saber Pro (adj.OR 1.03 [1.00,1.06]), comes from a rural region (adj.OR 3.13 [1.88,5.21]), had graduated from a public high school (adj.OR 1.42 [1.09,1.84]), and had been enrolled in industrial engineering program (adj.OR 2.92 [2.35,3.65]) were risk factors of low AP according to logistic regression.

Table 5

Factor	Variable	Adj. OR	p	Variable description
		95% CI in parenthesis
Pedagogical	Professor professional - PhD	0.56	.032	Protector
		(0.33, 0.95)
	Professor specialization - PhD	0.63	.044	Protector
		(0.4, 0.99)
	Professor master´s degree - PhD	0.59	.02	Protector
		(0.38, 0.92)
	Professor salary	1	< .001	-----
		(1, 1)
Institutional	Have subsidy	0.53	< .001	Protector
		(0.43, 0.65)
	Good grades in Critical Reading (CR)	0.43	.033	Protector
		(0.2, 0.94)
	Good grades in Midterm Exams	0.86	.007	Protector
		(0.77, 0.96)
	Good grades in the Final Exam	0.9	.041	Protector
		(0.81, 1)
	Be in High level or semester	1.51	.088	Risk
		(0.94, 2.42)
Sociodemographic	Male - Women	0.75	.016	Protector
		(0.59, 0.95)
	Student age	1.03	.081	Risk
		(1, 1.06)
	Metropolitan region - Medellin	1.73	< .001	Risk
		(1.29, 2.33)
	Rural nearest area - Medellin	3.13	< .001	Risk
		(1.88, 5.21)
	Public - private school	1.42	.009	Risk
		(1.09, 1.84)
	Computer eng. - Environment eng.	0.51	< .001	Protector
		(0.4, 0.67)
	Industrial eng. - Environment eng.	2.92	< .001	Risk
(2.35, 3.65)

Source: own

Figure 4 Source: own

Finally, the Area Under Curve (AUC) of the Receiver Operating Characteristic (ROC) (Fig. 4) was 0.739, which establishes that this model is only for explanation, and it is not possible to make accurate predictions. It is necessary to make modifications and adjust the model with variables that provide a complement to obtain an adequate ROC. Cognitive and non-cognitive variables in psychosocial factors could be considered.