This study was approached under a mixed methods design. It is assumed that the research processes are complex and, therefore, it implies creativity and innovation in the application of new methodological approaches. In this sense, it is considered pertinent to integrate various types of frameworks. This mixed methods study used both quantitative and qualitative designs. The qualitative design was used to review the literature and explain the perceptions expressed by the respondents. The qualitative design was used to carry out descriptive statistical analysis, correlational analysis, and multivariate analysis.

Additionally, a measurement instrument was created to determine the influence of entrepreneurial resilience on the dimension of entrepreneurship in a learning management model in incubators. In this methodological framework, the phases are as follows:

phase 1

Development of the state of the art that encompasses the updated and significant theoretical foundations of the entrepreneurial resilience factor as a variable in the dimension of entrepreneurship within the framework of a learning management model in incubators. For this, a review of the literature was used from documentary sources structured in formal databases such as Scopus, Web of Science and Science. This analysis allows the authors to identify models, variables, and trends in the research area.

phase 2

Performing a systematic literature review to identify the variables that influence the entrepreneurial resilience factor allows the authors to make the selection and validation of the most pertinent variables across the different publications. In this way, the models, dimensions, factors, and variables were identified, maintaining their relevance to the model under study.

phase 3

Definition of the variables of the entrepreneurial resilience factor as a component in the dimension of entrepreneurship in a learning management model in incubators. The model factor is oriented towards strengthening interpersonal and intrapersonal skills, and perceptions of entrepreneurial intention, through a survey-type instrument.

phase 4

Validation of the instrument through entrepreneurship experts based on a defined evaluation criterion, followed by the completion of a process of collection, organization and systematization of the data obtained from the field work. A probabilistic stratified sample of enterprises in Colombia was used, based on the size of the enterprise and/or microbusiness across economic sectors. The analysis, discussion and triangulation of the data was subsequently carried out through statistical techniques such as multivariate, correlation processes, and descriptive statistics.

A structured survey composed of 68 questions was applied; 13 items corresponded to characterization variables and 55 items to variables of the 9 factors immersed in the learning management model in incubators for entrepreneurs. One of the 9 factors corresponds to the entrepreneurial resilience, the factor which is subject in this research. This factor has 5 variables. The thirteen characterization questions are qualitative and quantitative questions, while the questions on the 9 factors are discrete quantitative.

A pre-validation exercise was conducted, in which 10 individuals with expertise and knowledge in entrepreneurship evaluated the relevance, coherence, and syntax of the survey instrument.

After the pre-validation exercise, 30 professionals from various areas of knowledge with expertise in entrepreneurship were contacted; they completed the survey and reported their observations to refine the instrument. In the validation process, the Cronbach's alpha statistical test was applied, whose index yielded a value of 0.967 and it is shown in Table 1. It indicates that the instrument is reliable to be applied it to the entrepreneurs.

A stratified probabilistic sampling was applied, which involves dividing the microbusiness population into smaller sub-samples known as strata, which are exhibited in Table 2. In this sense, strata were generated. For instance, strata E1 corresponds to the group of one-person microbusinesses; strata E2 corresponds to microbusinesses with 2 to 3 employees; strata E3 corresponds to microbusinesses with 4

Table 1

Cronbach's alpha	Cronbach's alpha based on standardized items	Number of elements
0,964	0,967	55

Source: The authors.

Table 2

Strata	Category	Population	Sample
E1	1	4,560,386	241
E2	2-3	1,041,586	478
E3	4-9	178,650	229
C1	APPCE	2955	61

Source: The authors.

Table 3

Source: The authors.

to 9 employees; and finally, a conglomerate C1 corresponds to a union of ventures in Colombia called Association of SMEs for Electronic Commerce in Colombia (APPCE). A highly representative sample of 1009 entrepreneurs who answered the questionnaire was achieved. Confidence levels of 95% and an error of 5% were established. The sample design based on the variation of the strata makes it possible to address a larger population, giving robustness and representativeness to the analysis.

The collection of data was conducted through a structured survey, selecting the five variables that correspond to the business resilience factor, exhibited in Table 3.

A multivariate analysis method was developed to estimate the underlying unobserved components based on the combined statistical properties of the data sets. These methods include principal component analysis (PCA). PCA is based on statistical analysis that converts multiple indicators into a few unrelated integral indicators, demonstrating most of the information provided by the source indicators, leading to dimensionality reduction.

The goal of temporal PCA is to decompose the observed signal into a set of underlying factors that summarize sampling points with a similar/consistent pattern of activity across participants, electrodes, and conditions. For this study, a 3-level principal component analysis was used using R software due to the nature of the variables.

In Fig. 1, a graph of loads corresponds to the graph of scores observed, in which the variance between the descriptors is represented. The axes of the score plot and the loading plot are the same, therefore, the information in the plots can be directly compared. The angles between the vectors make it possible to determine the correlation between the variables (the correlation corresponds to the cosine of the angle formed between the vectors). When two vectors are close together, making a small angle, the two variables they represent are positively correlated. If they are at 90°, it is a clear indication of non-correlation. When they diverge and form a large angle (close to 180°), they are negatively correlated.

The increase of the descriptors expands as their distance from the origin increases, observing in Fig.1. two different groups. The first group is composed of the variables VF5_5, VF5_2, VF5_3, VF5_1. The second group is composed of the variable VF5_4. It is clearly observed that the variable VF5_4 is not correlated with the variable VF5_1, since the two variables form an angle of 90°. It implies that entrepreneurial training variable is not associated with the variable of responding to complexity situations. It means that unions and academic institutions that support the training in entrepreneurship related activities may have to address the issue with more relevance.

It is observed that VF5_3 has more impact than VF5_2, because it has a greater distance from the point of origin. It means that the ability to adapt to unforeseen circumstances in the venture is associated with the variable to overcome obstacles that the entrepreneur venture faces. In this sense, the ability to adapt helps to overcome obstacles and it increases the entrepreneurial resilience.

Figure 1 Source: The authors.

Table 4

Variable	Contribution	Contribution percentage
VF5_1	0,2127	21%
VF5_2	0,2157	22%
VF5_3	0,2237	22%
VF5_4	0,1461	15%
VF5_5	0,2017	20%

Source: The authors.

The first analysis carried out was to examine whether the case of the PCA captures the differences between the different variables; the results of scores from this analysis are shown in Table 4. For this first level analysis of principal components, it is noted that VF5_1 captures 21% of the contribution, while VF5_2 and VF5_3 capture 22% of the contribution respectively. Moreover, VF5_4 captures 15% of the contribution and finally VF5_5 captures 20% of the contribution. Therefore, a data set of variables (5 initial descriptors in this case) cannot be reduced to a few variables since each of them contributes in a similar way. In other words, entrepreneurial resilience is composed of the 5 variables analyzed; they all constitute this factor, which is the object of the study. Therefore, if any entrepreneur or person wishes to address the issue of entrepreneurial resilience, they must do so using all the aforementioned variables.

Situation that can be demonstrated by observing Fig. 2. (*** indicate significance greater than 5%), where correlations are significant.

Given that the relative impact of each descriptor on a load score is determined by measuring the absolute distance from the origin, eq. (1) is presented below, which allows resilience to be measured based on the variables derived from the analysis:

In Fig. 2., the correlations between the initial variables and the main components of VF5 are presented. It is observed that VF5_4 represents the weakest correlation with respect to the other variables. However, the variable VF5_4 contributes 15% in the principal component analysis, as shown in Table 4, therefore, it should not be excluded. The reason why the

Figure 2 Source: The authors.

variable VF5_4 represents a weak correlation can be explained within the national context. According to the results of the AGER 2015 World Entrepreneurship Report, although 90% of Colombians have a positive attitude towards entrepreneurship, 70% consider that there are no specific institutional supports that favor the development of a social culture of entrepreneurship and innovation (2015). In other words, there is very little training for entrepreneurs.

In Fig. 3., a histogram is observed where the scores obtained for the entrepreneurial resilience factor are evidenced, based on eq. (1). Table 4 lists the main descriptive measures. The histogram shows that entrepreneurial resilience presents a bias to the left with accumulation of values to the right. This indicates that entrepreneurs have high levels of entrepreneurial resilience, and few have low values of this factor, obtaining an average of 8.08.

Figure 3 Source: The authors.

Moreover, the standard deviation returned was 1.3, which is shown in Table 5, thus, according to the dispersion, it can be affirmed that most of the data is concentrated between the values of 6.78 and 9.38; observing that the values are relative. Finally, applying Chebyshev's theorem, it is found that

Table 5

VF5	Average	Deviation standard	Q1	Median	Q3	Min	Max
Values	8,08	1,3	7,42	8,16	8,99	1	10

Source: The authors.

Table 6

Values	Average	Deviation standard	Q1	Median	Q3	Min	Max
VF5_1	7,93	1,51	7	8	9	1	10
VF5_2	8,04	1,5	7	8	9	1	10
VF5_3	8,09	1,51	7	8	9	1	10
VF5_4	7,91	1,93	7	8	9	0	10
VF5_5	8,38	1,51	8	9	10	0	10

Source: The authors.

approximately 68% of entrepreneurs in Colombia are resilient, falling within the aforementioned interval.

Table 6 describes the main descriptive measures obtained for each of the variables that affect the entrepreneurial resilience factor. In general terms, the average obtained is close to a score of 8, where VF5_5 shows the highest average obtained with 8.38, which indicates that Colombian entrepreneurs have great motivations towards the entrepreneurial trend. This highlights their optimism and resilience, despite the precarious conditions in terms of business economic support.

Similarly, the quartile 1 (Q1) obtained for each of the variables shows a score between 7 and 8, which indicates that Colombian entrepreneurs are very resilient towards the entrepreneurial spirit. Finally, the data obtained for the standard deviation shows a dispersion of the data of about 1.5 for the variables, except for VF5_4 which has a standard deviation of 1.93.

The results of the descriptive analysis for each of the variables show a high score. However, the variable VF5_4 represents the greatest dispersion of data; observed in Fig. 3 and Table 6, although this variable represents the least contribution, the correlation index is moderate and therefore it is not excluded from the study.

Similarly, as the first level was developed, the PCA was used to obtain the second level, based on the factors that affect the learning management model in incubators for entrepreneurs.

For this second level analysis through the PCA, the data set was produced by the R software. It reflects that the 3 factors called entrepreneurial motivational demand (VF3), business self-efficacy (VF4) and entrepreneurial resilience (VF5) contribute significantly to the dimension of entrepreneurship (VD2), as presented in Table 7.

Consequently, it is verified that the entrepreneurial resilience interest factor has a significant impact on this dimension, contributing about 33% to the learning management model in incubators. This indicates that 1/3 of entrepreneurship is made up of entrepreneurial resilience, a finding that makes evident the importance of this factor in the development of entrepreneurship.

Therefore, the structural eq. (2) that allows measuring entrepreneurship based on the factors obtained from the analysis is presented below:

Table 7

Factor	Contribution	Contribution percentage
Entrepreneurial motivational requirement	0,3337	33%
Business self-efficacy	0,3411	34%
Entrepreneurial resilience	0,325	33%

Source: The authors.

The PCA for the third level reveals that the component of interest for the entrepreneurship dimension (VD2) captures 35% of the contribution, being a highly relevant percentage. The data set produced by the R software, as can be seen in Table 8, indicates that the 3 dimensions in their order: environment in the incubation process (VD1), entrepreneurial spirit (VD2) and entrepreneurial vocational training (VD3); they contribute significantly to the learning management model in incubators for entrepreneurs (VM1).

Therefore, the structural eq. (3) that allows validating the learning management model in incubators for entrepreneurs is presented below, considering the dimensions obtained from the analysis:

Finally, the entrepreneurial resilience factor contributes 33% to the dimension of entrepreneurship, and this in turn affects the learning management model in incubators for entrepreneurs by 35%. It can be inferred that 12% of this model is being affected by entrepreneurial resilience, which is a great finding because it allows the observation of how this factor belongs to the idiosyncrasies of Colombian entrepreneurs, as can be seen in the Fig.4.

Table 8

Dimension	Contribution	Contribution percentage
Environment in the incubation process	0,3003	30%
Entrepreneurial spirit	0,3479	35%
Entrepreneurial vocational training	0,3517	35%

Source: The authors.

Figure 4 Source: The authors.