Introduction

Seniors graduating from high school seeking the admittance to a Higher Education Institution (HEI's) face a complex decision regarding selecting a bachelor program and the HEI to attend (^{Lei y Chuang, 2010}). Internal and external factors influence this decision (Beggs, Bantham, & Taylor, 2020; ^{Sundarrajh & Zulkfili, 2019}). The internal factors are those that intrinsically have to do with the vocation and interest of the student. In contrast, external factors, are all the elements of the environment that influence their choice of both career and HEI, among which are mentioned: family, friends, educational offer, career duration, safety, costs, professional myths, job opportunities (^{Canals 2013}) (^{Uddin et al., 2018}). Common practice supports this analysis. In high school, counselling offices help the seniors by determining their skills, capabilities, likes and dislikes, handicaps, delineating the admittance profile. In some cases, the process of selecting an HEI includes a search of occupational market demand and projections of income. Other environmental factors include the prestige of the HEI, costs, housing, and distance to home, among other factors.

The factors that influence the selection of the academic program and the HEI significantly impact the dropout of freshman (^{Nieves & Vivas, 2008}; ^{Ruiz, 2018}; Saldaña & Barriga, 2020; ^{Smulders, 2018}; Vergara, 2017). Which is also crucial to HEI's because the student desertion is an indicator of the quality of the HEI's academic program, for which the accreditation boards measure it carefully; then, the HEI's have to commit to its reduction. Accreditation boards also study the trends because they indicate the HEI's improvement efforts. Which explains the need to identify the factors influencing the academic program's selection and knowing those factors and the HEI's can develop measures to increase enrollment and improve education quality.

^{Guijosa (2018)} reports that more than 100,000 high school’s graduates have been surveying to identify these factors, determining the seven key reasons that intervene in the students' decision, being them, affordability, availability of the desired program, reputation of the university / academic quality, job opportunities upon graduation, the value of education for the investment, social pressure (sense of belonging), closeness to home. It is a common marketing practice that on their websites HEI's discuss the relative advantages of their program and the differentiation characteristics for the positioning of their educative offer.

Our affiliation schools are concerned about this issue because their industrial engineering programs are accredited by the corresponding boards and regarded as high-quality programs. We are committed to improving quality, therefore, the objective of this study was to design an instrument for the identification and determination of the relative impact of the factors that influence students' preferences towards the selection of an academic program on campus.

Methodology

The validation of the Measurement Instrument quality -MI (Table 6) is carried out through a three stages process. Stage one is the assessment of the validity of the content (^{Rodríguez et al., 2021}). In step two, an exploratory analysis of the data followed by factor analysis; in step three, the confirmatory factor analysis is performed (^{García et al., 2021}). This section begins with the questionnaire, followed by the sampling process, which precedes the validation, ends with the data analyses.

In step one based on the theory the IM was designed (^{Canals Cifuentes, 2013}; ^{Ruiz Palacios, 2018}; Vergara, 2017), although, given that the problem seems to be highly empirical, the review of literature be simplified, finding a relatively low number of reported factors, specifically sixteen. The complexity resides not on an ample theory, but on the individual impact of the student's preference, which is questioned on the instrument of measure (Appendix 1) and explained by six latent variables, see Table 1.

Regarding the sampling process, the questionnaire is applied for its validation at the Technological Institute of Ciudad Juarez (ITCJ) and at the Technological Institute of Guaymas (ITG), with the non-probability sampling technique known as Convenience Sampling, because of its advantages, lowest time consumption and integration of the sample of suitable elements, the respondents are selected because they are in the right place, at the right time, grouped. But caution must be exercised when interpreting the results (^{Malhotra, 2008}). Confidentiality in the use of the information was guaranteed so that students voluntarily participated and provided reliable data.

The analysis was made with Structural Equation Models (SEM) technique because it is a useful tool when there is a need to use multiple constructs or observed variables to explain interest phenomena since it allows structuring and to analyze more advanced and complex theoretical models. Using specialized software to analyze these models (^{Schumacker & Lomax, 2010}), using the free access software R. The Structural Equiation Modeling method has been applied in several fields in the search for predictors of effectiveness, for example, in organizational resilience (^{Noriega et al., 2019}), competitive intelligence (Poblano et al., 2019), Total Productive Maintenance (^{Hernández et al., 2018}), organizational philosophy (^{Dávila et al., 2017}), between others. For the validation of the MI, a linear model is constructed with six latent factors or variables, which explain sixteen measurable variables or items, as Table 1 presents.

The validation of the questionnaire contents is carried out in two stages, in the first one it is submitted to the validation by a group of four experts with four variables: sufficiency, relevance, clarity and coherence (^{Escobar-Perez and Cuervo Martínez, 2008}), and once their judgment has been made, the degree of agreement between them is established (^{Abdi, 2007}; ^{Kendall & Smith, 1939}) by the Kendall coefficient or the Friedman test for each of the four variables to test following hypotheses:

H₀: There are no significant differences among the experts' responses in the degree of sufficiency of the questionnaire.

H₁: There are significant differences among the experts' responses to the questionnaire's degree of sufficiency.

Regarding the other three variables, relevance, clarity and coherence, analogous hypotheses are established with a significance level of 5% using non-parametric analysis as an alternative to a bidirectional analysis of variance. The analyses were made using the Minitab17 statistical package. Once validated by the experts, the IM was applied to a sample of forty new students from the school.

Next, in stage two, an Exploratory Data Analysis is made, two samples of seventy newly recruited students are taken, one from the ITCJ, representing 30% of the new enrollments population, and the other from the ITG (45% of the target population). They are analyzed independently to determine if they are suitable for factor analysis. The presence of outliers and the correlation of the measurable variables or sampling adequacy are determined individually and in groups. The detection of the values to be considered candidates for outliers is performed by comparing the magnitude of the Malahanobis Distance for each of the sixteen measurable variables, against the critical value corresponding to the Chi-square Distribution with sixteen degrees of freedom with a 0.975 confidence level.

The decision to declare it as an "actual" outlier is made by deleting these records from the database, then the analysis is performed with this reduced database, if the results of this analysis differ from the results obtained with the complete database, then these values are considered outliers. Otherwise, it is declared an extreme value of these values' probability distribution (^{Aldás & Uriel, 2017}). Additionally, these candidates are compared against the aforementioned critical value, but now with a confidence level equal to 0.99, to determine whether these candidate values, -to be declared critical-, fall within the 99% variation range of this random variable corroborate them as extreme data.

Sample size validation, of both databases used in this work, was carried out proposing a null hypothesis and probe using Bartlett's sphericity test with a 5% significance level. This establishes that the matrix correlation of each data base equals the identity matrix. Next, the assumption that the variable correlations are null was done using the KMO (Kaiser Meyer Olkin) Index; finally, the proof that the partial correlations of each variable or item are valid was done using the MSA (Measure of Sampling Adequacy) measure. These analyzes are carried out using the statistical package R.

In stage three, confirmatory factor analysis is performed to test the null hypothesis that the sample covariance variance matrix (for the student samples taken from schools), is equal to the estimated covariance of the proposed model with a significance level equal to 0.05, using the Maximum Likelihood method, for which the Lavaan function of the statistical package R is used. Figure 1 shows graphically the linear model explaining the sixteen items by the six established latent factors or variables. The code can be seen in the questionnaire given in the Appendix.

Source: Self made

Figure 1 Linear Model, Factors and Variable 

The latent factors or variables are the Location (F1), measured with UBO2 and UBO3; Costs (F2), given by EC01, EC02, EC03; Infrastructure (F3), INO1 and INO2; School prestige (F4), measured with IM01, IM02, IM03; Services (F5), measured with SEO1, SEO2 and SEO3; and Others, (F6), EM01, EMO2 and EMO3. The measurement instrument -MI- is validated by analyzing three properties, reasonability, compatibility of the estimated parameters and reliability, as recommended by ^{Aldás & Uriel (2017)}, and validity of the model.

The MI Reasonability is analyzed by testing the null hypothesis previously stated with the chi-square probability distribution with a significance level of 5%, and the chi-square ratio divided by the number of degrees of freedom, also are considered the Mean Root of the Standardized Residuals (SRMR), the Root of the Square of the Error of Approach (RMSEA), the Tucker-Lewis Index (TLI) and the Comparative Adjustment Index (CFI). The estimated parameters can be compatible with those of the statistical model, under the condition that there are no correlations with a value greater than one, that the absolute value of the factorial loads is less than or equal to 1, that the standard errors are not abnormally large, there are no negative estimates of variance and that all estimated parameters are significant. To determine the MI reliability, Cronbach's Alpha coefficient and the compound reliability Index (CR) were used. The validity of the MI is determined by analyzing the validity of the content, as was commented. In contrast, the convergent validity is estimated by the indicator Extracted Average Variance (AVE) and the discriminant validity with confidence intervals to estimate the correlation coefficient with limits of plus or minus twice the standard error.

Results

The group of four experts considered the MI acceptable given levels of sufficiency, relevance, clarity and coherence as Table 2 presents.

The degree of agreement between them is verified by the Friedman test for each of the four items. The results of the verification of the hypotheses are sufficient, relevant, clear and coherent, as presented in Table 2. The p-value for each is greater than 0.05, so there is no enough evidence to reject H₀ for the four items. Therefore, it can be concluded that there is an acceptable agreement between the experts' judgments.

Figure 2 shows the Mahalanobis Distance graph, where values for each of the 70 data that correspond to the sample of the students from one of the schools -ITCJ. With a confidence of 97.5%, that none of these values, it is an outlier.

Soruce: Self made

Figure 2 Mahalanobis Squared Distances - ITCJ 

Figure 3 shows the Mahalanobis Distances graph for the 70 values that correspond to the sample of students at the other school - ITG, where it can be observed, there is only one outlier, considering a 97.5% confidence. This value is removed from the original database and the corresponding analysis is performed for the original database and the reduced database when comparing their results, no differences higher than two tenths in the values are observed, so the presumed outlier is regarded as an extreme data, so the original database is preserved for the next steps or stages. The Mahalanobis distance value corresponding to this point does not exceed the critical value of a 99% significance level, which reinforces the assumption that this is an extreme value that does belong to this probability distribution.

Source: Self made

Figure 3 Mahalanobis Squared Distances - ITG 

Table 3 shows the mean KMO values (Kaiser Meyer Olkin test). The Bartlett's sphericity test results for the data of the two samples of size 70 of newcomers from the two schools - ITCJ and ITG (Table 7 & 8 of appendix 2). It can be seen that the data of both samples are adequate, since the KMO value, in both cases, is greater than 0.70, and also, that there is the necessary correlation between the variables to perform a Factor Analysis, given that the p-value of the Bartlett Sphericity test is less than 0.05, ^{Levy et al. (2003)}.

The confirmatory factor analysis results are carried out with the Lavaan function of the R software; for the data corresponding to the samples of 70 students are shown in Table 4 -5. The comments made on the values of the indicators include both the results observed in the schools. The chi-square test does not show sufficient evidence to establish a significance level of 5%, as valid the equality between the variance-covariance matrix of the sample with the variance-covariance matrix of the model. However, the chi-square statistic value divided by the number of degrees of freedom is equal to 1,378 and 1,299 to both samples, and they are below the critical value for this criterion.

In Table 4 the values of the CFI, TLI, RMSEA, SRMR indicators meet the established criteria, along with the fact that there are no correlations greater than one, there are no absolute values of the factor loads greater than one, and all are significant. Regarding the regression coefficients, there are no variances with negative values. Therefore, it is concluded that MI is reasonable and that the estimated parameters are compatible with the theoretical model. Also, the MI is reliable, since the Cronbach coefficient values and the values of compound reliability exceed the critical values established. The model is regarded as valid, given the convergent and discriminant validities (Table 5).

Therefore, it is concluded that MI is reasonable and that the estimated parameters are compatible with the theoretical model. Also, the MI is reliable, since the Cronbach coefficient values and the values of compound reliability exceed the critical values established. The model is regarded as valid given the convergent and discriminant validities.

Conclusions and Recommendations

With the results obtained, the objective proposed in this study was reached, so an MI was designed and validated with the factors that influence Mid-High school graduates in the selection of an academic program at the undergraduate level. The identified factors are 5 and are composed of 16 variables, being the factors that influence the selection of the school are 1) Location, 2) Costs, 3) Infrastructure, 4) Prestige of the school and 5) Services. These factors were extracted from a review of the literature and validated from the opinion of experts on the subject, based on the hypothesis raised.

The statistical analysis shows that there is no significant difference between the opinion of the experts regarding the factors studied, therefore, the null hypothesis is not rejected, this means that the factors are precise and can be used to determine which ones affect specific programs.

The results of the confirmatory factor analysis - CFA allow us to conclude that the measurement instrument is valid, adequate to collect the necessary data for the construction of a model of structural equations, according to the set of latent and explained measurable variables.

The next step in the research is to aply the measurement instrument to build the structural equation model that identifies the relative weights of the most critical factors for the selection of the TecNM Campus (Cd. Juarez and / or Guaymas), so that the Principal Authority can develop measures to increase enrollment as well as build the structural equation model with a larger sample size.