*3.2. Discriminant Model Building*

Discriminant analysis model among universities was carried out. As predictors, 23 RC variables were used. The eight significant variables, which showed a *p*-value < 0.05, were selected for the construction of the discriminant model: Three related to the communication and five to the relationship dimension (Table 5). Accurate communication with administrative officers and lecturers, shared knowledge and mutual respect with classmates; and shared objectives with the representatives of the students belonged to the discriminant model. Additionally, shared goals with lectures and administrative officers, and the communication for solving problems among classmates were the variables with the three highest discriminant powers, showing a higher F-remove coefficient.


**Table 5.** Discriminant function for the organizational variables of three universities (ARCADA, UCO and ESPAM).

\* *p*-value < 0.05; \*\*\* *p*-value < 0.001.

The classification matrix offered a correct ascription percentage of 69.32, obtaining assignment errors only in ESPAM (data not presented). The organizational differences of the three analyzed universities are shown in Figures 2 and 3. In the first one, in which the Mahalanobis distances obtained from the relational coordination indicators were graphically represented, a first cluster grouped ARCADA and ESPAM University and second cluster made up UCO. The students from UCO showed greater separation, and, therefore, greater relational coordination differentiation, due to its lower RC rating. The existence of different relational models for each university were observed in Figure 3, which showed a spatial distribution of each university with overlap of some individuals of ARCADA and ESPAM, but strong distance from UCO showed a clear differentiation.

**Figure 2.** Cluster from Mahalanobis distances for three universities.

**Figure 3.** Plot of the individual observation discriminant scores obtained with the canonical discriminant function for three universities.

#### **4. Discussion**

The relational coordination framework provides an excellent basis for investigating the types of organizational models at universities [7,16,17,47]. According to [47], higher levels of relational coordination improve results. RC model can be useful to achieve excellent results in higher education where high levels of task interdependence, uncertainty, time restrictions and tacit knowledge are required [7]. In the case of higher education, it is important to identify best organizational practices to apply at universities, as well as the differences among universities, which contribute to the global knowledge of the importance of RC on the results of the organization [16,20]. The methodology developed in this research has allowed, in a first step, identifying the relational coordination variables that promote differences among universities and satisfaction levels. In a second stage, according to Addi-Raccah and Gavish [25], Lee and Yu [26] and Noël et al. [27], a canonical discriminant function for the ARCADA, UCO and ESPAM universities, in three countries and very different socioeconomics contexts has been built.

RQ1 was not validated in this study. According to De-Pablos-Heredero et al. [19], an improvement in organizational practices leads to an improvement in results regardless of the socioeconomic context.

RQ2 was validated, finding a positive relationship between RC and student satisfaction level. In the three universities there is a positive effect between RC and satisfaction. This link is more prominent in the case of ESPAM (Figure 1). In ESPAM, with high levels of RC, the highest values of satisfaction have been obtained. In ESPAM, which is a small size public university in a developing country with low economic growth, the level of satisfaction is very sensitive to the modifications in RC in the administrative officers profile [7]. According to the Pisa-D report [34] Ecuador requires an improvement in digital literacy, so there is a greater dependence on administrative officers [7]. Therefore, the different social contexts could explain part of the differences in organizational patterns [28].

Accurate and solving problem communication, mutual respect and shared knowledge and goals are strategic factors to improve de RC. The results obtained show that the personalized service to the student is positively valued by considering individual circumstances. Gallego et al. [16,17] and Margalina et al. [7] proofed how in universities with high quality levels, the institutional coordination with students was stronger. Havens et al. [15] and Haider et al. [13] paid attention to the similarities between teamwork quality and RC. Lacayo-Mendoza and De-Pablos-Heredero [48] indicated that the majority of students highly value the facilities provided by educational staff. Finally, results show that other outstanding attributes are shared goals with students' representatives and with administrative officers. Gallego et al. [16,17] and Margalina et al. [7] concluded how in universities exhibiting high quality levels, the institutional coordination with students is strong.

The construction of a discriminant model verified RQ3. Knowing the variables with the greatest discriminant power, it is possible to propose concrete, simple and economic measures to improve educational quality. The results of this research allow establishing the organizational differentiation among three Universities though discriminant analysis. Shared goals, with lectures and administrative officers, and the communication for solving problems among classmates were the variables with the highest discriminant power. UCO was the most differentiated university according to RC (Figures 2 and 3). This differentiation explains the fact that it is the highest ranked university in the world ranking of universities (Table 1).

Three different universities could be discriminated by the organizational model generated. Shared goals are a key piece for university excellence [17], therefore measures that allow sharing the objectives of the students with lectures and administrative officers are crucial. In order to enhance this, improvements are proposed in digital literacy for communication with administrative officers [7] and changes in the teaching guides, where the lectures establish specific objectives for the students in each subject, are welcomed. Solving problem communication shows that the students use the educational ecosystem in moments of lack of information [16,17]. This way, the creation of direct communication mechanisms among students and other profiles is proposed to solve the problems of university life.

Apart from this, it would be of great interest to develop prediction models for each set of organizational variables over satisfaction. This issue could be developed in future research lines by applying structural equation models. This approach could be extended to different universities and contexts.

#### **5. Conclusions**

This research contributes to a novel approach since it allows identifying the organizational differences among three universities with different socioeconomic contexts.

In each university, as the relational coordination dimensions are improved, the level of satisfaction increases. However, an association among universities located in countries with a higher level of economic resources and a higher level of relational coordination, has not been verified. Those universities that implement a program of best practices in relational coordination will achieve higher levels of quality in terms of student satisfaction, regardless the socioeconomic context.

The canonical discriminant model built according to the relational coordination dimensions showed that three organizational variables were enough to explain differences among universities. These variables were shared goals, with lectures and administrative officers, and the communication oriented to solve problems among classmates. Therefore, the discriminant analysis is useful for designing the improvement of the relational practices in each university.

The proposed model can easily be adapted and applied to different contexts and, therefore, they can be of great interest for the improvement of quality at universities. The results were validated but are conditioned in each university by its standard of satisfaction values. **Supplementary Materials:** The following are available online at https://www.mdpi.com/article/10 .3390/educsci11080445/s1, Figure S1: Statistical parameters of the student satisfaction value, Table S1: Relational coordination survey.

**Author Contributions:** Conceptualization and methodology, all authors. Formal analysis, software, data curation, data processing, A.L.C.; statistical analysis, C.C.-M. and S.H.; validation and investigation, C.D.-P.-H. and A.G.; supervision, A.G., C.D.-P.-H. and C.C.-M.; project administration, C.D.-P.-H. and A.G.; data acquisition, A.L.C. and A.G. All authors have been involved in developing, writing, commenting, editing and reviewing the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Data Availability Statement:** This is not applicable as the data are not in any data repository of public access, however if editorial committee needs access, we will happily provide them, please use this email: pa1gamaa@uco.es.

**Acknowledgments:** We want to thank the RED-RC, the open research and innovation network for the improvement in higher education among Quevedo State Technical University (Ecuador), University of Cordoba (Spain) and Agricultural Polytechnic of Manabi "MFL" (Ecuador). The authors are thankful for the funding provided to the research project by the competitive scientific and technological research funds of Agricultural Polytechnic of Manabi "MFL" (Ecuador).

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

