ABSTRACT
Objective: The objective of this research was to compare the results of structural equation models with latent variables (SEM) using the covariance-based maximum likelihood method, employing two different software applications for this purpose (Amos and R Studio Lavaan).
Theoretical Framework: This article presents the main concepts and theories underlying this research, addressing the use of SEM in organizational climate analysis and its importance in the educational context to evaluate key constructs in institutional dynamics.
Method: The constructs were derived from an organizational climate evaluation of a higher education institution in Mexico. The "Organizational Climate Inventory" was applied, selecting five subscales: Satisfaction, Pride and Belonging, Clarity of Goals and Objectives, Collaborative Work, and Efficiency and Effectiveness. Administrative, managerial, academic, and service staff were invited to participate, achieving a sample of n = 801.
Results and Discussion: The results from Amos vs. R Studio Lavaan confirmed that there were no significant differences between the SEMs regarding paths, standardized regression coefficients, R2, goodness-of-fit indices, and correlation coefficients. Efficiency and Effectiveness (83.0%) was explained by the influence of Clarity of Goals and Objectives (0.11), Satisfaction (0.26), Collaborative Work (0.31), and Pride and Belonging (0.37) based on standardized regression coefficients. Collaborative Work (52.0%) was explained by the influence of Clarity of Goals and Objectives (0.49) and Pride and Belonging (0.29). The instrument demonstrated reliability levels above 0.70, as well as convergent validity greater than 0.50 and discriminant validity above 0.70 across all subscales.
Research Implications: Theoretical and practical implications of this study highlight the feasibility of using free software for SEM analysis, offering institutions an efficient and accessible alternative.
Originality/Value: This Study Contributes to the Literature by Validating the Use of Free Software as An Effective and Accurate Tool for Structural Analysis in Educational Contexts Without Additional Costs.
Keywords: Organizational Climate, Structural Equation Models, Software Application, Work Satisfaction
RESUMO
Objetivo: O objetivo desta pesquisa foi comparar os resultados de modelos de equações estruturais com variáveis latentes (MEE) utilizando o método de máxima verossimilhança por covariância, empregando para isso duas aplicações de software diferentes (Amos e R Studio Lavaan).
Referencial Teórico: Este artigo apresenta os principais conceitos e teorias que sustentam esta pesquisa, abordando o uso de MEE na análise do clima organizacional e sua importância no contexto educacional para avaliar construtos-chave da dinâmica institucional.
Método: Os construtos foram derivados de uma avaliação de clima organizacional em uma instituição de ensino superior no México. Foi aplicado o "Inventário de Clima Organizacional", selecionando-se cinco subescalas: Satisfação, Orgulho e Pertencimento, Clareza de Metas e Objetivos, Trabalho Colaborativo e Eficiência e Eficácia. Convidou-se a participar, de forma voluntária, o pessoal administrativo, diretivo, acadêmico e de serviços, resultando em uma amostra de n = 801.
Resultados e Discussão: Os resultados do Amos e do R Studio Lavaan confirmaram que não houve diferenças significativas entre os modelos SEM em termos de trajetórias, coeficientes de regressão padronizados, R2, índices de qualidade de ajuste e coeficientes de correlação. A Eficiência e Eficácia (83,0%) foi explicada pela influência de Clareza de Metas e Objetivos (0,11), Satisfação (0,26), Trabalho Colaborativo (0,31) e Orgulho e Pertencimento (0,37), com base nos coeficientes de regressão padronizados. O Trabalho Colaborativo (52,0%) foi explicado pela Clareza de Metas e Objetivos (0,49) e pelo Orgulho e Pertencimento (0,29). O instrumento demonstrou níveis de confiabilidade acima de 0,70, bem como validade convergente superior a 0,50 e validade discriminante superior a 0,70 em todas as subescalas.
Implicações da Pesquisa: As implicações teóricas e práticas deste estudo destacam a viabilidade do software livre para análise de MEE, oferecendo às instituições uma alternativa eficiente e acessível.
Originalidade/Valor: Este estudo contribui para a literatura ao validar o uso de software livre como uma ferramenta eficaz e precisa para análise estrutural em contextos educacionais, sem custos adicionais.
Palavras-chave: Clima Organizacional, Modelos de Equações Estruturais, Aplicação de Software.
RESUMEN
Objetivo: El objetivo de la investigación consistió en comparar los resultados de modelos de ecuaciones estructurales con variables latentes (MEE) bajo el método de máxima verosimilitud de covarianza empleando para tal efecto dos aplicaciones informáticas diferentes (Amos y R Studio Lavaan).
Marco Teórico: En este artículo se presentan los principales conceptos y teorías que sustentan esta investigación, abordando el uso de MEE en el análisis de clima organizacional y su importancia en el contexto educativo para evaluar constructos clave de la dinámica institucional.
Método: Los constructos se tomaron de una evaluación de clima organizacional de una institución de educación superior en la República Mexicana. Se aplicó el "Inventario de clima organizacional" y se seleccionaron 5 Subescalas: Satisfacción, Orgullo y pertenencia, Calidad de metas y objetivos, Trabajo colaborativo, así como Eficacia y eficiencia. Se invitó a participar libremente a personal administrativo, directivo, académico y de servicio; logrando aplicar a una muestra n = 801.
Resultados y Discusión: Los resultados de los programas Amos vs R Studio Lavaan confirmaron que no existen diferencias importantes entre los SEM en lo que respecta a las trayectorias, los coeficientes de regresión estandarizados, las R2, los índices de bondad de ajuste y los coeficientes de correlación. El 83.0% de la Eficacia y eficiencia se explica por la influencia de la Claridad de metas y objetivos (0.11), la Satisfacción (0.26), el Trabajo colaborativo (0.31) y el Orgullo y pertenencia (0.37) a partir de sus coeficientes de regresión estandarizados. El 52.0% del Trabajo colaborativo se explica por la influencia de la Claridad de metas y objetivos (0.49), así como el Orgullo y pertenencia (0.29). El instrumento mostró niveles de confiabilidad superiores a 0.70, así como también de validez convergente mayor a 0.50 y discriminante por arriba de 0.70 en todas las subescalas del instrumento.
Implicaciones de la Investigación: Las implicaciones teóricas y prácticas de este estudio resaltan la viabilidad del software libre para el análisis de MEE, proporcionando a las instituciones una alternativa eficiente y accesible.
Originalidad/Valor: Este estudio contribuye a la literatura al validar el uso de software libre como herramienta efectiva y precisa para el análisis estructural en contextos educativos sin costos adicionales.
Palabras clave: Clima Organizacional, Modelos de Ecuaciones Estructurales, Aplicación Informática, Satisfacción Laboral.
1 INTRODUCTION
The use of Structural Equation Models (SEMs) as a method for measuring and analyzing relationships between latent variables began to develop in the early 20th century, following the pioneering work of the geneticist Sewall Wright, who introduced the trajectory model in his 1916 study to describe the genetic influence between individuals of the same litter in experiments with guinea pigs and rats (Wright, 1916). According to Manzano-Patiño (2017), between the 1940s and 1970s there was a significant advance in the analysis of trajectories, laying the foundations for the current MEEs. At this stage, Lawley's (1940) contributions were crucial, especially his study of estimating load factors by the maximum likelihood method, which would later inspire the Swedish statistician Karl Jöreskog. From this influence, Jöreskog developed the confirmatory factor analysis model (Jöreskog, 1969) and subsequently, together with Sörbom, designed the first structural analysis software based on covariance, the well-known LISREL (Jöreskog and Sörbom, 1973).
Over time, other programs for structural analysis emerged, such as EQS (Bentler, 2006; Bentler & Wu, 2002), AMOS, developed for the Analysis of Moment Structures (Arbuckle, 2003), and STATA. These programs, although advanced and precise, require a paid license whose cost can range from $99 to $370 per year, which can represent a significant economic barrier for researchers or institutions with limited resources (Schumacker & Lomax, 2016). Alternatives such as SmartPLS, based on the partial least squares (PLS) method, also require licenses with similar costs (Hair et al., 2020).
On the other hand, the emergence of free software such as R and the Lavaan package (Rosseel, 2012) has revolutionized access to MEE techniques. Lavaan allows analysis by both the covariance method and least squares and has gained popularity in the last decade for being free, open source, and for its ability to adapt to various operating systems. However, its use requires knowledge in advanced programming and statistics, which can be a challenge for some users (Flora et al., 2021). Despite these difficulties, recent research has shown that the results obtained with Lavaan are statistically equivalent to those generated by commercial software such as AMOS in terms of regression coefficients, goodness of fit and R2, among other indices (Rhemtulla et al., 2020; Green, 2019).
This study addresses a research gap by comparing the performance of AMOS and R Studio Lavaan in an analysis of organizational climate in a higher education institution in Mexico, assessing whether free software can offer comparable results to a commercial one in estimating structural relationships between latent variables. The key question of the research is whether free software, with the right tools and capabilities, can match the efficiency of paid programs in obtaining statistically valid, accurate, and replicable results, as suggested by recent studies (Rosseel et al., 2020; Rhemtulla et al., 2020).
The manuscript is structured in several sections, each dedicated to exploring in detail the use and comparison of commercial and free software for the analysis of Structural Equation Models (SEM), as well as the specific context of the research and the relevant variables for the study of the organizational climate in an educational institution. The introduction also describes research gaps, noting that although there are studies on the effectiveness of paid programs such as AMOS and free as R, there is a lack of research that directly compares the results obtained by both types of software in a specific context of the organizational climate. Subsequently, the methodology details the procedures followed for the collection and analysis of the data, describing the sample used and the measurement instruments, as well as the structural analysis performed. Later, in the results, a comparative analysis with the results of both programs is presented, comparing the goodness of adjustment, standardized regression coefficients and R2 indices and correlations. Finally, the discussion and conclusions interpret the results and explore the implications for researchers and professionals, as well as the limitations, opportunities for future research and contrast with previous studies.
Based on this problem, the following research question arises: Are the results obtained using open access MEEs such as R Studio Lavaan similar and as reliable as those obtained in quota software such as AMOS for covariance-based MEE models? Taking as a reference the problem and the question of research, the following objective of study is raised: Compare the results of the analysis of ESM with latent variables under the method of maximum likelihood of covariance in two types of computer program, being Amos vs R Studio Lavaan.
Among the studies with similar characteristics is included the contribution made by Paredes-Zempual et al. (2020) when studying the association that managerial Skills could have with the Organizational Climate in 53 managers of SMEs of the Mexican trade sector. The study had a quantitative, descriptive and correlational-causal approach. The reliability of the instrument tested through the Cronbach's Alpha revealed values above 0.80 in all indicators. The authors used the partial least squares technique (PLS) to show the MEE model that includes the subscales of the Management Skills (Decision Making, Leadership, Communication, Negotiation and Teamwork), as well as the dependent variable (Organizational Climate). Among the main findings, the researchers documented that the managerial skills: Negotiation and Leadership were linked in a positive and statistically significant way with the Organizational Climate, explaining 80.4% of the variability of said construct, so, their empirical evidence confirmed what was indicated in the literature used for this purpose.
2 THEORETICAL FRAMEWORK
Chiang-Vega et al. (2021) studied the influence between job satisfaction and interpersonal trust with the organizational climate in 344 hospital staff members, through a cross-sectional, correlational study and with the following measurement questionnaires: for the first construct, the contribution was from Chiang et al. (2008), for the second, the contribution was from McAllister (1995), and the last, Koys and Decottis (1991), adapted and validated by Chiang et al. (2008). In their results section they checked the original model: Organizational climate=β1·Job satisfaction + β2·Interpersonal confidence + Error and the alternative model: Organizational climate = β1·Job satisfaction + Error). The authors found that job satisfaction had a positive and statistically significant relationship with the organizational climate, here satisfaction with the working group and the opportunity for development are privileged; on the other hand, interpersonal trust was not statistically outstanding in the observed environment.
Favila Flores et al. (2022) examined the relationship that organizational culture could have with the work climate, based on the expectation of the employees of a service station. The research was non-experimental, descriptive, correlational and transversal. The information was obtained by means of a survey, using for this purpose the Organizational Culture Assessment (OCAI) instrument proposed by Cameron and Quinn (1999), consisting of 77 reagents, valued by a Likert scale of five options. The reliability of the instrument obtained a favorable result (0.897), according to Cronbach's Alpha coefficient; the statistical analysis was executed by Spearman's Rho correlation coefficient, documenting empirical evidence to confirm that organizational culture correlated positively with the work climate.
Cossio Hernández (2022) analyzed the link that the organizational climate has with the labor performance in 111 collaborators of the transport service. It was a study with a quantitative, descriptive-correlational and cross-sectional approach; on the other hand, the instrument with which the organizational climate was measured included the following subscales: Organizational culture, Organizational design and Human potential; on the other hand, the Work performance incorporated: Personal conditions, Work characteristics, Interpersonal relations and Personal policies, all measures with the Likert scale, proposed by MINSA and Rocca, respectively. The researcher documented levels of favorable reliability in both instruments (higher than 0.70); and through SPSS obtained Spearman's correlation analysis on the variables that led her to contrast her research hypotheses, demonstrating a positive relationship between the organizational climate and work performance, except that the last construct did not indicate a link with the subscales of organizational design and human potential. It was reported that the totality of those involved in the study oppose the organizational climate; while, a similar proportion (97.0%) expressed their disagreement with the Work Performance.
Zambrano Álvarez and Zambrano Montesdeoca (2022) analyzed the factors of job satisfaction that best affect the organizational climate in 156 teachers who provide their services in private educational institutions, for which they provided the Minnesota Satisfaction Questionnaire (MSQ); while, to assess the organizational climate they used the proposal of Ortega Santos (2016). Through descriptive analysis, the researchers documented the relationship between risk factors, as well as the causes and consequences that derived from the study phenomenon. The instrument's reliability results yielded very favorable results, namely 0.961 for Job Satisfaction and 0.971 for Organizational Climate. Among its main findings, it is indicated that the correlational analysis carried out using Spearman's Rho coefficient showed a strong positive and statistically significant correlation, interpreting it as follows: the greater job satisfaction among the teaching staff, the organizational climate will be more favorable.
Cabero-Almerara et al. (2019) documented the perception of 460 higher education students about social networks as an educational mechanism to strengthen collaborative work. The research carried out was ex post facto, non-experimental and descriptive; the instrument used for the collection of the data was the adaptation of Cabero (2014), which contemplates the following dimensions: preference to work in a group or individually, technological technical skills, experience in social software and use of different social software tools. The instrument's reliability test indicated favorable values between .074 and 0.91. Among the main findings, the authors documented that university students use the Internet for educational purposes. In the segment that is dedicated to doing research, the inclination of social networks in their academic training stands out. They also noted that students have a high inclination to work in groups.
Chacón Cuberos et al. (2019) analyzed the effective correspondences between Bullying, Cyberbullying and Cooperative Work constructs in 227 adolescents, through a nonexperimental, ex post-facto and descriptive research; using the following instruments for this purpose: Cyberbullying, validated by Garaigordobil (2013); on the other hand, the Teamwork questionnaire was of its own elaboration. The authors generated empirical evidence that confirms what was expressed in previous studies with similar characteristics, namely, collaborative work was higher in women and decreases as the age of adolescents increases; no statistically significant differences were observed by sex where students are victims or witnesses of Cyberbullying; however, the older a higher level of victimization and aggression associated with Cyberbullying is recorded.
Jaramillo Ostos et al. (2021) examined the link between transformational leadership, interpersonal relations and collaborative work, in a group of employees who perform managerial, teaching, administrative and service functions, in the education sector. The research was basic, transversal and non-experimental design. The sample was made up of 75 collaborators (non-probabilistic sampling), out of 380 subjects who integrated the study population. In the instrument, the Interpersonal Relations section included the dimensions: Communicative Skills and Organizational Commitment; the Collaborative Work section had the dimensions: Group Process, Collaborative Skills, Promotional Interaction, Positive Interdependence and Individual Responsibility; and the Interpersonal Relations section included the following dimensions: Group Process, Collaborative Skills, Promotional Interaction, Positive Interdependence and Individual Responsibility. As far as transformational leadership is concerned, its components were: idealized influence, inspirational motivation, intellectual stimulation and individual consideration. The authors documented the following findings: at the construct level, transformational leadership significantly influenced interpersonal relationships and collaborative work; on the other hand, the subscales: individual consideration and intellectual stimulation favorably affected interpersonal relationships and collaborative work.
Tantaléan González et al. (2022) studied how transformational leadership is linked to collaborative work in 104 teachers who provide their services in the subsector of basic education (primary and secondary). The study was quantitative, non-experimental design, descriptive, correlational, hypothetical deductive method. The perception that users expressed about the constructs used was Bass (1998) for Transformational Leadership, with the subscales: Intellectual Stimulation, Inspirational Motivation, Individual Consideration and Idealized Influence and Johnson et al. (1999) for collaborative work with the following dimensions: Positive Interdependence, Individual and Group Responsibility, Face-to-face Interaction, Interpersonal and Team Techniques and Group Evaluation. The authors concluded that there was a moderate and strong correlation between Transformational Leadership, Intellectual Stimulation, Inspirational Motivation, Idealized Influence and Individual Consideration with Collaborative Teaching Work, in the research staff.
Mehdipour, Y. and MohebiKia, S. (2019) explored the link that Participatory Leadership produces Effectiveness and Efficiency, in 570 teachers who served as teachers in primary schools. The study was descriptive-correlational. The questionnaires used were: Participatory Leadership, Castelli (2012) and Castelli et al. (2017), including the subscales: experience opening, goal, meaning, challenge and feedback; Organizational effectiveness of the teacher, Parsons (Zaki et al., 2006), with these components: innovation, organizational commitment, job satisfaction and organizational health. Finally, the Efficiency of the teacher, Bani Hashemian (2009), with its factors: talent, characteristics of work tools and work climate, have the experience, skills and information about work, motivation and organizational climate. The authors documented a significant correlation between Participatory Leadership and the effectiveness and efficiency of teachers, producing empirical evidence that conforms to what was expressed in previous and similar studies.
As a theoretical basis it is expressed that in the field of social sciences researchers use various statistical analysis techniques to develop their hypotheses and confirm their scientific findings, among these are the first generation such as: factor analysis and regression analysis that were used intensively in the 1980s of the last century. However, since the 1990s, it has been the second generation methods that have experienced a significant growth in their use and in research disciplines such as the administration and management of human resources, they represent about 50% of the techniques in empirical research (Hair et al. 2017). ESMs are part of multivariate analysis, which involves the use of statistical methods that simultaneously analyze multiple variables. In particular, these methods are second generation that allow the incorporation of non-observable variables (latent variables) that are indirectly measured by means of observable variables or indicators and in turn facilitate the explanation of the measurement error in the observable variables (Chin, 1998).
Statistical analysis methods when applied to research questions can be used either to look for patterns and relationships between data in an exploratory way or to confirm a priori established theories, so there is an exploratory or confirmatory use of the models. In this case the MEEs do not escape this dynamic, the MEEs that are used to explore relationships are based on the partial least squares (partial least squares) method, on the other hand, for the confirmation of theories MEEs that are based on covariance are used (Chin, 2010; Hair et al., 2017; Henseler et al., 2015). Regarding the question of which method of structural equations to use, Hair et al. (2012) and Rigdon (2012) recommend using the method based on partial least squares (SEM PLS) for situations in which the theory is less developed and for the case of prediction and explanation of key constructs the method based on covariance (SEM CB).
The methods used for estimating the PLS SEM and CB SEM structural equations differ in how each of these treat the latent variables included in the model. In CB SEM constructs are considered as common factor models that explain the covariance among their associated indicators, the scores of these factors are not known and are not needed to estimate the parameters of the model (Hair et al, 2017). On the other hand, in PLS SEM, approximations (proxies) are used to represent the constructs of interest, which are weighted compounds of the indicator variables linked to each construct. It is important to note that the approximations generated by the PLS SEM model should not be considered as identical to the construct they represent, they are approximations. As a consequence of this, some scholars have considered CD SEM as a more accurate and precise method to empirically measure theoretical concepts, while PLS provides approximations (Hair et al, 2017). However, other authors such as Rigdon (2012) and Rossiter (2011) indicate that this is a rather limited idea since the common factors derived from CB SEM are not necessarily equivalent to the theoretical concepts that are the object of research.
3 METHODOLOGY
3.1 TYPE OF STUDY
The study is exploratory, correlational and ex post facto, due to the comparison of the results provided by the MEE solution in AMOS and R Studio Lavaan computer programs, in which the data of a study carried out on how motivation, satisfaction, recognition, pride/belonging and clarity of goals/objectives impact the efficiency and effectiveness of collaborators in the work and influence collaborative work are analyzed.
3.2 POPULATION AND SAMPLE
Institution of Private Higher Education with presence throughout the Mexican Republic. A sample of n = 801 employees from different areas was used, being: administrative, management, teachers and service.
3.3 IMPLEMENTATION PROCEDURE
Application by system or Google Drive, voluntarily guaranteeing its confidentiality. The information collected was integrated into a database that was edited in Excel and later in R Studio Lavaan (Version R Studio 2023.03.03+386) and in Amos (Version 27).
3.4 INSTRUMENT
Organizational climate, consisted of 14 subscales, with 3 reagents each, 42 reagents in total, being: Work environment, Clarity of goals and objectives, Compensations and benefits, Communication, Growth and development, Leadership, Motivation, Pride and belonging, Recognition, Satisfaction, Institutional values, Effectiveness and Efficiency, Collaborative work and Working conditions. For the present study, only 5 of the mentioned ones were selected: Satisfaction, Pride and belonging, Clarity of goals and objectives, Collaborative work, in addition to Effectiveness and efficiency. For all reagents, a 5-rank Likert scale was used as response options, where respondents had to indicate their level of agreement with the statements according to the following criteria: Totally disagree=1, Partially disagree=2, Neither agree, nor disagree=3, Partially agree=4, Totally agree=5.
3.5 SOCIO-DEMOGRAPHIC AND ORGANIZATIONAL DATA
The age distribution was as follows: 44.5% (f=352) between 46 and 60 years, 36.4% (f=292) between 31 and 45 years, 13.0% (f=103) up to 30 years and 6.1% (f=54) over 60 years. Age was 36.0% (f=287) to 5 years old, 22.0% (f=176) to 11 to 20 years old, 21.0% (f=168) to 6 to 10 years old, 15.0% (f=119) to 21 to 30 years old, 6.0% (f=46) to 60 years old, and the remaining 1.0% (f=5) unspecified. Marital status was assigned as follows: 51.0% (f=410) are married, 35.0% (f=282) are single, and the remaining 14.0% (f=109) are other. The level of studies was divided as follows: 30.0% (f=244) with master's degree, 25.0% (f=204) with bachelor's degree, 20.0% (f=164) until technical level or baccalaureate, 18.0% (f=142) with doctorate and 1.0% (f=21) with postdoctoral studies.
4 RESULTS
In this work, the method of structural equations based on covariance (CB SEM) was selected to determine the relationships between variables. On the other hand, the model was run in both AMOS software and R Studio Lavaan, this with the intention of verifying that the results of these softwares are similar and understanding that there is a difference between the application of these softwares, especially because of the cost implications they have in their use. The EMS is presented in Figure 1. In this regard, the hypothesis of the study is as follows:
H1: There are no significant differences between the SEM results obtained between the AMOS software and R Studio Lavaan.
4.1 COVARIANCE MODELS
The results of the SEM analysis performed at R Studio Lavaam are shown in Figure 2 below:
Also, in Figure 3 below, the SEM CB run in AMOS is observed:
Later, in Table 1, we can observe the specific hypotheses raised that were analyzed in AMOS:
4.2 RESULTS OF SPECIFIC SCENARIOS
As can be seen from Table 1, only one hypothesis was rejected, Hypothesis 5, where satisfaction was not significant. The other hypotheses demonstrated significant regression coefficient loads. Also, in Table 2, the same hypotheses are observed, now analyzed in R Studio Lavaan:
As can be seen in Table 2, the same results are obtained as in AMOS, rejecting only hypothesis 5 as the burden of regression coefficients is not significant. Also, below is seen in Table 3, the comparative of goodness of fit tests in both programs:
It can be seen in this table that the results obtained in the goodness of fit tests in both programs are exactly the same.
4.3 STRUCTURAL MODELING INDICES
Chi square/degrees of freedom=358.58, Degrees of Freedom (DF)=95, Chisq/Df=3.77, being less than 4, is acceptable to take into account the SEM, CFI (Normed Parsimony Fit Index)=0.97, is very good, being close to 1, TLI (Tucker-Lewis Fit Index), tLI or Rho2=0.96, is very favorable to be close to 1, RMSEA (Root Mean Square Error of Approximation)=0.06, is suitable to a confidence interval of 0.90), RMR. (Normed Fit Index), NFI or Delta= 96, is acceptable to be a value close to 1, RFI (Relative Fit Index), RFI or Rho 1 = 0.95, is very good to be near 1, IFI (Normed Parsimony Fit Index), PNFI = 0.75, had a moderate behavior, more could improve, AGFI (Adjusted Goodness of Fit Index) = 0.92, reported a favorable value and close to 1, PGFI (Parsimony Goodness-of-Fit Index) = 0.66 proceeded moderately, but could improve. By looking at the goodness of fit indices of the SEM model in general, one could catalog the result as very good.
4.4 SEM HYPOTHESIS TESTING
Hypothesis 1: was accepted, stating that Satisfaction has a significant direct influence on Efficiency and efficacy from its standardized beta coefficient of regression of 0.26.
Hypothesis 2: was accepted, stating that Pride and belonging have a significant direct influence on Efficiency and efficacy from its standardized beta coefficient of 0.37 regression.
Scenario 3: accepted, stating that Clarity of goals and objectives have a significant direct influence on Efficiency and effectiveness from its standardized beta coefficient of 0.11 regression.
Hypothesis 4: was accepted, stating that Collaborative Work has a significant direct influence on Efficiency and Effectiveness from its standardized beta coefficient of 0.31 regression.
H1: to H4: they were able to explain the influence of Satisfaction (0.26), Pride and belonging (0.37), Clarity of goals and objectives (0.11), Collaborative Work (0.31); they explain approximately 83% of Efficiency and effectiveness from their R square.
Hypothesis 5: rejected, Satisfaction does not have a significant influence on Teamwork.
Hypothesis 6: was accepted, stating that Pride and belonging have a significant direct influence on Collaborative Work from its standardized beta coefficient of 0.29 regression.
Hypothesis 7: accepted, stating that the Clarity of goals and objectives have a significant direct influence on Collaborative Work from its standardized beta coefficient of 0.49 regression.
H6: to H7: they were able to explain the influence of Pride and belonging (0.29) and Clarity of goals and objectives (0.49); they explain approximately 52% of Collaborative Work from their R square. The above can be seen in more detail in Tables 1 and 2.
4.5 RELIABILITY AND VALIDITY
The reliability of the instrument was calculated under Cronbach's Alpha and Omega indices. The first was adequate, having a score greater than or equal to 0.70 on all subscales; its fluctuation was 0.82 on the Efficiency and Efficacy subscale up to 0.92 on the Pride and Membership subscale; meanwhile, on the second, all were adequate, having a score greater than or equal to 0.70 on all subscales; its fluctuation was 0.82 on the Efficacy and Efficiency subscale up to 0.93 on the Pride and Membership subscale.
The validity of the instrument was calculated under the AVE coefficient (Average explained variance). The AVE coefficients were adequate, having a score greater than or equal to 0.50 on all subscales; their fluctuation was 0.52 on the Collaborative Work subscale up to 0.86 on the Pride and Belonging subscale. Another indicator that was used to complement the validity was the Discriminant Coefficient (Square Root of AVE). Discriminant coefficients were adequate, having a score greater than or equal to 0.70 on all subscales; their fluctuation was 0.72 on the Collaborative Work subscale to 0.93 on the Pride and Belonging subscale.
5 DISCUSSION, CONCLUSIONS AND IMPLICATIONS
The statistical results of the MEE developed in the Amos and R Studio Lavaan computer programs, under the maximum likelihood method with latent covariance variables showed statistical equality in all areas, being: Goodness of fit indices, standardized correlations, standardized beta coefficients of regression, R2, etc. The possible differences were not statistically significant and vary only by one tenth, was observed in the PNFI Index, the R2 of the P6 reagent of the subscale Clarity of goals and objectives, as well as in the weight of the standardized coefficient of regression in the P39 reagent of the subscale Pride and belonging. From the ESM the following findings were observed: The subscales that explained approximately 83.0% of the Efficiency and effectiveness are: Satisfaction (0.26) + Pride and belonging (0.37) + Clarity of goals and objectives (0.11) + Collaborative Work (0.31). The subscales that expressed approximately 52.0% of the Collaborative Work are: Pride and belonging (0.29) + Clarity of goals and objectives (0.49).
5.1 ADVANTAGES AND DISADVANTAGES OF AMOS
Among the advantages is that it is an intuitive software, which allows you to make multivariate models from drawings or modeling. It is not necessary to know multivariate statistics to understand structural modeling, because intuitively the program will guide you with the drawing. You have the possibility to "design" the models of the shape or trajectory that you have in mind. It has as disadvantages that it is a paid program, in addition to being expensive.
5.2 ADVANTAGES AND DISADVANTAGES OF R STUDIO LAVAAN
Among the virtues, it is a free software that can be used without having a time limit, in addition to being very powerful for research; it has a scientific and technical community that provides support at all times; includes a series of very robust multivariate statistical tools; it allows to save the syntax for use in other projects; it has the possibility of saving the different windows in a single project or file and returning where the project was advanced; it is constantly updated by the scientific community itself, allowing the collaboration of experts; it allows to work on different operating systems: UNIX, Windows, Linux and MacOS; it supports Excel, SPSS, SAS databases; it works with several formats: pdf, word, html. The drawbacks include, among others, the need to program with syntax; you do not have total control over the plotter or drawing of the SEM that is programmed in the syntax, so it is "drawn alone"; you do not work directly with the SEM chart; it takes time to learn how to use the R Studio Lavaan to make SEM models properly; you must make the updates of the program to know how to properly use the syntax; you need to know a little multivariate statistics to understand the programming in the syntax of the program.
5.3 CONCLUSIONS
As there are no statistical differences in the use of the software Amos and R Studio Lavaan, researchers can use these tools at their convenience, taking into account the advantages and disadvantages outlined above, considering the economic aspect that involves the payment of a license, where R Studio Lavaan is a software at no cost. A practical implication linked to the findings of the study is precisely the decision to conveniently use the Amos and R Studio Lavaan programs to analyze structural equations with the same results; on the other hand, in this work a test was carried out with a case study, so that more research could be worked on to reaffirm what was found in this work, which constitutes a line for future research.
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Abstract
Objective: The objective of this research was to compare the results of structural equation models with latent variables (SEM) using the covariance-based maximum likelihood method, employing two different software applications for this purpose (Amos and R Studio Lavaan). Theoretical Framework: This article presents the main concepts and theories underlying this research, addressing the use of SEM in organizational climate analysis and its importance in the educational context to evaluate key constructs in institutional dynamics. Method: The constructs were derived from an organizational climate evaluation of a higher education institution in Mexico. The "Organizational Climate Inventory" was applied, selecting five subscales: Satisfaction, Pride and Belonging, Clarity of Goals and Objectives, Collaborative Work, and Efficiency and Effectiveness. Administrative, managerial, academic, and service staff were invited to participate, achieving a sample of n = 801. Results and Discussion: The results from Amos vs. R Studio Lavaan confirmed that there were no significant differences between the SEMs regarding paths, standardized regression coefficients, R , goodness-of-fit indices, and correlation coefficients. Efficiency and Effectiveness (83.0%) was explained by the influence of Clarity of Goals and Objectives (0.11), Satisfaction (0.26), Collaborative Work (0.31), and Pride and Belonging (0.37) based on standardized regression coefficients. Collaborative Work (52.0%) was explained by the influence of Clarity of Goals and Objectives (0.49) and Pride and Belonging (0.29). The instrument demonstrated reliability levels above 0.70, as well as convergent validity greater than 0.50 and discriminant validity above 0.70 across all subscales. Research Implications: Theoretical and practical implications of this study highlight the feasibility of using free software for SEM analysis, offering institutions an efficient and accessible alternative. Originality/Value: This Study Contributes to the Literature by Validating the Use of Free Software as An Effective and Accurate Tool for Structural Analysis in Educational Contexts Without Additional Costs.