Introduction

Over the course of several decades, psychology focused solely and exclusively on symptom and disease. Most of the publications focused on symptom and disease instead of on the positive psychological resources of individuals (^{Myers, 2000}; ^{Schaufeli & Salanova, 2007}). However, this paradigm of psychology lost emphasis with the publication of ^{Seligman and Csikszentmihalyi (2000}), who defended that psychology should evolve in the direction of studying the strengths and psychological capacities of individuals and organizations, and how these can be improved. As such, positive psychology emerges as a paradigm that presupposes a watershed from three pillars: (a) the study of positive emotions; (b) the study of positive traits, strengths, and virtues of individuals; and (c) the study of positive institutions that manifest virtues and are sustained from positive emotions (^{Seligman, 2003}). But what positive psychology has promoted is the study of the positive aspects of the human being in a context that has given, for a long time, too much importance to negative aspects (^{Csikszentmihalyi, 2014}).

Positive Organizational Behavior (POB) is linked to positive psychology principles and is proposed as a new heretical paradigm that studies the nature and application of positively oriented psychological strengths and abilities. POB has basic criteria essential to consider constructs as positively oriented, such as: (a) having a solid theory and research; (b) being state-like (and therefore, with the possibility of learning and development through prevention and intervention programs); and (c) having a positive impact on job performance (^{Luthans, Youssef-Morgan, & Avolio, 2015}; ^{Youssef-Morgan & Luthans, 2015}). Positive psychological capital respects all the above-mentioned criteria and, as such, can be integrated in the POB (^{Luthans & Youssef, 2004}, ²⁰⁰⁷). This concept comes to suppress the limitations of other types of capital (economic, social, and human), which have been shown to be ineffective in the face of the social, economic, and labor changes in recent years (^{Luthans, Luthans, & Luthans, 2004}). These changes had negative consequences for workers, such as labor precariousness and decreased well-being (^{Luthans et al., 2015}).

Thus, this construct emerged with the aim of improving the psychological resources of workers, which has led to a great development in related studies (^{Avey, 2014}). Positive psychological capital is defined as:

an individual’s positive psychological state of development and is characterized by: (a) having confidence (self-efficacy) to take on and put in the necessary effort to succeed at challenging tasks; (b) making a positive attribution (optimism) about succeeding now and in the future; (c) persevering towards goals and, when necessary, redirecting paths to goals (hope) in order to succeed; and (d) when beset by problems and adversity, sustaining and bouncing back and even beyond (resiliency) to attain success (^{Luthans, Youssef, & Avolio, 2007}, p.3).

Method

Statistical Analysis

Given that the PCQ-12 has a predefined factorial structure, the analysis of the properties of the instrument was conducted through a CFA performed with the software Analysis of Moment Structures (AMOS) version 20. Prior to this analysis, the authors assessed the multivariate normal distribution through the values of skewness and kurtosis. In addition, the value of the Mardia test was also considered for the multivariate normal distribution, this test must present values lower than 5 (^{Byrne, 2010}). The result of the Mardia test was higher than the referred value. Despite this result, and in accordance with ^{Iacobucci (2010}), if the values of skewness and kurtosis are not too high, the distance from normality is not enough to question the results of a model.

There is no consensus in the literature regarding the values that indicate the existence of a multivariate normal distribution, however some authors (e.g., ^{Curran, West, & Finch, 1996}) consider that for the maximum likelihood estimation method, the most used in structural equation modeling, skewness and kurtosis values of 2 and 7, respectively, indicate the presence of a multivariate normal distribution. The results obtained respected the above-mentioned values and they were not too high. Therefore, we used the maximum likelihood estimation method to evaluate the data, since it is more robust regarding possible breaches from multivariate normality (^{Iacobucci, 2010}; ^{Marôco, 2010}) (Table 1).

Table 1: Uni and Multivariate Statistical Analysis (N = 396). 

Note. M = Mean; SD = Standard-deviation; SI = Skewness Index; KI = Kurtosis Index.

Three models were initially proposed to analyze the structure of the data: second-order model, first-order model, and four-correlated factors model. The second-order model (model 1) consisted of four factors: self-efficacy, hope, resilience, and optimism linked to a second-order factor called positive psychological capital. The variance of this model was established as one. In the case of first-order model or one-dimensional model (model 2), it was decided that the first item should present a factor loading of one. Finally, in the four-correlated factors model (model 3), it was decided that the first item on each of the dimensions should present a factor loading of one.

The Chi-squared goodness-of-fit test (χ²) was used to evaluate the quality of the model. However, this test presents a limitation related to the sample size, in large samples it may indicate the existence of statistically significant differences despite they are not present. To overcome this limitation, the Comparative Fit Index (CFI), the Root Mean Square Error of Approximation (RMSEA), the Standardized Root Mean Square Residual (SRMR), and the Normed Chi-squared (χ²/df) indexes were considered. CFI values between .90 and .95 are considered good, and values above .95 are very good (^{Byrne, 2010}; ^{Marôco, 2010}). A RMSEA between .05 and .10 is acceptable and below .05 is good (^{Byrne, 2010}; ^{Marôco, 2010}). In addition, a confidence interval of 90% was also considered for this index (90% RMSEA). A value of SRMR below .08 indicates a good fit (^{Hu & Bentler, 1999}). Finally, values of χ²/df lower than five are acceptable.

The factor loadings obtained were compared with the values proposed by ^{Comrey and Lee (1992}), excellent (>.71), very good (> .63), good (> .55), acceptable (> .45), and poor (> .32). The modification indices of the models were observed to improve their quality. The difference between the models was evaluated through the ΔCFI, values greater than .01 indicate that the models are statistically different (^{Cheung & Rensvold, 2002}).

Convergent and discriminant validity were also assessed. To observe the existence of convergent validity the values of Average Variance Extracted (AVE) were evaluated, which must be greater than .50 (^{Bagozzi & Yi, 1988}; ^{Sharma, 1996}). Discriminant validity was analyzed through the comparison between the AVE values of each construct and the values of their squared correlations (^{Fornell & Larcker, 1981}).

Finally, reliability was assessed by using the Cronbach’s Alpha and Composite Reliability (CR) coefficients. The results obtained were classified according to the proposal of ^{Sharma (1996}), values above .90 are excellent, between .80 and .90 are very good, between .70 and .80 are adequate, and below .50 are poor.

Results

Model 1 (second-order model) showed a poor fit. The same situation was observed in model 2 (first-order model), only the SRMR index respected the cut-off defined. In opposition, model 3 (four-correlated factors) showed a good fit (Table 2).

Table 2: Fit Indexes for the Assessed Factor Structures (N = 396). 

Note. Model 1 = second-order model; 2 = first-order model; Model 3 = four-correlated factors model; ^** p < .01; df = degrees of freedom.

All the factor loadings were statistically significant and possessed the expected sign (Table 3). Item nine had a poor factor loading in model 2 (first-order model), according to the classification of ^{Comrey and Lee (1992}).

Table 3: Factor Loadings of the Items of PCQ-12 in the Proposed Factors Structures (N = 396). 

Note. Model 1 = second-order model; 2 = first-order model; Model 3 = four-correlated factors model; ^aFactor Loadings; ^bItem uniqueness; ^cCronbach’s Alpha and Composite Reliability coefficients.

After the initial evaluation of the factor structures proposed, we analyzed the modification indices for improvements in the fit of the models, especially regarding possible covariances between the errors of the items of PCQ-12. We identified two items, items nine and ten, and then their statistical significance was assessed. Therefore, the three models were re-specified considering this covariance (Table 4).

Table 4: Fit Indexes for the Re-specified Factor Structures (N = 396). 

Note. Model 1 = second-order model; 2 = first-order model; Model 3 = four-correlated factors model; ^** p < .01; df = degrees of freedom.

All the factor loadings were statistically significant and showed the expected sign (Table 5). As in the previous case, item nine in models 2 and 3, reported a low factor loading (^{Comrey & Lee, 1992}).

Table 5: Factor Loadings of the Items of PCQ-12 in the Re-specified Factor Structures (N = 396). 

Note. Model 1 = second-order model; 2 = first-order model; Model 3 = four-correlated factors model; ^aFactor Loadings; ^bItem uniqueness; Cronbach’s Alpha and Composite Reliability coefficients.

Model 1 (second-order model) obtained a poor fit, not respecting any of the cut-off values for the indexes considered. In turn, model 2 (first-order model) and 3 (four-correlated factors) presented a good fit, however they were statistically different (ΔCFI = -.62). Model 3 had the best fit showing good values for all the selected indexes. These results are contrary to H1, in which it was mentioned that the second-order model would be the most suitable for conceptualizing positive psychological capital in a sample of Mexican workers. Thus, it can be affirmed that the advanced research hypothesis was not corroborated by the obtained data. In relation to the factor loading of the items, except item nine in models 2 (λ = .23) and 3 (λ = .28), all the remaining items ranged from acceptable (λ = .47) to excellent (λ =.88). This classification is based on the assumptions of ^{Comrey and Lee (1992}), allowing us to state that the indicators of this instrument, excluding item nine, possess individual reliability, given that their factor loadings was higher than .45.

Since model 3 presented a better fit, we calculated the discriminant and convergent validity considering its results. The AVE values met the cut-off point defined in the literature (.50) except for the resilience dimension. If the convergent validity of this dimension is calculated by deleting item nine, because this item obtained a poor factor loading, it can be observed that the values achieved improve (.42) (Table 6). However, this value is not sufficient to consider that this dimension has convergent validity. Discriminant validity values can also be found in Table 6. From the analysis of this table it can be concluded that the dimensions of the instrument under analysis have adequate discriminant validity. Finally, regarding reliability, all values were acceptable, ranging from acceptable (.79) to good (.89) (^{Sharma, 1996}). An exception occurred in the resilience dimension in models 1 and 3.

Table 6: Convergent and Discriminant Validity Values (N = 396). 

Note. AVE values are indicated in bold. The other values are the squared correlations.

With the goal of addressing the limitations posed by item nine, both at the individual reliability of items and the reliability of the resilience dimension, we calculated model 3, which had a better fit, without including the item referred above. The results obtained considered the cut-off values defined (χ2 (39) = 107.592, p < .01; χ2/df = 2.579; RMSEA = .067; 90%RMSEA = (.052-.082); SRMR = .058; CFI = .966), which were, in general, good. Table 7 reports the values of the factor loadings of the items of PCQ-12 and the reliability results for model 3 with the exclusion of item nine.

Table 7: Factor Loadings of the Items of PCQ-12 for Model 3 Excluding Item Nine (N = 396). 

Note. Model 3 = four-correlated factors model; ^aFactor loadings; ^bItem uniqueness; ^cCronbach’s Alpha and Composite Reliability coefficients

As it can be observed, deleting item nine in model 3 led to a better individual reliability of the items of PCQ-12, varying their factor loadings between .64 and .88, in accordance to the classification of ^{Comrey and Lee (1992}), between very good and excellent. At the internal consistency level, deleting item nine did not produce significant changes, since the dimension resilience continued to present a value lower than .70.

Discussion

The objective of this study was to evaluate the psychometric properties, validity and reliability, of the PCQ-12 in a sample of Mexican workers and to observe if positive psychological capital behaves as a second-order construct. In this work, through a CFA, three concurrent models were analyzed, and it was found that the four-correlated factors model was the one that showed a better fit, which indicates that each of the four dimensions of positive psychological capital have their own identity and interact with each other. These results did not coincide with what was stated in H1, which suggested that positive psychological capital, as measured by the PCQ-12, in a sample of Mexican workers, would present a factor structure composed by a second-order construct.

Our results are consistent with those obtained in Portugal, Spain, and Brazil (^{Formiga, Viseu, & Jesus, 2014}; ^{Lopez-Núñez et al., 2018}; (^{Viseu et al., 2012}) who also describe a four-correlated factors model and equally represent Latin cultures, different from the population that led to the creation of the PCQ-12, providing new information about the behavior of this construct in cultures with languages other than English, possibility previously suggested by ^{Rus et al. (2012}). ^{Azanza, Domínguez, Moriano, and Molero (2014}) underlined how tests performed with different samples and with varied compositions may lead to distinct factor arrangements.

The results showed a very good global internal consistency for the PCQ-12 in the studied sample. The option to present a global value was based on the works of ^{Avey et al. (2011}), ^{Rus et al. (2012}), and ^{Viseu et al. (2012}). This situation allows to resolve an issue raised by past studies (e.g., ^{Léon-Pérez et al., 2017}), where it was verified that there is great variability in the reliability values of this instrument, thus an overall reliability value should be presented, and the CFA results must be valued (^{Rus et al. (2012}; ^{Urbina, 2004}). The results obtained are in line with the reliability analyses performed in other countries (e.g., China, Australia, and Romania reported overall values of .68, .88, and 90, respectively, not presenting results by dimension) (^{Wernsing, 2014}).

Regarding the analysis performed by dimension, ^{Dawkins et al. (2013}) observed in a review of 29 psychometric studies that optimism and resilience dimensions tend to be lower than the dimensions self-efficacy and hope. As for the resilience dimension, previous validation studies in other populations also reported a poor reliability (^{León-Pérez et al., 2017}; ^{Lopez-Núñez et al., 2018}; ^{Viseu et al., 2012}). This seems to indicate that the resilience dimension tends to show a lower reliability, suggesting that there is a great fluctuation of answers and that this dimension does not properly discriminate this construct (^{Martínez, Hernández, & Hernández, 2014}). This situation was also observed in our study where, except for resilience, all the other dimensions obtained very good results (^{Sharma, 1996}). The factor loadings of the items varied between acceptable and excellent, except for item nine (belonging to the dimension resilience) in models 2 and 3 (^{Comrey & Lee, 1992}). Given that model 3 had a better fit, we tested its functioning with the removal of the item in question. Thus, it was possible to verify that in this situation, the items of the four-correlated factors model possessed factor loadings that ranged from very good to excellent (^{Comrey & Lee, 1992}). These results were higher than those obtained in previous studies (e.g., ^{López-Núñez et al., 2018}; ^{Rus et al., 2012}; (^{Viseu et al., 2012}).

The results suggest that, although being complementary concepts and act synergistically, self-efficacy, optimism, resilience, and hope are different constructs (^{Bagozzi & Yi, 1988}; ^{Fornell & Larcker, 1981}; ^{Sharma, 1996}). However, these results are far from diminishing the interest of this paper but add interesting information to the research on the PCQ 12 and the theoretical conceptualization of psychological capital in cases in which it has a different behavior from that referred by the authors of the instrument (^{Rego, Marques, Leal, Sousa, & Pina e Cunha, 2010}). ^{Dawkins et al. (2013}), go beyond these considerations and point out that: “additional studies, outside the core PsyCap authorship team (so to encourage independent replication)” (p. 355-357) and in this sense, “a contra-theorical result may be as valuable as a supportive one” (^{Rego et al., 2010, p. 1533}).

The results indicate that the PCQ-12 may be considered a valuable instrument to measure positive psychological capital in samples of Mexican workers, but it is necessary to fill some of the gaps found in the dimension resilience, as verified in studies conducted in other countries (e.g., ^{López-Núñez et al., 2018}; ^{Viseu et al., 2012}). The data obtained from the reliability and validity analysis suggest that item nine in this dimension is deleted. By deleting it, it was possible to observe an improvement in individual reliability. However, reliability and convergent validity values for the resilience dimension did not significantly improve. Therefore, the limitations identified may not be of the item nine per se, but of the resilience dimension. One possibility is that the resilience dimension should be reformulated trying new combinations of items. To achieve this goal, items of the resilience dimension of the PCQ-24 could be selected and included in the PCQ-12 replacing the original items. Future studies can follow this line in two ways, (a) perform an exploratory factor analysis (EFA) of the items in the PCQ-24 and select the best items for each dimension, including resilience, while trying to keep the original number of items of each dimension; or (b) conduct a CFA with the original items of the PCQ-12 for the self-efficacy, hope, and optimism dimensions, and include new combinations of items for resilience to test those that best suit the factorial solution.

This paper is not exempt from limitations that should be considered, for example the sample size. The number of participants is not representative of the Mexican working population, so the sample should be expanded both geographically and in employment characteristics, as well as using procedures that represent the sample assessed (whether by population, by economic sector, by status, etc.). Regarding the use of the assessment instrument and research design, it would have been useful to evaluate other variables (e.g., job satisfaction) to observe the behavior of the PCQ-12. The use of a cross-sectional design also presents its difficulties, because positive psychological capital can be influenced by sociodemographic variables, such as years of experience, and organizational culture, climate, and organizational health.

Future research should analyze the convergent and discriminant validity of positive psychological capital with respect to other constructs (^{Antunes et al., 2017}). Another line of research would be the use of longitudinal studies with antecedent variables that may influence this construct (e.g., demographic variables and variables linked to the job context) as suggested by ^{Avey (2014}). Also, it would be useful to understand how positive psychological capital behaves as a moderating and mediating variable, an aspect that would promote a development in this research field, since so far it has solely focused on the outcomes of this construct (^{Newman, Ucbasaran, Zhu, & Hirst, 2014}). Other validation studies should consider the content of the items of the PCQ-12, using simultaneously other assessment tools of psychological capital (e.g., OREA Questionnaire; ^{Meseguer-de Pedro et al., 2017}), because the formulation of some items may not be relevant for all types of workers (^{Meseguer-de Pedro et al., 2017}). Finally, cross-cultural studies are also needed to measure how this construct behaves both in terms of factor structure and in terms of its relationship with other variables in different contexts.

It is also desirable to highlight the implications of this paper, which provides interesting and novel data with respect to the PCQ-12 and the theoretical conceptualization of positive psychological capital. Also, it overcomes some limitations regarding the psychometric assessment of this instrument, since typically only reliability values of the PCQ-12 are reported, without including validity evidences (^{Viseu et al., 2012}). In this work we tested alternative solutions to eliminate the psychometric limitations observed, particularly at the reliability level of some dimensions and individual reliability of the items (^{Dawkins et al., 2013}), and included data on discriminant and convergent validity. In our sample, it was observed that all dimensions of the presented instrument have an adequate convergent validity, excluding the resilience dimension. In terms of discriminant validity, it is possible to affirm that the dimensions of positive psychological capital are independent, even if they act synergistically, to promote the positive psychological resources of individuals, which have practical implications in the organizational environment because each dimension can be identified and developed to improve performance, as well as to promote the psychological capital of employees (^{Dawkins et al., 2013}; ^{Rego et al., 2010}).