Social capital at work: psychometric analysis of a short scale in Spanish among Mexican health workers

Abstracts

La mayoría de estudios sobre capital social y salud se realizan con grandes encuestas en hogares, olvidando que muchas interacciones entre los individuos ocurren en el ambiente laboral. Este estudio tuvo como objetivo evaluar las propiedades psicométricas de una escala en español para la medición del capital social en el trabajo. La escala de Kouvonen y colaboradores fue traducida al español y evaluada mediante la teoría clásica de las pruebas, la teoría de respuesta a los ítems y análisis factorial confirmatorio. Participaron 152 trabajadores de la salud mexicanos de diferentes contextos socioculturales. La consistencia interna fue alta (alfa de Cronbach= 0.88). El capital social en el trabajo se correlacionó adecuadamente con dos dimensiones del Cuestionario de Contenido del Trabajo. Se detectó un efecto techo y se cuantificó la dificultad de los ítems. El análisis factorial confirmatorio mostró los componentes teóricamente esperados de vinculación, puente y confianza del capital social en el trabajo. La escala tuvo un aceptable comportamiento psicométrico, por lo que podrá ser utilizada en futuros estudios.

Capital social; Salud ocupacional; Psicometría; Epidemiología social

ORIGINAL ARTICLES

Social capital at work: psychometric analysis of a short scale in Spanish among Mexican health workers

Alvaro J. Idrovo^I; Anabel Camacho-Avila^II; Javier García-Rivas^II; Arturo Juárez-García^II

^ICentro de Investigación en Sistemas de Salud, Instituto Nacional de Salud Pública. Cuernavaca, Morelos, México

^IIUnidad de Investigación y Servicios Psicológicos (UNISEP), Facultad de Psicología, Universidad Autónoma del Estado de Morelos. Cuernavaca, Morelos, México

Solicitud de sobretiros

ABSTRACT

Most studies on social capital and health are carried out with large home-based surveys, neglecting that many interactions among individuals occur in the workplace. The objective of this study was to explore the psychometric properties of a scale in Spanish used to measure social capital at work. The scale designed by Kouvonen et al was translated into Spanish and tested under classical test theory, item response theory, and confirmatory factorial analysis; 152 public health workers from different socio-cultural contexts participated in the survey. Internal consistency was high (Chronbach's alpha = 0.88). Social capital at work correlated properly with two Job Content Questionnaire dimensions. A ceiling effect was detected and item difficulty was quantified. The confirmatory factor analysis showed the expected theoretical components of social capital: bonding, bridging and trust. The scale has acceptable psychometric properties, thus it can be used in future studies.

Keywords: Social capital. Occupational health. Psychometrics. Social epidemiology.

Introduction

Social capital is considered an important determinant of individual and population health¹. Although there are several definitions of social capital, the most commonly used in public health is Robert Putnam's one. He uses the concept to refer to features of social organization which promote or improve the acquisition of skills, agreements, trust and networks that facilitate social functioning to achieve common goals². This definition has allowed quantitative approximations given that it can be related to indicators such as the level of trust, perceived reciprocity and the density of membership to civic associations³. Other definitions such as James Coleman and Pierre Bourdieu´s tend not to be used in epidemiology since their approaches are more extensive and difficult empirical operationalization. The first defines social capital in terms of its role in the facilitation of individual or group action, while the latter emphasizes the fungible nature of social capital within the political economy⁴.

Evidence from political sciences indicates that communities with greater cohesion, by having greater participation by civil society, tend to be more efficient in its operation, creative in political initiatives, more successful in the implementation of policies, and less corrupt². The same review by Kawachi & Berkman also reports observations from criminology that support this type of evidence, by stating that societies with higher levels of organization tend to have less crime and fewer suicides. Other studies have shown fewer behavioral problems among minors and better economic and labor development in societies with greater social capital².

The vast majority of studies conducted in developed countries suggest that social capital is part of the causal mechanism whereby acts the income inequality on health ("income inequality hypothesis")⁵; however, there is evidence that this does not occur in other countries with lower level of economic development^6,7. In Latin America and the Caribbean, studies on the subject are still scarce and tend to repeat the same findings observed in other developed countries⁸. Perhaps the most relevant exception are the contrary effects described in the studies where it seems to have a "perverse" connotation^9-11; in other words, with harmful effects on health.

Most epidemiological studies on social capital have been carried out with general population using large-scale surveys^1,8. This has disregarded that much of the interactions of individuals occur in working environments, which is why it is highly relevant to assess social capital at work; in these contexts, important interactions take place between peers and between leaders and subordinates, which may reflect the general organization of society as a whole¹². In addition, the notion of social capital, recently has received greater attention as a possible explanation to the disparities in health and its social gradient¹³.

A breakthrough in this topic was the development in Finland of a short scale to measure social capital at work¹⁴. This scale has the prospect of an inequality perspective of the efficacy of social capital; with only eight items (table 1), it seeks to explore whether people feel respected, valued and treated with equality at work. Theoretically, the scale incorporates cognitive (items 3, 5 and 8) and structural components of social capital (items 1, 2, 4, 6 and 7), it also incorporates the linking social capital (items 3, 4 and 5), the bridging or relational social capital (items 6 and 7) and the bonding social capital (items 1, 2 and 8)¹⁴. The cognitive component makes reference to perceptions of support, reciprocity, exchange and confidence, while the structural refers to the extent and intensity of the links. Another classification identifies union social capital in relations among individuals of the same social group, while it includes the bridging social capital to refer to connections between people from different social groups¹⁴.

These dimensions represent the core axes of social capital in the labor context, and therefore the most representative indicators for its assessment, regardless of other cultural, occupational or geographical aspects¹⁴. It is important to note that the measurement of social capital in epidemiological studies tends to be one-dimensional and based on relationships of trust and respect^15,16, so this proposal incorporates the key elements for an adequate measurement of social capital.

An initial assessment of the scale, based on the classical test theory, was performed with the answers given by Finnish workers in the public sector. The evaluation included validation of appearance by an expert; internal consistency analysis; correlations between items and the total score; convergence validity with procedural justice (Moorman's scale)¹⁷, effort-reward imbalance (Siegrist's Effort-Reward Imbalance scale)¹⁸, and Job control (Karasek's Job Content Questionnaire)¹⁹, and divergence validity with anxiety traits (Trait Anxiety Inventory)²⁰, and the magnitude of changes at work (single question with values of one to seven, interpreted as larger and more significant changes). The psychometric results obtained during this analysis were satisfactory¹⁴.

The few studies on social capital at work and health consistently show a positive effect, although it should be noted that they all have been in countries with significant differences in comparison with Latin America. For example, an ecological study in Russia used the quality of relationships at work as an indicator of social capital. This allowed identifying a relationship between social capital and life expectancy and mortality²¹. Other data of the Saskatchewan working population in Canada show that those who frequently socialized with coworkers tend to have better health, compared with those who do not socialize²²; something similar was reported by Lindström et al. with Swedish workers. They used participation in trade union meetings or study in labor circles as indicators of social capital²³.

In a multilevel analysis, it could be shown that Finnish employees working in places with low social capital tend to have more health problems, in contrast with those who work in companies with high social capital²⁴. Also in Finland, Liukkonen et al. demonstrated that better self-reported health and less psychological distress occur among workers who have a contract with job security and confidence in the support of co-workers²⁵. More recently, Suzuki et al. measured social capital at work, through trust and reciprocity, in 1800 workers in 60 Japanese companies. Then, through a multi-level analysis, they explored the effect of these indicators on the individual and enterprise. It was found that only the level of corporate mistrust is associated with a greater likelihood of individual smoking²⁶.

All these studies used different ways to measure social capital, which is a common trait in investigations on the subject²⁷. However, the need for a uniform vision of the construct and its measurement remains an area of opportunity. One advantage of Kouvonen´s model and scale is the fact that it incorporates the most important dimensions of social capital in only a few items, and that regardless of culture they can be considered universal dimensions, which led to the use of this scale in Latin American populations. In this way, and given the need for standardized ways to measure social capital, the objective of this work was to evaluate the psychometric properties of a brief measurement scale of social capital at work. This seeks to contribute to the achievement of a standard measure that allows future studies to explore on key indicators of the level of social capital present in the workplace.

The psychometric testing of the scale is part of a study on work characteristics of the health services context and its impact on population health. In this context, it is assumed that social capital and organizational characteristics are positively associated with organizational performance, workers' health, and consequently the health of individuals who receive their services^28-30.

Materials and methods

Participants in the study. The study was performed in the municipalities of Guachochi (Chihuahua), Jojutla (Morelos) and Tizimín (Yucatán), all in the Mexican Republic, which were selected to incorporate the inherent variability between the North, Center and South of Mexico. In each of these locations, workers in the state health services or the Institute of social security and social services for workers of the state were invited to participate. To collect the data, managers were first contacted to explain the study in detail. Meetings were then held with workers with the same objective, emphasizing that their participation would be voluntary, anonymous, and without labor implications for those who decide to answer the questionnaire or not. Informed consent with signature from each participant was obtained. This study was approved by the Ethics Committee of the National Institute of Public Health in Mexico.

Construction of the scale in Spanish. Based on the original scale, an initial translation into Spanish was done, and then back-translated into English to verify that the content of the original scale was maintained³¹. Pilot tests were conducted with 22 health professionals. This allowed modifying sentences to make them understandable for individuals from the three participating regions. The original and final items in English and Spanish, respectively, are found in table 1.

Assessment psychometric. Guidelines of the classical theory of test, confirmatory factor analysis and item response theory were followed in order to elucidate the psychometric properties of the scale. Classical theory considers that the scores obtained by individuals have a component that reflects the magnitude of the construct measured and an error component. Additionally, it assumes that the true score corresponds to the mathematical expectation of the empirical score, that the value of the real score of an individual is independent of the score error, and that the errors of measurement in a test are independent of errors in other tests³².

Firstly, an exploratory factor analysis with the eight items was conducted, seeking to identify the latent variables not observed and the structure foundation of the construct³³; in order to do this, an a-priori criterion was established to consider that a factor was relevant if it presented a proportional contribution exceeding 5%. Then Cronbach's internal consistency was assessed. We explored the concurrent validity through Spearman correlations among the scores obtained in the scale and the dimensions of supervisor/boss social support and co-workers social support from the job content questionnaire (JCQ)²⁹, in its version validated for Mexico^34,35. This is one of the few validated scales in Mexico related to the construct at issue. Analyses were done with the statistical program Stata 11 (Stata Corporation, College Station, Texas).

Given that the classical theory does not allow the comparison of a same construct scores obtained with different instruments, and the inability to identify differences in the difficulty of items and the skill of those who respond, among other limitations, we carried out a follow-up assessment with some elements of the item response theory. With this analysis, the difficulty of each item in relation to the ability of people can evaluated. This facilitates the obtaining of total scores and incorporating these features on a linear scale³⁶. Moreover, among other advantages, it can express parameters of items and people in the same units, which allows to identify the items that an individual can resolve with greater or lesser difficulty; it facilitates proper assessment even when there is missing data, estimates the accuracy of measurement, and detects data that do not conform to the model and outliers. From this approach, an efficient item must follow a logistic curve in a manner that should only be properly answered by individuals who possess the skills required by the cognitive demands intended to be measured³⁶.

Since on a Likert scale, as the one evaluated here, a total score of the construct is obtained by the sum of the scores obtained in each item, an initial exploration was carried out with data from all workers using the Partial Credit Model³⁷. Under this model, the distances between the categories within the items are not assumed as uniform. Data adjustment with the model was then estimated with statistics of internal and external adjustment of workers and items, thus identifying outliers that did not conform to the model. The quality of the instrument was determined with criteria suggested by Fisher³⁸. Curve characteristics of each of the items were estimated. This allows looking at the relationship between the candidates' level of skills and the probability of correct answer to each item. All these analyses were undertaken with Winsteps ^TM39.

Lastly, taking into consideration the information obtained in the previous analyses and conceptual foundations of Kouvonen et al.'s scale, confirmatory factorial analyses were done. This technique has shown its value to validate new questionnaires and adaptations of questionnaires developed in other languages or implemented in populations with different cultures⁴⁰. The first model was made for the single factor model (model 1) according to what was obtained in the exploratory analysis; model 2 explored two factors (structural and cognitive components of social capital) following the theoretical concepts referred by Kouvonen et al¹⁴. Finally, a three factor model was assessed (linking, bridging and bonding components of social capital). Schumacker & Lomax and Hair et al.'s indexes and recommended values were used for the evaluation of adjustment^41,42. These analyses were done with use of the AMOS 4.01 program⁴³.

Results

Information was obtained from 152 health workers, most of them were women (62.8%), with ages between 16 and 60 years (median = 34). The main activities of the participants were nursing (38.16%), administrative (28.95%) and medicine (15.79%). Scores according to their occupation can be seen in Figure 1, where the similarity of scores is noticeable, however, with a tendency to be higher among doctors. During factor analysis it was noted that a single factor, with eigenvalue of 3.94, explained 94.13% of the variance. After a varimax rotation, it was observed that factor loading greater than 0.65 were those for items c3, c4, c5 and c7. After calculating the Kaiser-Meyer-Olkin measures of sampling adequacy, values exceeding 0.80 were obtained for each item and in overall, except for item c2 (0.78), which can be considered as "appropriate"⁴⁴. A Cronbach's alpha of 0.88 showed that all items have the same direction and a high internal consistency.

Table 2 shows Spearman correlations with their respective 95% confidence intervals between scores on the scale and dimensions of the JCQ. Social capital at work positively correlated with the two dimensions of the JCQ that evaluate the level of support provided by the boss (rho 0.66, p <0.01) and co-workers (rho 0.54, p <0.01). The other dimensions showed several positive correlations, as expected theoretically, but not with the same magnitude. These findings suggest that there is a single construct that can be called social capital at work, with an acceptable concurrent validity.

Item difficulty was quantified by means of logit, obtained by multiplying the response odds ratios to each item of the natural log. Thus it was observed that the easiest item was c1 (- 0.51); followed in increasing order by items c2 (- 0.32), c8 (- 0.11), c4 (- 0.02), c7 (0.11), c3 (0.19), c5 (0.28), and c6 (0.37). This is summarized in table 3. In the Wright map, it was evident that workers have a much greater dispersion in skill to respond, in comparison with the items (figure not shown). The three easiest items were those part of the trust relationships component. In the same table, it can be seen that the internal (infit) and external (outfit) adjustment statistics show values between 0.8 and 1.3, which is evidence of an appropriate adjustment.

Finally, table 4 shows the adjustment indexes for the one-, two- and three-factor models, using confirmatory factor analysis. The indexes were satisfactory in the three-factor model (Figure 2), except for the evaluation using the x ² test, which could have been due to sample size⁴⁵.

Discussion

This study presents the results of several psychometric analyses on the Spanish version of Kouvonen et al.'s social capital at work scale. The findings showed a good performance of the scale in terms of classical theory. While globally acceptable performance was observed from the item response theory, it also allowed identifying some weaknesses in the scale. A ceiling-effect was evident in 8.55% of the participants, which exceeds the expected (a maximum of 5% to be "acceptable")³⁸, and this thus suggests the need to have items that explore higher levels of social capital at work and/or that workers responses were biased.

A differential in the difficulty of items was also established, those related to trust (c1 and c2) being the easiest. While possible complementary items should seek the incorporation of cognitive, structural, linking, bridging and bonding, it is suggested that these latter ones are prioritized in terms of the construction of items of greater difficulty. This should be explored in greater depth as most of the epidemiological studies on social capital use measures based on this type of indicators. If this is repeated in other types of populations, it may be that the attempts to measure social capital have only partially explored its effects. Model 3 shows the presence of dimensions of linking, bridging and bonding of social capital with use of confirmatory factor analysis.

Some methodological issues must be considered to adequately interpret the validity of the results. The sample size can be considered small, however, this turns out to be sufficient for the Rasch analysis, where it is well known that even in samples with less than 150 individuals have more than 99% probability that the estimated value of the difficulty of the item is not further than ± 1 logit of its stable value^46-49; something similar happens in the case of factor analysis, where good estimates can be obtained when high commonalities are present⁵⁰, as seen in this study. In the case of confirmatory factor analysis, it is important to remember that only the Tucker-Lewis index is independent of sample size⁵¹, and good a index was obtained in this analysis. While acknowledging that a larger sample would have allowed a more detailed assessment, all the findings suggest that the sample size was sufficient to have a global scale psychometric assessment.

The results of this study support the conclusion that we can rely on a short Spanish scale which includes the components of linking, bridging and bonding, with acceptable psychometric properties to measure social capital at work in contexts where expected levels are not too high, or when aggregate indicators of a group are intended, for example through medians, means or standard deviations. For social epidemiology, organizational psychology, and occupational health, it is an important step to have an efficient and consistent measurement method based solidly on the theory. This was evaluated using elements of classical theory, confirmatory factor analysis and Rasch method. The cross-cultural adaptation of this scale integrated elements of three complementary approaches that allow greater validity of the results of the analysis of the differential functioning of items⁴⁰.

In conclusion, this scale may be used in future studies with similar populations to the ones studied here taking into account the aforementioned constraints. Experience in this study allows us to point out that when there is a need to use an already-built-scale in a different population or population, it is insufficient to rely on classical test theory. It is advisable, and of low cost and simplicity, to make a more detailed explorations of the psychometric properties by incorporating elements of other psychometric approaches. The incorporation of the Rasch model and confirmatory factor analysis for the psychometric assessment of complex constructs in public health should become a regular practice, which will result in improving the validity of its findings. Having a scale to measure social capital at work, with acceptable psychometric results, will allow research in Spanish-speaking countries on the subject to have greater validity of its findings.

Acknowledgements

The authors wish to thank the directors of institutions and health workers that participated in the study. This study was sponsored by the National Council of Science and Technology - Conacyt, through Grant No. 87719 2008.

References

• 1. Pattussi MP, Moysés SJ, Junges JR, Sheiham A. Capital social e a agenda de pesquisa em epidemiologia. Cad Saúde Pública 2006; 22(8): 1525-46.
• 2. Kawachi I, Berkman L. Social cohesion, social capital, and health. En: Berkman L, Kawachi I (editores). Social epidemiology. New York: Oxford University Press; 2000: 174-190.
• 3. Putnam R. Making democracy work: civic traditions in modern Italy. Princeton, NJ: Princeton University Press; 1993.
• 4. Portes A. Social capital: its origins and applications in modern sociology. Annu Rev Sociol 1998; 24:1-24.
• 5. Gold R, Kennedy B, Connell F, Kawachi I. Teen births, income inequality, and social capital: developing an understanding of the causal pathway. Health Place 2002; 8(2): 77-83.
• 6. Coburn D. Beyond the income inequality hypothesis: class, neo-liberalism, and health inequalities. Soc Sci Med 2004; 58(1): 41-56.
• 7. Idrovo AJ, Ruiz-Rodríguez M, Manzano-Patiño A. Beyond the income inequality hypothesis and human health: a worldwide exploration. Rev Saúde Pública 2010; 44(4): 695-702.
• 8. Kripper CE, Sapag JC. Capital social y salud en América Latina y el Caribe: una revisión sistemática. Rev Panam Salud Publica 2009; 25(2): 162-70.
• 9. Rubio M. Perverse social capital-some evidence from Colombia. J Econ Iss 1997; 31(3): 805-16.
• 10. Idrovo AJ. Capital social, muertes violentas y mortalidad por cáncer en Colombia: una aproximación poblacional. Rev Salud Pública (Bogotá) 2006; 8(1): 38-51.
• 11. Hurtado D, Kawachi I, Sudarsky J. Social capital and self-rated health in Colombia: The good, the bad and the ugly. Soc Sci Med 2011;72(4):584-590.
• 12. Fernandez RM, Castilla EJ, Moore P. Social capital at work: networks and employment at a phone center. Am J Sociol 2000; 105(5): 1288-356.
• 13. Oksanen, T. Workplace social capital and employee health. Turku, Finland: University of Turku; 2009.
• 14. Kouvonen A, Kivimäki M, Vahtera J, Oksanen T, Elovainio M, Cox T, et al. Psychometric evaluation of a short measure of social capital at work. BMC Public Health 2006; 6: 251.
• 15. Moore S, Haines V, Hawe P, Shiell A. Lost in translation: a genealogy of the "social capital" concept in public health. J Epidemiol Community Health 2006; 60(8):729-34.
• 16. Szreter S, Woolcock M. Health by association? Social capital, social theory, and the political economy of public health. Int J Epidemiol 2004; 33(4):650 - 67.
• 17. Moorman RH. Relationship between organizational justice and organizational citizenship behaviors: Do fairness perceptions influence employee citizenship? J Appl Psychol 1991; 76(6): 845-55.
• 18. Siegrist J, Starke D, Chandola T, Godin I, Marmot M, Niedhammer I, Peter R. The measurement of effort-reward imbalance at work: European comparisons. Soc Sci Med 2004; 58(8): 1483-99.
• 19. Karasek RA, Brisson C, Kawakami N, Houtman I, Bongers P, Amick B. The job content questionnaire (JCQ): an instrument for internationally comparative assessments of psychological job characteristics. J Occup Health Psychol 1998; 3(4): 322-55.
• 20. Spielberger CD, Gorsuch RL, Lushene R, Vagg PR, Jacobs GA. Manual for the State-Trait Anxiety Inventory (form Y) Palo Alto, CA: Consulting Psychologists Press Inc; 1983.
• 21. Kennedy BP, Kawachi I, Brainerd E. The role of social capital in the Russian mortality crisis. World Development 1998; 26(11): 2029-43.
• 22. Veenstra G. Social capital, SES and health: an individual-level analysis. Soc Sci Med 2000; 50(5): 619-29.
• 23. Lindström M, The Malmö Shoulder-Neck Study Group. Psychosocial work conditions, social participation and social capital: A causal pathway investigated in a longitudinal study. Soc Sci Med 2006; 62(2): 280-91.
• 24. Oksanen T, Kouvonen A, Kivimäki M, Pentti J, Virtanen M, Linna A, et al. Social capital at work as a predictor of employee health: Multilevel evidence from work units in Finland. Soc Sci Med 2008; 66(3): 637-49.
• 25. Liukkonen V, Virtanen P, Kivimäki M, Pentti J, Vahtera J. Social capital in working life and the health of employees. Soc Sci Med 2004; 59(12): 2447-58.
• 26. Suzuki E, Fujiwara T, Takao S, Subramanian SV, Yamamoto E, Kawachi I. Multi-level, cross-sectional study of workplace social capital and smoking among Japanese employees. BMC Public Health 2010; 10: 489.
• 27. Narayan D, Cassidy MF. A dimensional approach to measuring social capital: development and validation of a social capital inventory. Curr Sociol 2001; 49(2): 59-105.
• 28. Davies H. Falling public trust in health services: implications for accountability. J Health Serv Res Pol 1999; 4(4):193-4.
• 29. Koeck C. Time for organisational development in healthcare organisations. Br Med J 1998; 317(7168):1267-8.
• 30. Moss F, Garside P, Dawson S. Organisational change: the key to quality improvement. Qual Health Care 1998; 7(suppl): s1-2.
• 31. Brislin R. Back-translation for cross-cultural research. J Cross Cult Psychol 1970; 1(3):185-216.
• 32. Muñiz J. Classical test models. En: Everitt BS, Howell DC (eds.). Encyclopedia of statistics in behavioral science Vol. 1. Chichester: John Wiley and Sons; 2005: 278-82.
• 33. Widaman KF. Common factor analysis versus principal component analysis: Differential bias in representing model parameters? Multiv Behav Res 1993; 28(3): 263-311.
• 34. Cedillo L. Estudio de los factores psicosociales laborales entre trabajadoras de la industria maquiladora de exportación en Sonora México. En: Juárez-García A, Ramírez JA (editores). Estrés Psicosocial del trabajo: dónde y quiénes estamos en México. Compartiendo experiencias con investigadores norteamericanos. México: FES Iztacala UNAM; 2005.
• 35. Juárez-García A. Factores psicosociales y personalidad en relación a la salud laboral: desarrollo de un modelo (Tesis). México: Facultad de Psicología UNAM, 2005.
• 36. Bond TG, Fox CM. Applying the Rasch model: Fundamental measurement in the human sciences. Mahwah, NJ, LEA; 2001.
• 37. Masters GN. A Rasch model for partial credit scoring. Psychometrika 1982; 47(2): 149-74.
• 38. Fisher WP. Rating scale instrument quality criteria. Rasch Measure Transac 2007; 21:1095.
• 39. Linacre JM. WINSTEPS^TM Rasch measurement computer program. Beaverton, Oregon: Winsteps.com; 2009.
• 40. Tomás-Marco I, González-Romá V, Gómez Benito J. Teoría de respuesta al ítem y análisis factorial confirmatorio: dos métodos para analizar la equivalencia psicométrica en la traducción de cuestionarios. Psicothema 2000; 12(Supl. 2): 540-4.
• 41. Schumacker RE, Lomax RG. A beginner´s guide to structural equation modeling. New York: Psychology Press; 2004.
• 42. Hair JF, Anderson RE, Tatham RL, Black WC. Análisis multivariante. Madrid, España: Prentice Hall; 1999.
• 43. Arbuckle JL. AMOS (Version 4.01) Chicago: SmallWaters Corp; 1994.
• 44. Kaiser HF. An index of factor simplicity. Psychometrika 1974; 39(1): 31-6.
• 45. Kenny DA, McCoach DB. Effect of the number of variables on measures of fit in structural equation modeling. Struct Equat Model 2003; 10(3): 333-51.
• 46. Linacre JM. Sample size and item calibration stability. Rasch Measure Transac 1994; 7(4): 328.
• 47. Wright BD, Tennant A. Sample size again. Rasch Measure Transac 1996; 9(4): 468.
• 48. Draxler C. Sample size determination for Rasch model tests. Psychometrika 2010; 75(4): 708-24.
• 49. Smith AB, Rush R, Fallowfield LJ, Velikova G, Sharpe M. Rasch fit statistics and sample size considerations for polytomous data. BMC Med Res Methodol 2008; 8: 33.
• 50. McCallun RC, Widaman KF, Preacher KJ, Hong S. Sample size in factor analysis: The role of model error. Multiv Behav Res 2001; 36(4): 611-37.
• 51. Marsh HW, Balla JR, McDonald RP. Goodness-of-fit indexes in confirmatory factor analysis: the effect of sample size. Psychol Bull 1988; 103(3): 391-410.

Publication Dates

• Publication in this collection
  18 Oct 2012
• Date of issue
  Sept 2012

History

• Received
  05 Sept 2011
• Accepted
  06 Feb 2012