Validation of a Multidimensional Social Cohesion Scale: A Case in Urban Areas of Mexico

Abstract

People have been interested in social cohesion and its implications in different areas of social life from the classic sociology authors until today. Besides its multidimensional nature, this complex construct also faces the issue of measurement. For this reason, the objective of this article is to adapt and validate a scale that measures in a multidimensional way social cohesion for urban areas. The results obtained through Cronbach’s α coefficient, McDonald’s Ω coefficient, and confidence intervals for both coefficients show that the resulting questions have high levels of discrimination and an acceptable reliability, so the scale developed is valid methodologically.

Keywords

social cohesion micro meso and macrolevels scale validation urban areas México

The idea of social cohesion and its consequences has been central to sociology (Durkheim 1951; Giddens 2008; Simons, Vermeulen, and Knoben 2016). Explanations of the factors that create it vary according to theoretical schools and methodological perspectives, but there is a common denominator: Social cohesion is built around the problem of the construction and reproduction of the social order, that which unites a society without the need for coercion (National Council for the Evaluation of Social Development Policy 2015a). To reach this state of unity, there must be a sense of belonging, trust in others and in institutions, and a willingness to assist and to participate (Chan, To, and Chan 2006).

Social cohesion has brought together under the same umbrella today’s most pressing topics (Bernard 2000): unemployment, poverty, discrimination, exclusion, a lack of trust in political institutions, and others. It is not surprising that much of the effort to measure and account for cohesion comes from governments and international institutions such as the Canadian federal government’s “Social Cohesion Network,” the European Union (Jeannotte 2000), the Organization for Economic Co-operation and Development, and the World Bank (Ritzen, Easterly, and Woolcock 2000), to name a few.

Associated with the need to overcome economistic approaches to development and to consider the importance of creating social value, the concept of social cohesion has seen considerable growth over the last few decades and has been related to social equality (Economic Commission for Latin America and the Caribbean 2007) and the sustainability of economic growth (Organization for Economic Co-operation and Development 2011). In the case of European societies, it could be explained by the tradition of social citizenship and the intrinsic relationship between social inclusion and the provision of mechanisms of integration and complete membership in society. From the welfare state perspective, social cohesion synthesizes mechanisms of integration and well-being with the social belonging of individuals (Economic Commission for Latin America and the Caribbean 2007:16).

The Multidimensionality of Social Cohesion

In cohesive societies, work is done to achieve “the wellbeing of all members,” “exclusion is fought against,” “trust is promoted,” and there is “an opportunity for upward social mobility” (Organization for Economic Co-operation and Development 2011:53). In Europe, the idea is geared toward reducing inequality and in general toward protecting against social exclusion (Berger-Schmitt 2000; Comisión Europea 2004). Besides this macro approach, social cohesion has also been considered for its importance in the micro- and meso-social arenas (Whelan and Maître 2005).

Along these lines, Whelan and Maître (2005) show that networks of links between individuals can be in three social settings: at the micro-, meso-, and macro-levels; nevertheless, it is difficult to clarify where one level ends and the next begins, due to their characteristics and the effects linked to them. The micro-level is seen in relationships with primary groups such as the family and close friends. The meso-level includes interactions with secondary groups in the community setting such as neighbors and like-minded people with shared interests and values. The macro-level refers to the sense of belonging to society and to institutional trust; it includes participation in social or political organizations, or both (civil or religious associations, unions, and political parties).

Research has studied social cohesion in a fragmented way; for example, the community setting or meso-level has been studied because of its implications on territorial development and evolution (Esparcia, Escribano, and Serrano 2016; Granovetter 1973), organizational behavior (Simons et al. 2016), and public safety (Lee 2000) but also because of its favorable effects on individual health and well-being (Cagney et al. 2009; Cohen et al. 2005; Franzini et al. 2005). The theory of collective efficacy explains this relationship better, by specifying the impact of the neighborhood factors (social resources such as mutual trust, solidarity, and expectations for action—informal social control) on the individual-level results (Sampson, Raudenbush, and Earls 1997). To a lesser degree, some authors consider the concept’s multidimensional nature (Dickes, Valentova, and Borsenberger 2010; Dickes and Valentova 2013). Although these authors are aware of the micro-, meso-, and macro-levels of social cohesion, the data available in the European Values Study do not cover these levels.

An approach to social cohesion based on these settings or levels (micro-, meso-, and macro-social) helps us understand its multidimensional nature, its objective and subjective components (Chan et al. 2006), and the many characteristics and dimensions where it operates—from common values and identity, sensations of belonging, citizen participation in common organizations, and community interaction and cooperation to aspects such as political legitimacy and democratic participation, which are fundamental in uniting a society without using coercion (Vergolini 2011).

Closely related to the several existing approaches to this construct and to its multidimensional nature is the issue of how to measure it (Vergolini 2011). Social cohesion has been measured with either aggregate or individual data. In the first approach, it is identified as a property of the social system, so it is measured at the macro-level, and the main indicators used are crime rates, unemployment rates, the number of voluntary cultural associations (Rajulton, Ravanera, and Beaujot 2007), and even income inequality (National Council for the Evaluation of Social Development Policy 2010). From the individualist approach, it is the result of attitudes, behaviors, and social interactions (Sampson 1991; Villareal and Silva 2006) that take place at the micro-level, and it is seen in individuals’ perception of different levels of cohesion in any given context.

Two of the main categories or factors that make up the construct from the individualist approach are civic integration and relative density. According to Vergolini (2011), the former includes trust in institutions, interpersonal trust, and the perception of quality of services. The latter includes participation in associations, the desire to cooperate, and isolation. Likewise, services in the neighborhood, friendship ties and family relations, and participation in organizations have been included (Sampson and Groves 1989). Collective efficacy has also been established as social cohesion combined with informal social control (Sampson et al. 1997).

Considering the aspects mentioned (Chan et al. 2006; Whelan and Maître 2005), we define social cohesion as the attribute or state of things that includes interactions among members of societies at the micro-, meso-, and macro-levels. These interactions have subjective components (referred to as norms, feelings of trust, a sense of belonging, and a willingness to assist) and objective components (including real cooperation and participation at the three levels).

Taking into account the multidimensional nature of social cohesion, and recognizing its implications for the different levels of social life, the objective of this research is to adapt and validate a scale that measures in a multidimensional way the social cohesion for urban areas of Mexico.

Method

Context

According to the National Institute of Statistics and Geography (National Institute of Statistic and Geography 2011), Nuevo León has the eighth-largest population in the country and ranks 15 of the 32 states in terms of population density (National Institute of Statistic and Geography 2014). It is the state with the lowest percentage of poverty at different levels including extreme and the fourth in income inequality as calculated by the Gini coefficient (National Council for the Evaluation of Social Development Policy 2015b). Its urban area¹ is made up mainly of 10 municipalities (Apodaca, Cadereyta Jiménez, García, General Escobedo, Guadalupe, Juárez, Monterrey, San Nicolás de los Garza, San Pedro Garza García, and Santa Catarina) where 84.79 percent of the state population lives (National Institute of Statistic and Geography 2015).

These municipalities are characterized by very low marginalization levels (San Pedro Garza García [−2.22], San Nicolás de los Garza [−2.10], Guadalupe [−1.92], Monterrey [−1.90], Apodaca [−1.89], Santa Catarina [−1.85], General Escobedo [−1.75], García [−1.62], Juárez [−1.62], and Cadereyta Jiménez [−1.56]). Less than 5.8 percent of the population lives in localities of less than 5,000 inhabitants (National Population Council 2015). In addition, their level of violence is low; according to the index of municipal violence of Mexico’s Citizens’ Council for Public Security and Criminal Justice (Seguridad, Justicia, and Paz 2015), the violence in 229 municipalities, which have more than 100,000 inhabitants, ranged from 2.32 to 72.60. The municipalities selected for this study have an index ranging from 9.45 to 19.36.

Sample and Participants

Using a combination of purposive and randomized sampling, 156 questionnaires were applied to residents of the urban area of the city of Monterrey, in Nuevo León, Mexico. The size of our sample is justified by three reasons; first, the literature (Gorsuch 1983; Guilford 1954; Lindeman, Merenda, and Gold 1980; Loo 1983) recommends between 100 and 200 observations, based on the argument that the correlation coefficient in the sample is an adequate estimator of the population correlation coefficient when the sample reaches this size (Guadagnoli and Velicer 1988). Second, the sample size depends on the number of questions on the scale; in this case, the ratio between the number of questions and the size of the sample needed is at least 1:4 (Rumel 1970) to 1:10 (Schwab 1980). In addition, several studies have used small samples in scale validation (Renshaw 2015; Schmidt et al. 2015; Usluel et al. 2016).

Third, in studies with results obtained in scale simulations (Guadagnoli and Velicer 1988), it was found that if in a factor analysis the components have four or more questions with factor loadings above .60, the results are valid regardless of the sample size; likewise, if the factors are made up of many questions (10–12) with low factor loadings, the results are valid for a sample size of at least 150. Furthermore, if the results of the factor analysis show that the construct has a small number of factors, as well as moderate and high communalities—as would probably be obtained in a sample of between 100 and 200 entries—the population factors are represented adequately (MacCallum et al. 1999). In this investigation, we comply with these three criteria, so we can ensure that the sample size is adequate for the validation of the scale.

With purposive form, 10 municipalities with the lowest marginalization index were selected. In each municipality, a number of colonies was selected in proportion to the total population of the municipality. The colonies were chosen randomly, with a probability proportional to the population they contained. In each of these colonies, the home to be interviewed was chosen randomly, and all the homes had the same probability of being chosen. In each home, the head of household was interviewed when it was possible; otherwise, a family member at least aged 18 was interviewed. The information obtained comes from 129 different colonies located in 10 municipalities of the urban area of Nuevo León, Mexico.

Of those surveyed, 98 were women (62.82 percent) and 58 were men (37.18 percent). The average years of schooling of those surveyed was 12. Forty percent of the participants have undergraduate studies, 25 percent have high school, and 35 percent have elementary or junior high school level, so all those surveyed can read. Of the participants, 55.56 percent come from a nuclear-family home, 23.53 percent come from an extended nuclear family, 16.99 percent come from a compound family, 2.61 percent come from a one-person household, and 1.31 percent come from a coresident home. On average, the homes of those surveyed are made up of four people.

According to the methodology to determine socioeconomic level (Mexican Association of Market Research Agencies 2008), 64.86 percent of those surveyed came from a high socioeconomic level, 14.41 percent from a middle-high level, 6.31 percent from a middle level, 8.11 percent from a middle-lower level, and 6.31 percent from a lower level. No homes were reported from an extreme poverty socioeconomic level. Of those families surveyed, 75 percent had a male head of household and 25 percent had a female head of household; they were on average 47 years old and had 11 years of schooling; 31.26 percent have undergraduate studies, 25 percent have high school, 40.63 percent have elementary and junior high education, and 3.13 percent of heads of household have no schooling.

The Scale of Social Cohesion

Based on our definition of social cohesion, the instrument used was designed to analyze the multifactorial character of the concept, based on 37 items (Online supplemental material). Table 1 shows a theoretical–methodological summary to explain the multidimensional proposal of the validated measurement scale.

Table 1.
Theoretical–Methodological Summary of the Validated Measurement Scale.

Levels Objective Components Subjective Components

Micro Belonging to interest groups and networks of friends

Willingness to support these networks

Meso Links to neighborhood/community members Norms and values of neighbors and of the community

Willingness to assist the neighborhood/community Trust in neighborhood networks

Macro Belonging to institutions/organizations of interest

Willingness to help solve city problems Trust in civil associations/political, religious, union, financial, judiciary, and public order institutions

Source: Authors’ elaboration.

For the construction of the scale, four surveys were taken and were adapted as follows: Questions 1–19 of our instrument come from the “Social Capital Survey” (National Survey of Social Capital 2011); they were adapted to Likert-type questions with four possible answers (questions 1–15) and dichotomous questions (items 16–19). Questions 20–25 come from the “National Survey of Victimization and Perception of Public Security” (2014), and the responses were adapted to dichotomous format. Questions 26–34 come from the survey “Prevención de la Violencia en el Valle de Aburra” (Survey of Violence Prevention in the Aburra Valley 2003). After adaptation, nine Likert-type questions with three possible answers were obtained. Finally, the fourth survey used was “The Victimization Survey in Belo Horizonte” (2002); questions 35–37 have been translated and adapted, resulting in Likert-type questions with six or seven possible answers.

The final instrument uses various response formats, like other instruments such as the Neighborhood Environment Walkability Scale, the Dyadic Adjustment Scale, and the Locke-Wallace short marital-adjustment scale, which have been validated by the factor analysis method in many studies (Cuenca Montesino et al. 2013; Cerin et al. 2009; Jiang et al 2013).

To assess the understandability of the questions and the possible difficulties when responding to the instrument, a pilot test was carried out. After this pretest, some questions were corrected with an expert opinion, and a second questionnaire was created. Another pilot test was carried out with the second version, and no difficulties in answering the questions were observed. The data were collected from May to October 2015. The participants were informed of the voluntary nature, anonymity, and confidentiality of the responses to the survey, which was approved by the ethical commission of the Iberoamericana University in Mexico.

Techniques Used for the Validation of the Scale

The validation process of the social cohesion scale went through four phases, and all estimates were made using R software (version 3.1.2), which allows us to deal adequately with the ordinal character of the scale.

Phase I. With the information gathered, the means, standard deviations, skewness, and kurtosis of each item were calculated; this process allowed us to verify that no item had problems in being included in the factor analysis.

Phase II. Next, basic sample adequation tests were carried out to verify that the factor analysis techniques had been correctly applied to the gathered information. Basic tests assess the suitability of the correlation matrix of the questions with two statistics: Bartlett’s sphericity test and the Kaiser–Meyer–Olkin test (KMO). Bartlett’s sphericity test allows us to contrast the null hypothesis that the correlation matrix is an identity matrix, in which case there would be no significant correlations between the items, and a factor analysis model would not be pertinent. Bartlett’s test’s statistic is as follows:

$B = - (n - 1 - (\frac{2 p + 5}{6})) ln | R^{} | .$
1

Under the null hypothesis, it is distributed as a chi-squared variable with $(\frac{p^{2} - p}{2})$ degrees of freedom; n is the sample size, p is the number of questions, and $| R^{} |$ is the determinant of the correlation matrix. If the null hypothesis is accepted (low test value linked to a high significance level), there would be little or no correlation among the questions, and any type of factor analysis should be questioned.

On the other hand, the KMO test quantifies the suitability of the information to carry out a factor analysis; it compares the values of the correlation coefficients observed between the variables with the partial correlation coefficients between the variables (Cerny and Kaiser 1977). The KMO statistic is calculated with

$KMO = \frac{\sum \sum_{i \neq j} r_{j i}^{2}}{\sum \sum_{i \neq j} r_{j i}^{2} + \sum \sum_{i \neq j} a_{j i}^{2}},$
2

where r_ji is the correlation coefficient observed between the i and j variables. a_ji is the partial correlation coefficient between variables i and j, meaning that it measures the correlation between variables i and j once the influence of the other variables on them has been eliminated. In general, a KMO > .7 value indicates high correlation between the questions and the suitability of applying a factor analysis to the data.

It is important to consider that the variables must be intercorrelated, but they should not correlate too highly (extreme multicollinearity and singularity) because it would cause difficulties in determining the unique contribution of the variables to a factor. The multicollinearity can be detected via the determinant of the correlation matrix; if the determinant is greater than .00001, there is no multicollinearity problem (Field 2000).

Phase III. After sample adequation tests, exploratory factor analysis with maximum likelihood extraction and Varimax rotation method were conducted for scale validity. It allows us to identify the number of underlying factors that the designed scale is attempting to measure and can be used to assess which variables to drop from the model. In many social studies, the criteria used in exploratory factor analysis to determine the factors and their items include the following: factors have eigenvalues greater than 1.0, each factor should have at least three items, and the items should have factor loadings greater than .4 (Wang and Chui 2017). Other authors suggest that pattern coefficients higher than .30 are satisfactory (Alkis, Kadirhan, and Sat 2017; Stevens 2009); Yong and Pearce (2013) consider that a rotated factor loading would need to be at least .32 to be considered statistically meaningful because a factor loading of .32 gives us approximately 10 percent of the overlapping variance, $% o v e r l a p p i n g v a r i a n c e = {(F a c t o r l o a d i n g)}^{2}$ .

Principal component factor analysis with iteration and orthogonal Varimax rotation was also used to confirm and establish the structure and validity of the scale. Principal components analysis is used to extract maximum variance from the data set with each component, thus reducing a large number of variables into a smaller number of components (Yong and Pearce 2013). The factors identified by this method correspond to the eigenvectors of correlation matrix.

Meanwhile, there are multiple goodness-of-fit tests that can be used to evaluate the model’s fit to the data. In this study, the following measures were assessed: degree of freedom (gl), root-mean-square residual (RMR), nonnormed fit index (NNFI), and model chi-square (χ²). The model indicates a good fit to the data when NNFI is greater than .97, RMR is between 0 and .05, and model chi-square is not significant or $χ^{2} / g l < 3$ (Browne and Cudeck 1993; Schermelleh-Engel, Moosbrugger, and Müller 2003).

To carry out the analysis, the ordinal character of the scale was considered. The standard procedure of estimation used by the statistical packages is to carry out the factor analysis based on Pearson’s correlation matrix; it is correct when talking about continuous scales, but Pearson’s correlations are product–moment correlations that do not take into account the ordinal character of some scales. Therefore, in ordinal scales, Pearson’s correlations matrix can be a distorted matrix (Oliden and Zumbo 2008). Theoretically, if the instrument designed has ordinal-type scales, the matrix used in the analysis must be the polychoric correlations matrix, which estimates the linear relation between two unobserved continuous variables that lie beneath two observed ordinal variables that are manifest indicators of the latter (Flora and Curran 2004).

Phase IV. The goal of this phase was to show the validity and reliability of the scale developed. The validity refers to the instrument’s ability to measure the construct it attempts to quantify, and reliability refers to the property to show similar, error-free results in repeated measurements (Kaplan and Saccuzzo 2006).

To determine the reliability of the scale, two internal consistency measurements were used: Cronbach’s (1951) α coefficient, and McDonald’s (1970) Ω coefficient, given these names because they refer to the degree at which the items on a scale correlate among themselves, and they explore the magnitude to which they measure the same construct (Streiner 2003).

Cronbach’s α coefficient is defined by the elements of the factor analysis (Gadermann, Guhn, and Zumbo 2012) as

$α = [\frac{p}{p - 1}] [\frac{p γ_{p r o m}^{2} - h_{p r o m}^{2}}{p γ_{p r o m}^{2} + u_{p r o m}^{2}}],$
3

where p is the number of items that make up the factor, γ_prom is the average of the factor loadings, $h_{p r o m}^{2}$ is the average of the communalities of the items that make up a factor, and $u_{p r o m}^{2}$ is the average of the uniqueness, where communality h² and uniqueness u² of an item add up to 1. We should mention that the communality is the proportion of the variance explained by factors or constructs identified in a variable. There are other equivalent definitions in terms of the correlations between the items (Cronbach 1951; Li, Rosenthal, and Rubin 1996; Osburn 2000; Van-Zyl, Neudecker, and Nel 2000).

Meanwhile, the Ω coefficient (McDonald 1999; Tejedor, García-Valcarcel, and Prada 2009) is calculated as follows:

$Ω = 1 - \frac{n - \sum h_{j}^{2}}{n + 2 \sum r_{j h}},$
4

where, n is the number of items that make up the factor, h_j is the estimated communality of item j, and r_jh represents the correlation between items j and h.

Because it is an ordinal scale, we recommend using the polychoric correlations matrix to calculate the internal consistency coefficients; in this case, they are called ordinal α and ordinal Ω. They are unbiased estimators of theoretical reliability of ordinal data and tend to estimate reliability more exactly (Gadermann et al. 2012).

One of the main problems in the scale validation studies is to report only the point estimate of α and Ω coefficients (Raykov 2002; Terry and Kelley 2012), and very rarely the level of confidence of the values that the coefficients show, in order to incorporate the sensitivity that they present to the number of items, the size of the sample, and the intercorrelations of the items (Iacobucci and Duhachek 2003). With the goal of obtaining a level of confidence in the point estimator, confidence intervals on the possible values of ordinal α and Ω were estimated.

The confidence interval expresses the range of possible values for α and Ω associated with a level of confidence. All the values that make up the interval are statistically possible. There are several methods for building confidence intervals of Cronbach’s α; one of them is the bootstrap method (Iacobucci and Duhachek 2003). This method involves repeated resampling with replacement from a sample to obtain an empirical distribution of an estimator such as ordinal α and ordinal Ω. Once the distribution has been obtained, the confidence interval can be built directly from the empirical distribution.

Results

In Table 2, the mean, standard deviation, skew, and kurtosis of each item are given. As it can be seen, 18 of them show positive skew, meaning that the values tend to gather more on the left side of their respective means; the other items show negative skew. Regarding magnitude, except for questions 16 and 17, all of them have skew lower than three in absolute value, which satisfies the normality assumption (Marôco 2010). With respect to the kurtosis, questions 3, 6, 16, 17, 21, 35, 36, and 37 have positive values and leptokurtic distribution. Also, except for question number 16, all of them have a kurtosis below 10 in absolute value, so it is correct to assume their normality (Marôco 2010).

Table 2.
Statistical Description of Items.

Question Mean Standard Deviation Skew Kurtosis

Answer range from one to four

1 3.013 1.087 −0.75 −0.79

2 2.045 0.792 0.15 −0.88

3 1.587 0.737 1.01 0.22

4 2.903 0.828 −0.57 −0.07

5 2.039 0.889 0.26 −1.05

6 1.572 0.724 1.05 0.41

7 2.189 0.793 0.05 −0.72

8 1.927 0.841 0.40 −0.86

9 2.112 0.865 0.15 −0.98

10 2.584 0.883 −0.34 −0.64

11 2.032 0.768 0.29 −0.48

12 1.901 0.814 0.40 −0.83

13 2.074 0.874 0.22 −0.97

14 2.047 0.844 0.25 −0.88

15 2.247 0.843 −0.01 −0.86

Answer range from one to two

16 1.940 0.238 −3.68 11.65

17 1.921 0.271 −3.08 7.53

18 1.748 0.435 −1.13 −0.72

19 1.715 0.453 −0.94 −1.12

A 1.623 0.256 −1.16 −1.56

B 1.545 0.432 −2.54 −2.34

C 1.643 0.345 −1.05 −1.80

20 1.462 0.500 0.15 −1.99

21 1.840 0.370 −1.82 1.34

22 1.410 0.493 0.36 −1.88

23 1.686 0.466 −0.79 −1.38

24 1.583 0.495 −0.33 −1.90

25 1.763 0.427 −1.22 −0.51

Answer range from one to three

26 2.500 0.586 −0.68 −0.54

27 2.329 0.717 −0.57 −0.91

28 1.923 0.744 0.11 −1.20

29 2.377 0.617 −0.44 −0.69

30 2.007 0.807 −0.01 −1.47

31 1.929 0.817 0.13 −1.50

32 2.355 0.722 −0.64 −0.87

33 2.294 0.785 −0.56 −1.18

34 2.274 0.837 −0.54 −1.37

Answer range from one to seven

35 2.37 1.81 1.41 1.03

36 2.12 1.61 1.73 2.25

Answer range from one to six

37 1.51 1.21 2.57 5.81

Source: Authors’ elaboration.

The factor analysis was started with 40 items; the adequation of sample gives a KMO = .7113, and the Bartlett test shows a significance level of p < .00037 (B = 920 with 780 degrees of freedom), so the exploratory factor analysis was applied to the 40 items, and four factors were retained according to the eigenvalue greater than 1 (Table 3). It was seen that one item had a pattern coefficient lower than .40, and two other items loaded on two factors. For this reason, the following items were dropped: (a) Are you a member of any group of neighbors or in your colony? (b) Are you a member of any political group? (c) Are you a member of any trade union?

Table 3.
Discriminant Matrix on Exploratory Factor Analysis.

Item Trust in Institutions Participation in Organizations Collective Efficacy Friendship Ties

1 .28 .14 −.22 .53

2 .63 .08 −.21 −.01

3 .70 .20 .10 .05

4 .55 −.01 −.05 .21

5 .78 .01 .09 .02

6 .77 .09 .15 −.10

7 .57 −.03 −.17 −.13

8 .80 .11 .02 −.11

9 .75 .11 .06 .03

10 .59 .04 −.05 .14

11 .53 −.11 .10 −.04

12 .80 .09 .13 −.04

13 .76 .12 .12 .11

14 .80 .08 .13 −.02

15 .64 .12 −.21 .10

16 .14 −.06 .59 −.08

17 .13 −.03 .62 .14

18 −.08 .03 .75 −.10

19 −.04 −.05 .82 .03

A .21 .12 .38 .11

B .42 .12 .41 .09

C .11 .42 .40 .03

20 −.06 .57 −.12 −.21

21 .10 .50 −.13 .25

22 −.15 .60 .03 −.25

23 .20 .54 −.15 −.21

24 .06 .48 .14 −.01

25 .18 .47 .01 −.11

26 −.01 .54 −.23 .03

27 .05 .67 −.03 .15

28 .10 .78 −.07 −.01

29 .10 .66 −.11 .11

30 .09 .80 .09 .13

31 .07 .68 .09 .21

32 −.08 .60 .13 .19

33 .11 .64 −.02 .06

34 .09 .71 −.14 .17

35 −.10 .03 −.18 .77

36 −.03 .06 .08 .77

37 −.02 .11 .16 .64

Note: boldface values represent the highest factor loading of each item.

Source: Authors’ elaboration.

With respect to the 37 items, the analysis of adequation of the sample gives a value of KMO = .7703, which indicates a high level of correlation between the questions and suggests that a factor analysis with the data should be done. The statistic of Bartlett’s sphericity test shows a value of B = 1,583, with 666 degrees of freedom and a significance level of p < .00001, so we reject the null hypothesis, which establishes that the correlations matrix is the identity matrix, showing the ability of the data to be submitted to a factor analysis. Likewise, the interitem polychoric correlation matrix for all items is presented in Table 4; the determinant of this matrix is 1.4 × 10⁻⁵, which suggests there is no multicollinearity problem.

Table 4.
Interitem Polychoric Correlation Matrix

Note: italicized values indicate the item number.

Source: Authors’ elaboration.

The principal component analysis with Varimax rotation was employed to confirm the four-factor structure; the extraction of factors required seven interactions, and the rotation of factor matrix required six interactions. The four-factor structure explains 73.72 percent of the total variance (Table 5); the first factor has an eigenvalue of 7.034, explains 30.83 percent of the variance, and includes 14 items about trust in institutions. The factor loadings go from .54 to .83, with only one question having a factor loading of .40. The second component groups the questions on participation in organizations, which had an eigenvalue of 7.003, explains 23.99 percent of the variance, and includes 15 questions—all with high factor loadings, ranging from .55 to .85, and only one with a factor loading of .43.

Table 5.
Factor Loadings, Eigenvalues and Variance Explained.

Item Trust in Institutions Participation in Organizations Collective Efficacy Friendship Ties Communalities

1 .45 .36

2 .64 .51

3 .73 .59

4 .40 .21

5 .81 .66

6 .81 .68

7 .59 .39

8 .83 .71

9 .76 .60

10 .57 .36

11 .54 .32

12 .82 .69

13 .78 .65

14 .82 .69

15 .66 .51

16 .80 .70

17 .81 .67

18 .78 .66

19 .88 .78

20 .65 .75

21 .43 .42

22 .72 .65

23 .59 .61

24 .55 .34

25 .61 .57

26 .56 .37

27 .70 .59

28 .82 .70

29 .70 .52

30 .85 .78

31 .75 .67

32 .68 .55

33 .73 .54

34 .78 .66

35 .70 .60

36 .66 .47

37 .69 .51

Eigenvalues of each factor

Factor 1 Factor 2 Factor 3 Factor 4

7.034 7.003 2.678 1.602

Proportion of variance explained for each factor

Factor 1 Factor 2 Factor 3 Factor 4 Accumulated

.3083 .2399 .0949 .0941 .7372

Source: Authors’ elaboration.

The third component includes four questions on collective efficacy with very high factor loadings, all above .78. This factor explains 9.49 percent of the variance and has an eigenvalue of 2.678. Finally, the fourth factor contains questions on friendship ties, which have an eigenvalue of 1.602, explaining 9.41 percent of variance. This factor includes four questions with adequate factor loadings, ranging from .45 to .70. In general, each question in its respective main factor reaches a saturation of more than .40, satisfying a conventional criterion in this type of analysis.

Likewise, in the correlation matrix (Table 4), four clusters of variables with high intercorrelations are represented; it could be manifestations of the same underlying variable. Regarding residual correlations, which is the matrix of differences between the reproduced and original correlations, for any given pair of variables, the reproduced correlation is the product of the factor loadings on the first factor plus the product on the second factor, and so on, for all factors. The closer the residuals are to zero (i.e., low or nonsignificant), the more confidence the researcher has in his or her selection of the number of factors in the solution (Field 2000). In this analysis, there are 27 nonsignificant residuals greater than .05 (4 percent), which is a low percentage. The four-factor model fit index values were found to be NNFI = .99, $χ^{2} / g l = 1.076$ ( $χ^{2} = 564, g l = 524, p = .11$ ), indicating a good fit to the data, and RMR = .06, indicating a moderate fit.

Table 6 shows the point estimator of the internal consistency coefficient of each factor, nonordinal Cronbach’s α, $α_{N O - O R D}$ , of .92, .87, .75, .68, and of the complete scale of .85, respectively. Even though the instrument does not satisfy the assumption of continuous scales on which the nonordinal α coefficient is based, the values obtained for the first three factors are greater than .75, which, according to Nunnally and Bernstein (1994), indicates a sufficient level of reliability. Also, the complete instrument presents a coefficient of .85, which indicates a good level (George and Mallery 2003).

Table 6.
Point and Intervals Estimation of Cronbach’s α Coefficient

Factors Nonordinal α Coefficient $α_{N O - O R D}$ Interval at 95 Percent of $α_{N O - O R D}$ Pearson’s Correlation Average of Questions Ordinal α Coefficient α_ORD Interval at 95 Percent of α_ORD Attenuation Percent: $100 \times (\frac{α_{N O_O R D -} α_{O R D}}{α_{O R D}})$

Trust in institutions .92 [.89, .93] .44 .94 [.92, .96] −2.12

Participate in organizations .87 [.84, .90] .30 .92 [.88, .95] −5.43

Collective efficacy .75 [.67, .80] .43 .94 [.89, .98] −20.21

Friendship ties .68 [.60, .76] .35 .76 [.68, .84] −10.52

Entire scale .85 [.81, .88] — .89 [.86, .92] −4.49

Source: Authors’ elaboration.

Table 6 also shows the ordinal α coefficient, α_ORD, calculated based on the polychoric correlations matrix. It is a more exact estimation of the internal consistency due to the instrument’s ordinal character. The values of the ordinal α are higher than the nonordinal α, as the theory states (Gadermann et al. 2012); thus, trust in institutions, participation in organizations, and collective efficacy factors have excellent values (George and Mallery 2003) of .94, .92, and .94, respectively; the factor of friendship ties has a sufficient coefficient of .76, and the complete scale has a coefficient of .89. In the last column, the attenuation percent is established, meaning the correction percent of estimation error between the nonordinal α and the ordinal α. The most relevant percentages can be seen in collective efficacy and friendship ties factors at 20.21 percent and 10.52 percent, respectively.

Regarding the level of reliability of values obtained, the confidence intervals of the ordinal α coefficient are reported, having been calculated with the bootstrap method (Dunn, Baguley, and Brunsden 2014; Iacobucci and Duhachek 2003), with a number B = 1,000 simulations. The meaning of the level of reliability is that, when the sampling of the instrument is repeated several times in the population, 95 percent of ordinal α coefficient values will fall within the interval confidence obtained.

The results obtained prove that 95 percent of times, the trust in institutions factor will have excellent values, participation in organizations and collective efficacy have good and excellent values, and friendship ties will have sufficient and good values 95 percent of times; the full scale will give good and excellent internal consistency values, according to the parameters set for this type of test (George and Mallery 2003).

Table 7 shows the nonordinal Ω coefficient and the ordinal Ω coefficient, where the latter is higher in all the factors, especially in the third and fourth. We should point out that it shows minimal differences with the ordinal α (Table 6). The results in the confidence interval of the ordinal Ω coefficient are similar to those of ordinal α, because 95percent of the times that the sampling is redone on that population and according to the parameters set for this test (George and Mallery 2003), the coefficients of participation in organizations and collective efficacy factors and the complete scale will have good and excellent values, friendship ties will have sufficient and good values, and trust in institutions will always have an excellent value.

Table 7.
Point and Intervals Estimation of McDonald’s Ω Coefficient

Factors Nonordinal Ω Coefficient $Ω_{N O - O R}$ Interval at 95 Percent of $Ω_{N O - O R}$ Ordinal Ω Coefficient Ω_ORD Interval at 95 Percent of Ω_ORD Polychoric Correlation Average of Items Attenuation Percent: $100 \times (\frac{Ω_{N O_{O R} -} Ω_{O R D}}{Ω_{O R D}})$

Trust in institutions .92 [.89, .93] .94 [.92, .95] .53 −2.12

Participate in organizations .88 [.85, .91] .92 [.89, .94] .42 −4.34

Collective efficacy .80 [.75, .85] .95 [.89, .99] .79 −15.78

Friendship ties .71 [.64, .79] .78 [.72, .83] .45 −8.97

Entire scale .86 [.81, .90] .9 [.85, .94] — −4.44

Source: Authors’ elaboration.

Discussion

The validation and adaptation process developed here provides a reliable instrument for the multidimensional measurement of social cohesion at its three levels (micro, meso, and macro) and its objective and subjective components. Even though one of the limits of the study was that it was applied in only one city, and the heterogeneity of other contexts was not captured, the robustness of the tests used shows solid categories and a solid global construct. Even though it could have been proven with only Cronbach’s α coefficient, we felt that this estimator entails some problems as it takes on different assumptions of the τ equivalent models (McDonald 1999) that are difficult to prove, and when these assumptions are broken, the level of internal consistency is underestimated, which means there is a bias (Dunn et al. 2014).

Therefore, to avoid possible bias in estimating the internal consistency, we chose to use congeneric models instead of τ equivalent models. Congeneric models are less restrictive, so they take on fewer assumptions. Unlike τ equivalent models, congeneric models allow the variance of each question to be different (Dunn et al. 2014; Joreskog 1971). The statistical description of the questions, Table 2, agrees with the use of a congeneric model such as McDonald’s Ω coefficient.

Although it is not common to include McDonald’s Ω coefficient in studies to test scales, as the literature shows (Dunn et al. 2014; Graham 2006), it is a more exact estimator of internal consistency and, compared to α, it makes fewer and more realistic assumptions, so it is very useful to consider the information it provides.

The theory establishes that Ω is greater than α for the same group of data. In our results, the differences are quite subtle, so the Ω coefficient allows us to reaffirm the values given by the α coefficient (Zinbarg et al. 2005). Furthermore, including confidence intervals for α and Ω coefficients allowed us to add meaning to the estimation obtained.

Conclusions

The validation of the multidimensional scale in this research goes beyond partial measurements of social cohesion, by covering the three levels at which it is produced: the micro-, meso-, and macro-social levels, and by including its objective and subjective components. Even though it was carried out in the urban area of a Mexican state, it could be valid in other urban contexts in Mexico and Latin America, and even in rural contexts, so long as the objective component items are adjusted at the micro-level and the subjective component is adjusted at the macro-level, depending on the rural conditions of each context.

The previous paragraph is supported because the results of the test of the multidimensional construct of social cohesion showed that the four categories included were robust. Therefore, the scale showed an adequate internal consistency not only with respect to the criteria found in the literature (Cortina 1993; Iacobucci and Duhachek 2003; Nunnally and Bernstein 1994) but also in relation to other studies that have tested similar categories (Cohen, Inagami, and Finch 2007; Rodríguez and Cruz 2014; Ruiz 2010).

As a result, in this process, besides showing that the developed scale is consistent with previous studies, we also highlight the importance of revising the assumptions taken on when the factor analysis of the data is done and the internal consistency of a scale is determined. Aspects such as the continuous or ordinal nature of the data, the breaking of assumptions about the τ equivalent models, and the loss of information when reporting only a point estimate should always be taken into account.

Finally, because the scale is robust and measures social cohesion in a multidimensional way, it could be used in different studies as one of the factors to explain poverty, inequality, and health (Bernard 2000; Economic Commission for Latin America and the Caribbean 2007; Organization for Economic Co-operation and Development 2011) or as one of the dimensions of social well-being (Martínez-Martínez and Ramírez-López 2018).

Supplemental Material

Supplemental_Material - Validation of a Multidimensional Social Cohesion Scale: A Case in Urban Areas of Mexico

Supplemental_Material for Validation of a Multidimensional Social Cohesion Scale: A Case in Urban Areas of Mexico by Oscar A. Martínez-Martínez, Araceli Ramírez-López and Anidelys Rodríguez-Brito in Sociological Methods & Research

Levels	Objective Components	Subjective Components
Micro	Belonging to interest groups and networks of friends
Willingness to support these networks
Meso	Links to neighborhood/community members	Norms and values of neighbors and of the community
Willingness to assist the neighborhood/community	Trust in neighborhood networks
Macro	Belonging to institutions/organizations of interest
Willingness to help solve city problems	Trust in civil associations/political, religious, union, financial, judiciary, and public order institutions

Question	Mean	Standard Deviation	Skew	Kurtosis
Answer range from one to four
1	3.013	1.087	−0.75	−0.79
2	2.045	0.792	0.15	−0.88
3	1.587	0.737	1.01	0.22
4	2.903	0.828	−0.57	−0.07
5	2.039	0.889	0.26	−1.05
6	1.572	0.724	1.05	0.41
7	2.189	0.793	0.05	−0.72
8	1.927	0.841	0.40	−0.86
9	2.112	0.865	0.15	−0.98
10	2.584	0.883	−0.34	−0.64
11	2.032	0.768	0.29	−0.48
12	1.901	0.814	0.40	−0.83
13	2.074	0.874	0.22	−0.97
14	2.047	0.844	0.25	−0.88
15	2.247	0.843	−0.01	−0.86
Answer range from one to two
16	1.940	0.238	−3.68	11.65
17	1.921	0.271	−3.08	7.53
18	1.748	0.435	−1.13	−0.72
19	1.715	0.453	−0.94	−1.12
A	1.623	0.256	−1.16	−1.56
B	1.545	0.432	−2.54	−2.34
C	1.643	0.345	−1.05	−1.80
20	1.462	0.500	0.15	−1.99
21	1.840	0.370	−1.82	1.34
22	1.410	0.493	0.36	−1.88
23	1.686	0.466	−0.79	−1.38
24	1.583	0.495	−0.33	−1.90
25	1.763	0.427	−1.22	−0.51
Answer range from one to three
26	2.500	0.586	−0.68	−0.54
27	2.329	0.717	−0.57	−0.91
28	1.923	0.744	0.11	−1.20
29	2.377	0.617	−0.44	−0.69
30	2.007	0.807	−0.01	−1.47
31	1.929	0.817	0.13	−1.50
32	2.355	0.722	−0.64	−0.87
33	2.294	0.785	−0.56	−1.18
34	2.274	0.837	−0.54	−1.37
Answer range from one to seven
35	2.37	1.81	1.41	1.03
36	2.12	1.61	1.73	2.25
Answer range from one to six
37	1.51	1.21	2.57	5.81

Item	Trust in Institutions	Participation in Organizations	Collective Efficacy	Friendship Ties
1	.28	.14	−.22	.53
2	.63	.08	−.21	−.01
3	.70	.20	.10	.05
4	.55	−.01	−.05	.21
5	.78	.01	.09	.02
6	.77	.09	.15	−.10
7	.57	−.03	−.17	−.13
8	.80	.11	.02	−.11
9	.75	.11	.06	.03
10	.59	.04	−.05	.14
11	.53	−.11	.10	−.04
12	.80	.09	.13	−.04
13	.76	.12	.12	.11
14	.80	.08	.13	−.02
15	.64	.12	−.21	.10
16	.14	−.06	.59	−.08
17	.13	−.03	.62	.14
18	−.08	.03	.75	−.10
19	−.04	−.05	.82	.03
A	.21	.12	.38	.11
B	.42	.12	.41	.09
C	.11	.42	.40	.03
20	−.06	.57	−.12	−.21
21	.10	.50	−.13	.25
22	−.15	.60	.03	−.25
23	.20	.54	−.15	−.21
24	.06	.48	.14	−.01
25	.18	.47	.01	−.11
26	−.01	.54	−.23	.03
27	.05	.67	−.03	.15
28	.10	.78	−.07	−.01
29	.10	.66	−.11	.11
30	.09	.80	.09	.13
31	.07	.68	.09	.21
32	−.08	.60	.13	.19
33	.11	.64	−.02	.06
34	.09	.71	−.14	.17
35	−.10	.03	−.18	.77
36	−.03	.06	.08	.77
37	−.02	.11	.16	.64

Item	Trust in Institutions	Participation in Organizations	Collective Efficacy	Friendship Ties	Communalities
1				.45	.36
2	.64				.51
3	.73				.59
4	.40				.21
5	.81				.66
6	.81				.68
7	.59				.39
8	.83				.71
9	.76				.60
10	.57				.36
11	.54				.32
12	.82				.69
13	.78				.65
14	.82				.69
15	.66				.51
16			.80		.70
17			.81		.67
18			.78		.66
19			.88		.78
20		.65			.75
21		.43			.42
22		.72			.65
23		.59			.61
24		.55			.34
25		.61			.57
26		.56			.37
27		.70			.59
28		.82			.70
29		.70			.52
30		.85			.78
31		.75			.67
32		.68			.55
33		.73			.54
34		.78			.66
35				.70	.60
36				.66	.47
37				.69	.51
Eigenvalues of each factor
	Factor 1	Factor 2	Factor 3	Factor 4
	7.034	7.003	2.678	1.602
Proportion of variance explained for each factor
	Factor 1	Factor 2	Factor 3	Factor 4	Accumulated
	.3083	.2399	.0949	.0941	.7372

Factors	Nonordinal α Coefficient $α_{N O - O R D}$	Interval at 95 Percent of $α_{N O - O R D}$	Pearson’s Correlation Average of Questions	Ordinal α Coefficient α_ORD	Interval at 95 Percent of α_ORD	Attenuation Percent: $100 \times (\frac{α_{N O_O R D -} α_{O R D}}{α_{O R D}})$
Trust in institutions	.92	[.89, .93]	.44	.94	[.92, .96]	−2.12
Participate in organizations	.87	[.84, .90]	.30	.92	[.88, .95]	−5.43
Collective efficacy	.75	[.67, .80]	.43	.94	[.89, .98]	−20.21
Friendship ties	.68	[.60, .76]	.35	.76	[.68, .84]	−10.52
Entire scale	.85	[.81, .88]	—	.89	[.86, .92]	−4.49

Factors	Nonordinal Ω Coefficient $Ω_{N O - O R}$	Interval at 95 Percent of $Ω_{N O - O R}$	Ordinal Ω Coefficient Ω_ORD	Interval at 95 Percent of Ω_ORD	Polychoric Correlation Average of Items	Attenuation Percent: $100 \times (\frac{Ω_{N O_{O R} -} Ω_{O R D}}{Ω_{O R D}})$
Trust in institutions	.92	[.89, .93]	.94	[.92, .95]	.53	−2.12
Participate in organizations	.88	[.85, .91]	.92	[.89, .94]	.42	−4.34
Collective efficacy	.80	[.75, .85]	.95	[.89, .99]	.79	−15.78
Friendship ties	.71	[.64, .79]	.78	[.72, .83]	.45	−8.97
Entire scale	.86	[.81, .90]	.9	[.85, .94]	—	−4.44

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Research Institute for Development with Equity (EQUIDE) under Grant number 0060 EQUIDE and the Iberoamericana University Research Department under Grant number F111025 SNI.

Supplemental Material

Supplemental material for this article is available online.

Note

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