LA UTILIZACIÓN DE NUEVAS TECNOLOGÍAS COMO ALTERNATIVA A

Exploratory Factor Analysis (EFA) is variable reduction technique to identity the number of latent constructs underlying a set of variables (items). The number of constructs and

the underlying factor structure are identified by conducting an EFA. The researcher is able to explain the variation among variables by using the new created factors, resulting from reduction of the variables. The new created factors can be defined with a new meaning or content (latent constructs). The smaller set of new factors with a minimum loss of information is assumed to underlie the original variables (Hair et al., 2010). Hair et al. (2010) defines factor analysis as “…provides the empirical basis for assessing the structure of variables and the potential for creating these composite measures or selecting a subset of representative variables for further analysis “ (Hair et al., 2010, p.98).

This study examines a large set of variables derived from existing literature. The new setting and application due to translation, as well as the sample, requires an EFA to examine the instruments before proceeding with the CFA and SEM to test theory and the hypotheses. EFA is used to identify underlying dimensions (or factors) that explain the correlations among a set of variables. Secondly, to identify a new, smaller set of uncorrelated variables to replace the original set of correlation variables in subsequent multivariate analysis. And thirdly, to identify a smaller set of important variables from a large set in subsequent multivariate analysis (Malhotra, 2004).

Factor analysis is useful in developing and assessing theories, in which the researcher addresses questions about the underlying structure (Tabachnick and Fidell, 2007). The two major types of Factor Analysis (FA) are exploratory and confirmatory. In the early stages of research, EFA provides a tool to describe and summarise data by grouping the variables that are correlated. The exploratory factor analysis is a technique to identify the underlying structure of interrelationships (i.e. correlations) among a large number of variables in the analysis (Hair et al., 2010). The sets of variables that are highly interrelated are called factors, and assumed to represent dimensions within the data.

The assumption is to predict the relationship of the variables.

The EFA is theory development with the objective to produce reliable scales for each underlying construct. The EFA requires a minimum absolute sample size of fifty observations and preferably 100 or larger (Hair et al., 2010). However, correlation coefficients can be less reliable with small samples (Tabachnick and Fidell, 2007).

Tabachnick and Fidell (2007) indicate that it is sufficient to have 200 cases for factor analysis. In addition, solutions that have several high loading marker variables >0.80) would suffice with 150 cases. However, the loadings cannot be examined before the start of analysis, therefore during the EFA. This study fulfils the requirement of having more observations than variables to conduct an EFA (Hair et al., 2010).

The Principal Axis Factoring analysis (PAF) is most appropriate when the primary objective is to identify the latent dimensions or constructs represented in the original variables (Hair et al., 2010). This is in line with the current study. Common factor analysis is viewed as more theoretically based (Hair et al., 2010). Contrary to this, principal component analysis considers data reduction as a primary concern, with the minimum number of factors needed to account for the maximum of the total variance represented in the original set of variables, based on suggestions of prior knowledge.

The current study attempts to identify constructs represented in the original variables to assess structure, based on the theory. Cliff (1987) describes the debate on Principal Component Analysis and PAF as followed:-

“Some authorities insist that component analysis is the only suitable approach, and that the common factor methods just superimpose a lot of extraneous mumbo jumbo, dealing with fundamentally unmeasurable things, the common factors. Feelings are, if anything, even stronger on the other side. Militant common-factorists insist that components analysis is at best a common factor analysis with some error added and at worst an unrecognizable hodgepodge of things from which nothing can be determined. Some even insist that the term

"factor analysis" must not be used when a components analysis is performed”

(in Hair et al., 2010, p.107).

Principal Axis Factor analysis is a process of identifying the structure of inter-relationship among a large number of variables by defining a set of common underlying dimensions (Hair et al., 2010). It was selected to be applied in this study. The degree of correlation among the variables is desirable with the objective to identify interrelated sets of variables. The PAF (i.e. common factoring) is best in well-specified theoretical applications (Hair et al., 2010).

EFA defines factors derived from statistical results, not from theory. The statistical test is used to determine the underling pattern of the data, i.e. factor structure. The researcher applies EFA, and uses established guidelines to determine which variables load on a factor and how many factors emerge. As a result, the factors which emerge can be named after the analysis is performed.

Statistical results with EFA are the Bartlett’s test of sphericity, communality, eigenvalues, factor loadings and Kaiser-Meyer-Olkin (KMO). To determine the appropriateness of FA the correlation matrix is examined (Hair et al., 2010). To test the correlation among variables two measurements will be used; the Bartlett test of Sphericity and the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy.

The Bartlett test of Sphericity is a statistical test for correlations among variables. The number of factors will be determined by eigenvalues. The eigenvalues greater than one will be selected as the criteria for determining the number of factors to be extracted (Hair et al., 2010). The factor analysis undertaken involves an established approach consisting of principal axis factoring, with the established Kaiser criterion (involving the extraction of factors whose eigenvalues exceed one, thus each factor identified offering greater explanatory value of the data variance than an individual original variable) put in place to establish the number of factors, with rotation used to develop a group of factors that are statistically independent (Bryman and Cramer, 1994; Field, 2000).

The Bartlett test of sphericity and the Kasier-Meyer-Olkin measure of sampling adequacy were used to evaluate the correlation among the variables. The Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy (MSA) is to quantify the degree of inter-correlations among the variables. KMO index 0.9 or above is excellent, KMO index 0.8 or above is great, KMO index 0.7 or above is good. Variables with KMO less than 0.5 will be deleted (Hair et al., 2010). According to Tabachnick and Fidell (2007) values of 0.6 and above are required for good FA. The overall significance of the correlation matrix (e.g. the presence of correlations among the variables) is assessed with the Bartlett test of Sphericity (Hair et al., 2010). The statistical significance of correlation within the set of variables is assessed at the 5% level, which indicates that sufficient correlation exists to ensure the factorability within the set of measured variables.

The retention or elimination of factors is decided by applying the Kaiser criterion (i.e.

retaining factors whose eigenvalue is greater than one). All factors with an eigenvalue greater than one are retained for interpretation. The additional technique of a scree-plot test can provide clarity of deficiencies involving a retention or elimination. For example, if a factor has an eigenvalue of 1.05, this factor is accepted for retention. However, if the analysis identifies a factor just below the level of one, e.g. 0.97, this should be eliminated according to the guidelines of the Kaiser criterion of one. The scree-plot test presents a graph of the eigenvalues in descending order. The “elbow” in the scree test identifies the point at which the last significant break takes place. Factors above and excluding this point are retained.

The rotation of factors is a process by which the solution is made interpretable (Tabachnick and Fidell, 2007). Rotated solutions will improve the interpretation in the preliminary analysis, with the objective to obtain some theoretically meaningful factors.

Factor rotations of the variables can identify and define the character of each factor. The selection of the rotation method depends on the particular needs of a research problem.

Two types of rotation are possible, orthogonal and oblique rotation. Orthogonal rotation maintains statistical independence between the rotated factors (Hair et al., 2010). In contrast, the Oblique rotation allows correlations to exist between the factors.

The orthogonal Varimax rotation method attempts to maximise the variance of loadings within factors, i.e. the sum of variances of required loadings of the factor matrix (Tachnick and Fidell, 2007; Hair et al., 2010). The objective of the Varimax method is to maximise the variance of loadings by enabling high loadings to be higher and low loadings to be lower for each factor (Bryman and Cramer, 1994; Field, 2000). However, this rotation technique assumes factors to be uncorrelated. Therefore, it attempts to load variables that are highly correlated with each other into single factors (Tabachnick and Fidell, 2007). Direct Oblimin Oblique rotation technique simplifies factors by minimizing cross-products of loadings (Tabachnick and Fidell, 2007). The Oblique rotation produces additional matrices. A factor correlation matrix suggests that one or more factors may be combined into one single factor. A structure matrix is produced with correlations between factors and variables. The theoretical underlying dimensions discussed in Chapter Two are assumed to be correlated with each other (i.e. Bidimensional Acculturation variables;

Ethnic Identity; Media Use; Value priorities). Therefore this study selected the, Direct Oblimin Oblique rotation.

The oblique rotation method is selected when the research objective is to obtain theoretically meaningful factors or constructs. The “new” application of the instruments in this study assumes correlations for some factors in theory. However, this study is conducting an EFA based on the desirability of data reduction and simplification, given the relatively large number of variables established in previous studies. This is explicitly assessed within the study. The items and scales used in this study are new by application, language and construct relationships. The oblique rotation also identifies the extent of correlation between the factors assuming that dimensions could be correlated to justify the application of the oblique rotation. However, the oblique rotation, with the possibility of correlated factors can be specific to the sample (Hair et al., 2010).

Therefore, to select the best-suited rotation method, both rotation types are applied as recommended by Hair et al. (2010) in order to assess the comparability of the two rotation methods.

Tabachnick and Fiddell (2006) argue that:-

“Perhaps the best way to decide between orthogonal and oblique rotation is to request Oblique rotation (e.g., Direct Oblimin or promax from SPSS) with the desired number of factors and look at the correlations among factors” (p.646).

If the factor correlations are not driven by the data, the solution remains nearly orthogonal. The rule of thumb is correlations around 0.32 and above with a minimum of 10% overlap in variance among factors. This indicates the approval of the oblique rotation, unless there are compelling reasons for orthogonal rotation.

When the rotation is complete, the next step is to examine the rotated factor matrix (Hair et al., 2010). This allows the researcher to examine the patterns of significant factor loadings with the objective to find a simplified structure and detect problems, i.e. non-significant loadings for one or more variables, cross-loadings, or unacceptable communalities. If any problems are detected, a re-specification of the factor analysis should be considered. Hair et al. (2010, p.116) provides the following guidelines to examine significant loadings:

• Factor loadings in the range of ± 0.30 to ± 0.40 are considered to meet the minimum level for interpretation of structure;

• Loadings ± 0.50 or greater are considered practically significant;

• Loadings exceeding 0.70 are considered indicative of well-defined structure and are the goal of any factor analysis.

The guidelines above indicate that loadings in excess of 0.40 are acceptable. The greater the loading, the more the variable is a pure measure of the factor. Comrey and Lee (1992) suggest that loadings of 0.71 and higher, are considered excellent, 0.63 is very good, 0.55 is good, 0.45 is fair, and 0.32 is poor. However, the significance of a factor loading depends on the sample size. Hair et al. (2010) has recommended the following guidelines in Table 4.

Table 4. Identifying Significant Factor Loadings based on Sample Size

Factor loading Sample size

≥ 0.75 50

≥ 0.55 100

≥ 0.45 150

≥ 0.40 200

≥ 0.35 250

≥ 0.30 ≥ 350

Source: Hair et al. (2010, p.116)

The analysis in this study is carried out with the Oblique rotation method. The assumption is that some underlying structure exists in the set of selected variables, hence the FA, and that there is potential for association between the extracted factors, hence an Oblique rather than a Varimax rotation. The Oblique rotation is chosen on the premise that relationships are likely to exist between the identified factors. Rotation will be performed to simplify the interpretation of each factor and variables that have a loading of less than 0.4, which will be removed. Items which do not load on any factor or which load as a single factor (which is difficult to interpret) or load on several factors simultaneously will be deleted from the scale. The scores on factors are estimated for each subject, which are usually more reliable than scores on individual observed variables. The objective is to decide which variables make up which factor. The loadings on the factors will be examined, and each factor will be assigned a name relating to the content of the variables.

In order to check the reliability of the scale, reliability tests are carried out using Chronbach’s alpha coefficients. This is used to assess the internal consistency among the set of items on each factor. Cronbach’s alpha requires a 0.7 or higher for reliability.

The criteria for the EFA are summarised in Table 5.

Table 5. Criteria summary for EFA

Index Comment

KMO > 0.9

> 0.8

> 0.7

Excellent Great Good Bartlett’s’ test of Sphericity > 0.05 Significant

Cronbach’s alpha > 0.7 Reliable

The EFA is set by the criteria outlined above. A set of new factors is developed (e.g.

latent constructs). The factor solutions are obtained where all variables have a significant loading on a factor. The researcher will attempt to assign a meaning to the factors and name or label each factor presented. A consideration in labelling a factor is to place greater emphasis on those variables with higher loadings (Hair et al., 2010). The findings and analysis of the EFA are discussed in detail in Chapter 4. The next stage in factor analysis is the CFA and involves the assessment of the degree of generalisability of the results to the population (e.g. Turkish-Dutch) and the potential influence of individual respondents on the overall results (Hair et al., 2010).