Diseño del array de desfasadores en estructura microstrip

In those instances where confirmatory factor analysis results suggest a poor fit between the observed data and the theoretical model, exploratory factor analysis was used to identify the reasons for the poor fitting results.

Typically, the goal of EFA is to let the data determine the interrelationships among a set of variables. Although a researcher using EFA may have a theory relating the variables to one another, there are relatively few restrictions on the basic factor model in an EFA. First, the EFA is useful in data reduction when interrelationships among variables are not specified beforehand. A second benefit of EFA is the ability to detect a general factor. Thirdly, EFA is particularly useful in scale or test development because it allows the researcher to determine the dimensionality of the test and detect cross-loadings (correlations of variables with more than one factor (Fletcher, 2007).

Item analysis consists of exploratory factor analysis, as well as reliability analysis. An item analysis was conducted on the scales that were used for data gathering. The purpose of item analysis was twofold, namely to determine acceptable factor loadings, and to investigate reliability and inter-item correlations. In determining acceptable factor loadings the general rule used is that items have to have a loading of > .3 to be accepted (Hair et al., 2006). In the event of a two-factor (or more) structure, items are also analysed for possible cross-loadings. In the case of the latter, items may be removed to provide a simple structure.

The purpose of investigating reliability and inter-item correlations is to ascertain which of the items in a scale, if any, have a negative effect on the overall reliability of the scale due to their inclusion in the particular scale. If a significant improvement in overall scale reliability occurs as a result of excluding a particular item, such item is also excluded from the subsequent factor analysis. Exploratory factor analysis is conducted when there are no explicit expectations regarding the number and nature of the underlying factors in each of the constructs (Hair et al., 2006).

In order to conduct exploratory factor analysis on the identified variables in question, the following steps are proposed (Field, 2005; Grimm & Yarnold, 1995; Hair et al., 2006; Kerlinger & Lee, 2000): (a) deciding which method of extraction should be used to extract the factors, (b) identifying the most appropriate method of rotating the factors, (c) determining how many factors can be extracted, and (d) determining how factor scores must be computed if factor scores are of interest.

3.4.8.1 Determining the number of factors to be extracted.

Before determining how many factors can be extracted, it is important to first determine if the identified construct can be factor analysed. This was done by calculating both the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy and the Bartlett’s test of sphericity.

The KMO can be calculated for individual and multiple variables and represents the ratio of the squared correlation between variables to the squared partial correlation between variables. The KMO statistic varies between 0 and 1. A value of 0 indicates that the sum of partial correlations is large relative to the sum of correlations, indicating diffusion in the pattern of correlations, thereby deeming factor analysis inappropriate. A value close to 1 indicates that patterns of correlations are relatively compact and therefore factor analysis should present distinct and reliable factors.

The cut-off value that will be utilised in this study is .6 (Hair et al., 2006).

Another method of determining the appropriateness of factor analysis examines the entire correlation matrix. The Bartlett test of sphericity is one such measure as it is a test for the presence of correlations among the variables. It examines the correlations among all variables and assesses whether, collectively, significant intercorrelations exists (Hair et al., 2006). Significance is measured at the .05 level.

The factor analysis method employed to extract factors in the present research study was principal components analysis. Principle components analysis considers the total variance and derives factors that contain small proportions of unique variance and, in some instances, error variance. However, the first few factors do not contain enough unique or error variance to distort the overall factor structure. Specifically, with

component analysis, unities are inserted in the diagonal of the correlation matrix, so that the full variance is brought into the factor matrix (Hair et al., 2006).

Rather than arbitrarily constraining the factor rotation to an orthogonal solution, the oblique rotation identifies the extent to which each of the factors are correlated. The oblique rotation assumes that the extracted factors are correlated (Hair et al., 2006).

This method is deemed suitable “if the ultimate goal of the factor analysis is to obtain several theoretically meaningful factors or constructs” (Hair et al., 2006, p. 110).

Conclusions drawn from this method are restricted to the sample collected and generalisation of the results can be achieved only if analysis using different samples reveals the same factor structure (Field, 2005).

In deciding whether a factor in the factor analysis is statistically important enough to extract from the data for interpretation purposes, the decision is made on the eigenvalue associated with the factor. The eigenvalue (or Kaiser’s criterion) is based on the idea of retaining factors with associated eigenvalues greater than 1. The scree plot is consulted in the decision of extraction by looking at the point of inflection of the curve. However, previous research has identified parallel analysis as a more accurate method of estimating the number of factors to be extracted (Fletcher, 2007).

The following section focuses on the parallel analysis method of estimating the number of factors to be extracted that was utilised in this study.

3.4.8.2 Parallel analysis.

Parallel analysis involves comparing eigenvalues obtained from the data with eigenvalues that would be expected from random data with an equivalent number of variables and equivalent sample size. The number of factors retained is equivalent to the number of eigenvalues expected from the random data (Fletcher, 2007).

For example, when focussing on the transformational leadership component of the MLQ, if the original data set consists of 220 observations, then a series of random data matrices of this size (220 x 20) would be generated, and eigenvalues would be

computed for the correlation matrices for the original data and for each of the original data sets. The reason for the 20 items is that transformational leadership component consists of 20 items. The eigenvalues derived from the actual data are then compared to the eigenvalues derived from the random data. In Horn’s (1965) original description of this procedure, the mean eigenvalues from the random data served as the comparison baseline, whereas a currently recommended practice is to use eigenvalues that correspond to the desired percentile (typically the 95^th) of the distribution of random data eigen values (Cota, Longman, Holden, Fekken, & Xinaris, 1993; Glorfeld, 1995. Factors or components are retained as long as the ith eigenvalue from the actual data is greater than the ith eigenvalue from the random data.