Factor analysis of predictive variables

Factor analysis allows consideration of whether variables can be understood as part of a larger, over-arching framework. Creating a framework not only helps to understand the relationships between variables on a more conceptual level, but also allows individual variables to be reduced and composited into broader variables in order to produce a

simple, reduced model which can be tested. Whilst factor analysis is a quantitative method, the interpretation of the results is actually qualitative and is an example of qualitizing data, as adding names to the factors is subjective and the process is inductive; using the data to generate meaning and theory i.e. using the results to generate meaningful factor names (Bryman, 2008). This raises the question of whether factor analysis should be conducted with mean scores of a scale of items as opposed to individual items; whether ‘parcels’ or items should be used as the level of data to be analysed.

Parcelling

Using mean scores within statistical analysis is a measurement practice known as ‘parcelling’, whereby a parcel is defined as “an aggregate-level indicator comprised of the sum (or average) of two or more items” (Little, Cunningham and Shahar, 2002, p. 152).

Advocates of parceling would say that working at an item level creates too many ‘empirical wrinkles’ which distract from the recognition of useful measurement models within the data (De Bruin, 2004). Item responses, whilst being perhaps more empirical and stringent, can be difficult to interpret and can ‘muddy the waters’ (Little et al, 2002). However parceling is, of course, only acceptable if the construct has been measured reliably and validly, and based on a strong theoretical background in the first place (De Bruin, 2004). As Möbius (2003) argues, parceling is acceptable when the scales being parceled have been tested for their reliability then there is no real objection to their use.

In the present study, all of the mean scores were tested for their reliability using the Cronbach alpha to estimate reliability. Little et al (2002) also discuss the relative arguments for and against the use of parceling. They argue that whether you decide to use parcels or items depends on your philosophical stance. If one is taking an empiricist- conservative stance, whereby your research purpose is to identify the most predictive items in a questionnaire, regardless of their theoretically associated scale’s predictive efficacy, then each item response needs to be analysed and so parcelling would be inappropriate. However, if one is taking a more pragmatist- liberal philosophy (as taken in this thesis) whereby the research purpose is to measure the predictive efficacy of theoretical constructs using multiple items then parcelling is considered superior. Parcelling is a way of simplifying the data so that the meaningful interpretations can be made.

In the present study, the aim was to investigate how the proposed independent variables, as entire constructs, factor together in order to create composite variables that could be included together in the same ordinal logistic regression without violating the EPV requirement.

Principal Components Analysis

Principal Components Analysis (PCA) is a method of factoring used in Exploratory Factor analysis (EFA). EFA is used to identify an underlying structure of a set of variables. As opposed to Confirmatory Factor Analysis (CFA), EFA does not require an a priori assumption to be made regarding as to what the underlying structure might be. In relation to the current analysis, whilst a framework had been conceptually proposed, its development was not considered valid enough to make a definitive a priori assumption about. Hence, an exploratory approach was considered to be more appropriate. PCA aims to reduce the data to a relatively small number of dimensions that account for the variance in the items. As such, this was an appropriate method of EFA as the aim was to reduce all of the predictive variables into a set of distinct factors which could then indicate at a broader level the most important factors in predicting cancellation.

There are various thresholds and principles which need to be decided on and adhered to during factor analyses; factor loadings, number of factors to extract and rotation. The acceptable loading of variables onto factors is dependent on the sample size. Stevens (1992) recommends that with a sample of 100 there should be a loading of .384. In the present analysis, the analysis included n=630, a reduction from the overall sample of 716 after the missing data from the intention to use and perceived service quality variables. Therefore, any loadings less than .384 were suppressed. It is recommended that only factors that have eigenvalues of 1 or above are extracted and considered to be factors. With a level of 1 or above, factors are considered to account for enough variance in the overall dataset to warrant being a factor. As well as certain requirements that must be met in order to confidently conduct and interpret PCA, there are other choices that can be made regarding the factor solution i.e. regarding rotation. Rotating a factor solution helps to exaggerate any correlation and factor loadings found, by rotating the solution to make it ‘fit’ the loadings as closely as possible. This helps to obtain a clear, more definitive structure which is therefore easier to interpret.

Factors can be rotated orthogonally whereby it is assumed that the factors are considered to be uncorrelated or obliquely which assumes there may be some correlation between the variables. However, when working with psychological variables, as with the present study, it has been suggested that “there are strong grounds to believe that orthogonal rotations are a complete nonsense for naturalistic data, and certainly for any data involving humans.” (Field, 2005 p. 637). As such, direct oblimin, a form of oblique rotation was selected, as recommended by Field (2005). Now that the requirements for PCA have been discussed, the results of the PCA can now be reported.

Principal Components Analysis Results

Listwise PCA was conducted on the dataset, as pairwise analyses for any type of factor analysis can cause misleading results (Field, 2005). The Kaiser-Meyer-Olkin measure of sampling adequacy (KMO) was .85, suggesting that good sampling adequacy and that the data was suitable for factor analysis (Field, 2005). Table 7.7 below shows the total variance explained by the factors. The overall perceived service quality rating was included in the factor analysis an overall variable, to assess members’ broad rating(s) of the aspects of the service they felt they could rate (i.e. did not give a ‘not applicable’ score to). The objective of this study was not to identify which individual perceived service quality attributes were important (although this is detailed in the individual analyses), as it is difficult to measure this when members have such variety in the aspects of the service that they engage in i.e. classes, gym environment, pool/spa, bar/café. Thus, it was the role of a fitness club member’s overall perception of service quality that was of interest in this thesis.

Table 7.7 Total variances explained by factors predictive of intention to cancel

Factor

Initial Eigenvalues Extraction Sums of Squared

Loadings Total % of

Variance Cumulative % Total

% of Variance Cumulative % 1 5.15 32.20 32.20 5.15 32.20 32.20 2 2.86 17.89 50.09 2.86 17.89 50.09 3 1.32 8.25 58.34 1.32 8.25 58.34 4 1.21 7.53 65.87 1.21 7.53 65.87 5 1.01 6.31 72.18 1.01 6.31 72.18

As can be seen from table 7.7, there were five factors extracted, each above an eigenvalue of 1; five different factors that underpin sixteen of the predictors on intention to cancel. The table below (7.8) details the variables that loaded onto these factors.

Table 7.8 Pattern matrix of intention to cancel predictors Perceived service quality and brand External regulation and anxiety Internalised motivation Rapport Perceived value for money

Perceived service quality .65

Brand attractiveness .78

Brand distinctiveness .77

Brand prestige .82

Brand similarity .66

Individual stereotyping .67

Social physique anxiety .86

State anxiety- staff .91

State anxiety- members .93

External regulation .59 Identified regulation .89 Integrated regulation .74 Intrinsic regulation .57 Rapport –staff .91 Rapport –members .91

Perceived value for money .53

Composite variables were computed and labelled to represent these five factors, and were then taken forward to be included altogether to assess their efficacy in predicting intention to cancel membership, along with intention to use which, being ordinal, could not be included in the factor analysis.

7.4.3.4 ‘Internalised motivation' and 'external regulation and anxiety'

On the first analysis, ‘Rapport’ and ‘Service and brand’ and ‘Perceived value for money’ were not found to be predictive of intention to cancel whereas ‘Internalised motivation', 'External regulation and anxiety' and intention to use the club were. As such, the analysis was re-run, to include just ‘Internalised motivation', 'External regulation and anxiety' and intention to use the club as the independent variables. However, when these three were modelled together, intention to use the club was not significant. As such, the analysis was re-run, with just ‘Internalised motivation' and 'External regulation and anxiety' entered as the independent variables. This model was significant. This final model was then also tested on both halves of the dataset. The results are shown in Table 7.9.

Table 7.9 ‘Internalised motivation' and 'external regulation and anxiety' predicting intention to cancel Estimation SE Wald Model Chi- Square Full dataset (n=634)

External regulation and anxiety 0.43 0.09 23.71*** 94.91*** Internalised motivation -0.81 0.10 65.47***

First-half (n=306)

External regulation and anxiety 0.37 0.14 7.66** 44.02*** Internalised motivation -0.79 0.14 32.89***

Second-half (n=328)

External regulation and anxiety 0.48 0.12 16.37*** 51.31*** Internalised motivation -0.83 0.15 32.49***

Note: * p< .05. ** p< .01. *** p< .001.

On the full dataset both external regulation and anxiety, and internalised motivation, were predictive (External regulation and anxiety (Estimate=0.43, SE=0.09, Wald=23.71, p<.001), Internalised motivation (Estimate=-0.81, SE=0.1, Wald=65.47, p<.001). These results were verified on the first-half (External regulation and anxiety (Estimate=0.37, SE=0.14,

Wald=7.66, p<.001), Internalised motivation (Estimate=-0.79, SE=0.14, Wald=32.89, p<.001) and the second half (External regulation and anxiety (Estimate=0.48, SE=0.12, Wald=16.37, p<.001), Internalised motivation (Estimate=-0.83, SE=0.15, Wald=32.49, p<.001).