MUNICIPALIDAD DE TIBÁS PUBLICACIÓN DE TERCERA VEZ

Extracting factors via correlation and by-person factor analysis

The study’s quantitative data analysis phase involves data input and statistical tests using the PQMethod software (Schmolck 2014). In the study, correlation analysis was performed to assess the degree of (dis)similarity across the 99 Q-sorts in the sample. The correlation matrix was then subjected to centroid factor analysis31 _{followed by}

varimax rotation32 _{to condense into few factors or natural clusters of Q-sorts which}

have significant commonality in the way the cards were placed on the response grid. Each factor may be understood to represent a shared viewpoint on the working lives of cruise sector seafarers. By-person factor analysis can yield several acceptable solutions composed of factors between one and seven. A factor solution may be judged as ‘optimal’ if the following statistical and theoretical criteria are met:

a) A factor solution is good if it accounts for more than 35% of overall variance observed in the Q-sorts gathered (Watts and Stenner 2012). b) Given several factor solutions possible, an un-rotated factor may be

retained if it has an eigenvalue greater than 1.0. An eigenvalue is ‘indicative of a factor’s statistical strength and explanatory power’ (Watts and Stenner 2012 p.105).

31 _{Although there are other types of factor analytic techniques (e.g. principal components analysis) centroid} factor analysis is the preferred and recommended factor analytic technique for Q-studies because it is not restrictive to a just one best ‘mathematical’ solution but instead ‘leaves all possible solutions open, it allows to legitimately explore these possibilities through rotation and enables us to defer a decision about the best solution and the best criteria for making that decision until we have explored the data further’ (Watts and Stenner 2012 p.99).

32 _{Varimax is a type of factor rotation that ‘is intended to capture variation or variety in the results – that is,} to draw sharp distinctions between factors, as opposed to (say) blending them into a consensus point of view’ (Dryzek and Holmes 2002 p.28). Varimax rotation is ‘a good enough strategy’ to ‘rotate the factors in such a way that each Q-sort is maximized on a single factor and minimized on all other factors’ thus creating a ‘simple structure’ (Brown et al. 2008 p.737).

c) A factor is worth reporting if it is defined by five people or more although a factor defined by at least two people also deserves some look (Brown 1980; 2014).

d) Whilst statistical criteria are important in deciding how many factors to retain, a final consideration is ‘interpretive plausibility’ – that the factor adds valuable information quite different from what the other factors have covered (Dryzek and Holmes 2004).

Considering these criteria, factor solutions composed of two, three, four, five and six factors were trialled. All of the factor solutions tested met the statistical criteria set out above but the most theoretically relevant was the four-factor solution. It has simple, clear and distinct viewpoints (Webler et al. 2009). The statistical bases of this decision to report a solution composed of four factors are summarised in Appendix 7, p.281. All four factors had eigenvalues more than 1.0 and were each composed of more than five defining Q-sorts. Together the four factors explained 44% of the observed variance among the Q-sorts. The correlation coefficients between factors ranged from 0.42 to 0.67 which indicate a moderate to strong association (Linneman 2014; Dancey and Reidy 2007). This means that factors have an imperfect but high degree of similarity with each other. The four factors show ‘significant’ similarity yet each denotes a distinct social representation of working lives. The small distinctions between these viewpoints matter at the level of individuals and differences in meaning can be examined using interview data. This was typical of Q-studies as factor analysis was not used to identify completely uncorrelated factors but instead to search for shared viewpoints that when examined interpretively would reveal nuances in stance (Jeffares and Skelcher 2011).

The loading pattern of the person sample in a four-factor solution may then be described. This measures the extent to which each Q-sort is correlated to the factor

(Appendix 8, p.282). A significant loading33 _{means that the Q-sort of a participant}

exemplifies or is aligned with the viewpoint of that factor. Overall, 90% of participants (89 out of 99 completed Q-sorts) showed significant loading (correlation) to at least one of the four factors extracted. For a 48-item Q-set, the cut off for significant loading is 0.3723, p<0.01 (Jeffares 2013). Thirty participants showed alignment with Factor- 1; 31 for Factor-2; 38 for Factor-3; and 15 for Factor-4. Ten Q-sorts did not load significantly to any of the four factors which means their viewpoint is not typical of any of those identified.

A closer analysis of factor loadings shows that 24 Q-sorts were confounded or had significant factor loading to more than one factor (see Participant-66 to 89 in Appendix 8, p.282). Since a ‘Confounder’s’ overall stance is mixed, the Q-sort is excluded in the computation of factor array (Watts and Stenner 2012) because they do not help in providing a clear picture of the factor’s supposed viewpoint. A factor array is ‘an estimate of the factor’s viewpoint…prepared via a weighted averaging of all the individual Q-sorts that load significantly on that factor and that factor alone’ (Watts and Stenner 2012 p.129).

In the PQMethod software, the researcher can explicitly ‘flag’/select Q-sorts with significant loading from which the factor array of the idealised Q-sort is computed; or ‘un-flag’/deselect confounded/non-significant Q-sorts. Note that even if the confounders were excluded in the computation of factor array this does not affect the reliability of any of the factors. According to Brown (2014), ‘any number of flagged Q- sorts beyond five or six per factor is gravy and adds little to the reliability of the factor’. Also, dropping the ‘confounders’ does not mean they are completely ignored because their interview data remain relevant in interrogating meanings attached to evaluative stances on issues characterising that factor.

33 _{These loadings vary from “-1” indicating perfect dis-alignment between a person’s Q-sort and a factor, to} “+1” which indicates perfect alignment between a Q-sort and a factor.

A confounding Q-sort suggests that the participant, at that moment of sorting, identifies with the perspective captured by the factors it has significant loadings on. This is not surprising. Given two opposing views of conservative and liberal on any debate, we can expect that there will be individuals who simultaneously assume a conservative view on certain issues but maintain a liberal stance on certain aspects of the debate. A case in point is Participant-78, a 40 year-old, male cabin steward who has worked for 14 years on a cruise ship. His Q-sort is correlated with the viewpoint of Factors-1, 2 and 4 by 17%, 14%, and 20% respectively. His individual point of view is of course a valid stance to take but does not help to clarify viewpoint divergences.

Computing for factor array

Sixty-five Q-sorts loaded exclusively to just one of four factors and were considered as ‘defining’ Q-sorts. Factor-1 has 16 definers whilst Factors 2, 3 and 4 have respectively 16, 19, 23 and 7 definers (Appendix 3 and 4). Having identified the ‘exclusive contributors’ for each factor, an idealised Q-sort which estimates the viewpoint structure can now be calculated. An idealised Q-sort denotes a hypothetical Q-sort that has a loading of ‘1.0’ on that factor and zero on any other factor. It is computed via a weighted averaging of the defining Q-sorts for a factor (Watts and Stenner 2012). Whilst the idealised Q-sort is computed from the definers, no one among them has an exactly similar sorting pattern to the idealised Q-sort. This array of rating scores per factor (see Appendix 9 in p.285 for factor arrays and Appendix 10 in p.288 for idealised Q-sorts) is the most significant output in a Q-study because it is the basis for comparing the structure of shared viewpoints and highlighting their areas of consensus and conflict. For example, Participant-1 has a loading of 0.6627 on Factor-1. This means that his Q-sort is 39% similar34 _{to (or 61% unlike) the idealised}

Q-sort/factor array of Factor-1.