More information on factor analysis in this chapter

A set of observed variables (survey questions) were chosen to represent the factor (the latent quality) based on the hypothesised factor structure (see Table 2.6). It is tested initially using the confirmatory approach; however, an exploratory element is added as the model was modified further, informed by the modification indices after the analysis.

The correlation matrix was examined prior to conducting the FA (see Table 2.9). It shows that the survey questions (a) – (k) exhibit a reasonable degree of correlation for the survey questions theoretically mapped to the three factors. The first FA is based on the hypothesis in which a survey question is predicted by only one factor, called congeneric model. Some survey questions are theoretically relevant to more than one latent concept, for instance the survey question (e), which may be indicator for two latent variables jointly, requiring a cross-loading.

Anticipated modifications of potential cross-loadings are indicated by larger correlation coefficients shown in Table 2.9 outside the hypothesised groups. For example, the item (e) is not only relevant to the how one’s managing money today (financial resilience) but also the risk-aversion reflected in the time perspective of future (future orientation) (marked with *). The pair (b-h) show a correlation coefficient slightly higher than 0.2 (denoted with **). While this is not a high correlation, given the large number of observations used in this study (n=5,755), it may be picked up by modification indices, suggesting a cross-loading; or, the residual variance of these pairs may be high.

Nonetheless, the FA is tested from the simplest form of a congeneric model in order to test the subsequent hypotheses of cross-loading. The modelling sequence is as follows; if the first hypothesis is rejected, as a result of a poor model fit, then the next level hypothesis (a cross-loading) is tested. Failing to reject a hypothesis in this case would conclude that the model has an adequate fit not requiring any further modification. The final model then forms the basis for the next step of the analysis (Byrne, 2012).

Three FA models are tested. The three latent variables, financial resilience, future orientation and self-reported financial knowledge, are constructed as initially hypothesised but with a minor modifications based on modification indices. The first FA, the congeneric

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Table 2.9 Polychoric correlation matrix of the identified survey questions

Hypothesised Latent variable A: Latent variable B: Latent variable C: latent variables Financial Resilience Future orientation Financial knowledge

Observed items (a) (b) (c) (d) (e) (f) (g) (h) (i) (j)

(a) Runout (b) Bills 0.596 (c) Sustain 0.500 0.508 (d) Money-left 0.487 0.438 0.441 (e) Credit 0.231** _{0.140 0.177 0.280}* (f) Tomorrow 0.173 0.099 0.120 0.361* _0.278 (g) Long-term 0.105 0.026 0.081 0.305* _{0.281 0.497} (h) Retirement 0.140 0.088 0.127 0.266* _{0.166 0.473 0.533} (i) Understand 0.121 0.164 0.119 0.171 0.013 0.082 0.045 0.067 (j) WP-Pen 0.068 0.123 0.077 0.027 0.053 0.052 0.014 0.025 0.364

See Table 2.3 or the full description of survey questions. Observed items (survey questions) that contribute to the measurement model are included here. Correlation coefficients relevant to the latent variable A are underlined in bold, B in bold, and C, italicised in bold. The two pairs which may require configurational changes are indicated by * and **.

model, showed less than an acceptable goodness of fit, using the widely accepted goodness of fit criteria of RMSEA < 0.06, Comparative Fit Index (CFI) and Tucker-Lewis Index (TLI) > 0.950 suggested by Hu and Bentler (1999). A large modification index between a factor and an item indicates the level of correlation between them which is not accounted for in the model. The largest is observed for the pair – future orientation and item (d) (underlined with*). This indicates that individuals’ intention to reserve some part of the income, survey question (d) in Table 2.9, is also explained by individuals’ future orientation, of which relationship was suspected from the correlation matrix as discussed previously. This specification is tested in the second CFA model, resulting in a cross-loading model, as two factors now contribute to explaining individuals’ tendency to conserve resources.

While the model’s goodness of fit is improved in the second model, a higher residual correlation is noted between item (b) and (e) as suspected earlier; this reflects a degree of self-control in (item e) and individuals’ current money management tendency (financial resilience), which was also anticipated as per its relevance to impatience. Therefore, this link is retained in the third CFA model as for its substantive relevance – which is that withholding unaffordable consumption is highly relevant to spending sensibly without running out of money (item b). The goodness of the fit has improved to RMSEA is reported to be 0.038 (P-value RMSEA ≤0.05, 1.000), CFI: 0.982, TLI: 0.973, indicating a good fit.

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A few other pairs of factor-observed items with relatively large (>10) modification indices are also noted. However, a further modification could not be theoretically justified; that is, the substantive importance of suggested modifications does not outweigh the merit of a parsimonious model and clarity in factor interpretation. Furthermore, given the nature of the survey questions and individuals’ qualities this study aims to examine, it is somewhat unrealistic to expect an absolute conditional independence among observed items for the survey questions to be meaningful. Therefore, the third CFA model is used as a base measurement model in the following modelling stages.

The last two explanatory variables, funding retirement and saving sufficiency, and the outcome variable retirement saving are ‘observed’ as they represent one survey question or operationalised outside of the CFA framework.

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