Charles Adams Ilustración para The New Yorker inspirada en el Museo Guggenheim de Frank Lloyd Wright.

The Risk Tolerance Questionnaire (RTQ) developed by Grable and Lytton (1999) was used to measure Risk-Tolerance. This measure is a subjective, multidimensional measure that focuses on risky financial scenarios and situations, used to derive an individual’s level of Risk-Tolerance. It is a 13-item questionnaire that produces Risk-Tolerance scores for six domains: (a) the probability of gains, (b) the probability of losses, (c) the dollar32 amount of potential gains, (d) the potential dollar loss through the assessment of guaranteed versus probable gambles, (e) minimum probability of success given a risky course of action, and (f) minimum returns given a risky course of action.

Grable and Lytton (1999) reported an internal consistency reliability coefficient of .75 for the full scale. Factor analysis results indicated that the instrument measures financial Risk-Tolerance on three constructs: (a) Investment Risk, (b) Risk Comfort

32

For the purposes of this research, all references to “dollar” as a monetary unit were changed to “rand”.

and Experience, and (c) Speculative Risk. However, in the initial validation study

conducted by Grable and Lytton (1999) the coefficient alphas obtained for each of the three constructs were relatively low (.720, .502 and .443 respectively) and it was noted by the authors that the underlying dimensions “were not intended to be used as distinct measures” (Grable & Lytton, 1999, p. 177).

Correlation analysis between the RTQ and the Survey of Consumer Finances (a widely used proxy, consisting of one item for financial Risk-Tolerance in the United States of America) produced a coefficient of .54. Although moderate, the positive correlation may be an indication that the larger RTQ is measuring multiple dimensions of financial Risk-Tolerance that are not being measured by the SCF item (Grable & Lytton, 1999). A follow-up study conducted by Grable and Lytton in 2003 provided support for both the criterion-related and construct-related validity of the RTQ (Grable & Lytton, 2003).

3.5.7.1 Descriptive statistics and item analysis

The RTQ consist of 13 items. As proposed by the developers of the original instrument, item analysis was performed on the three underlying factors in order to demonstrate the dimensionality of the measure (see summary in table 3.24). The results were concerning as only one dimension, Investment Risk, obtained a satisfactory Cronbach’s alpha of .635. The other two dimensions yielded values of .410 and .295, respectively, which implied that less than 50% of the variance in the subscale items could be attributed to true score/systematic variance and thus, more than 50% was due to error variance.

Table 3.24

The means, standard deviation and reliability statistics for the RTQ subscales

RTQ Number of items M SD _αααα

Investment Risk 5 11.50 2.396 .635

Risk Comfort and Experience

5 10.35 1.971 .410

However, as noted by the authors of the article, the underlying dimensions “were not intended to be used as distinct measures” (Grable & Lytton, 1999, p. 177) and therefore the item analysis was done merely to demonstrate the multidimensionality of the instrument. In light of this, an item analysis was conducted on the full scale. These results are summarised in table 3.25.

Table 3.25

The means, standard deviation and reliability statistics for the RTQ (full scale)

RTQ Number of items M SD _αααα

RTQ 13 26.8585 4.17914 .676

The internal consistency reliability for the 13-item measure was .676, which is relatively close to the suggested 0.70 cut-off. The inter-item correlation matrix revealed that item RT03 correlated very low with the other items in the measure (- .069 to .135). The corrected item total correlation for this item was the lowest among the items at .102, as was the squared multiple correlation at .065. The results also suggested that the deletion of this item would result in an increase of the Cronbach’s alpha from .676 to .694. Based on these findings, item RT03 was deleted and the item analysis was repeated for the reduced item instrument (see summary in table 3.26). Subsequently the inter-item correlation matrix revealed that item RT10 correlated very low with the other items in the measure (-.094 to .176). The corrected item total correlation for this item was the lowest among the items at .102, as was the squared multiple correlation at .069. The recalculated item statistics presented in table 3.26 indicated that if item RT10 was deleted the internal consistency reliability would increase to .701 (see table 3.27 for the recalculated statistics). Consequently this item was also removed and the original scale was reduced from 13 to 11 items. Grable and Lytton (1999) recommended that a Risk-Tolerance assessment index produce reliability coefficients in the range of .50 to .80 in order to be considered acceptable. The reported final internal consistency value (table 3.27) falls within the upper end of this range.

Table 3.26

The means, standard deviation and reliability statistics for the RTQ (12 item instrument)

RTQ Number of items M SD _αααα

RTQ 12 25.0439 4.00282 .694

Table 3.27

The means, standard deviation and reliability statistics for the RTQ (11 item instrument)

RTQ Number of items M SD _αααα

RTQ 11 23.4 3.925283 .701

3.5.7.2 Confirmatory factor analysis

3.5.7.2.1 Measurement model specification and data normality

SEM was used to perform CFA on the RTQ measurement model. In line with the original scale developers, Grable and Lytton (1999), CFA was performed on a single dimension, as the measure was primarily designed to reflect an individual’s standing on the latent construct, Risk-Tolerance as a whole, and hence the computation of a total Risk-Tolerance score as opposed to subscale totals. Therefore, in the first instance the single latent factor measurement model was specified to consist of 11 observed variables (X’s) and one unmeasured latent factor (ξ; i.e. Risk-Tolerance), with single-headed arrows from the ξ to the X’s representing the proposed regression of the observed variables onto the latent factor.

Before CFA was performed, the variable type had to be considered. Most statistical methods for SEM assume that the data are observations of continuous variables. When multivariate datasets comprise of ordinal variables, they are typically treated and specified as continuous in order to overcome this problem. The use of Maximum Likelihood Estimation, in such an instance, is permissible to the extent that the scales consist of five or more scale points (Muthén & Kaplan, 1985). However, in this particular instance this approach may have yielded misleading results. Due to the varying nature of scale points, in terms of content and number of response categories (ranging from two to four in the RTQ), specifying the data as continuous and using Maximum Likelihood Estimation was not permissible. Hence, the data was treated as ordinal. When SEM is used to conduct CFA on ordinal data, the analysis

of polychoric correlations and an asymptotic covariance matrix is required (Jöreskog, 2005). In this instance, Robust Diagonally Weighted Least Squares estimation (RDWLS) is a more appropriate estimation method. The univariate and multivariate normality of the indicator variables of the RTQ was not inspected before conducting the CFA. The a priori assumption is that the intervals between adjacent categories in ordinal variables are arbitrary and thus, it is not meaningful to screen the data for normality.

3.5.7.2.2 Evaluation of the measurement model

The measurement model is visually represented in figure 3.8.

Table 3.28 contains the results of the range of fit indices obtained for the CFA of the single factor measurement model. The exact fit null hypothesis of the measurement model in question was tested by means of the Satorra-Bentler scaled chi-square (S- Bχ

2_{) statistic, which returned a value of 111.908 (p = .000). As a consequence, the} exact fit null hypothesis was rejected (p < .05). The RMSEA of 0.0870, comparative fit index (CFI = .899) and non-normed fit index (NNFI = .874) did not meet the benchmark values of acceptable fit and thus, painted a negative picture of the fit of the model. The SRMR exceeded the < .08 cut-off level corroborating the inference of mediocre model fit. Of the 11 items, seven items obtained significant factor loadings above the .40 cut-off. The loadings ranged from .403 to .720.

Table 3.28

Goodness of fit statistics for the RTQ measurement model (11 item instrument)

Goodness of Fit Statistics

Normal Theory Weighted Least Squares Chi-Square 210.585 (P = 0.0) Satorra-Bentler Scaled Chi-Square (S-Bχ2) 111.908 (P = 0.000)

Degrees of Freedom 44

S-Bχ2/ df 2.54336364

Non-Normed Fit Index (NNFI) 0.874

Comparative Fit Index (CFI) 0.899

Root Mean Square Residual (RMR) 0.0914

Standardised RMR 0.0914

Root Mean Square Error of Approximation 0.0870

90 Percent Confidence Interval for RMSEA (0.0672; 0.107) P-Value for Test of Close Fit (RMSEA < 0.05) 0.00166

The one-dimensional CFA yielded results that did not indicate good fit. It was decided to conduct a CFA on the three underlying dimensions of the measure i.e.

Investment Risk, Risk Comfort and Experience, and Speculative Risk, in order to

investigate the dimensionality of the measure. In this instance the model was specified to consist of 11 observed variables (X’s) and three unmeasured latent factors (ξ’s; i.e. Investment Risk, Risk Comfort and Experience and Speculative

Risk), with single-headed arrows from the ξ’s to the X’s representing the proposed regression of the observed variables onto the three latent factors.

The measurement model in this instance represented the relationship between the

Investment Risk, Risk Comfort and Experience and Speculative Risk constructs and

its manifest indicators, and can be viewed in figure 3.9.

Figure 3.9. Measurement model of the RTQ subscales (standardised solution)

Table 3.29 contains the results of the range of fit indices for the three factor measurement model. The Satorra-Bentler scaled chi-square (S-Bχ

achieved a value of 72.394 (p = .00179). As a consequence, the exact fit null hypothesis was rejected (p < .05), thereby implying imperfect model fit. The RMSEA of 0.0613, comparative fit index (CFI = .954) and non-normed fit index (NNFI = .938) strongly suggested a well-fitting model, as did the standardised root mean square residual (SRMR = .0796). The probability of obtaining this sample RMSEA value

under the assumption that the model fits closely in the population was sufficiently high at .201 not to discard the assumption as permissible (i.e. close fit was achieved). Of the 11 items, nine obtained significant factor loadings above the .40 cut-off. These loadings ranged from .467 to .757.

Table 3.29

Goodness of fit statistics for the RTQ measurement model (subscales)

Goodness of Fit Statistics

Normal Theory Weighted Least Squares Chi-Square 134.787 (P = 0.00) Satorra-Bentler Scaled Chi-Square (S-Bχ2) 72.394 (P = 0.00179)

Degrees of Freedom 41

S-Bχ2/ df 1.7657

Non-Normed Fit Index (NNFI) 0.938

Comparative Fit Index (CFI) 0.954

Root Mean Square Residual (RMR) 0.0796

Standardised RMR 0.0796

Root Mean Square Error of Approximation 0.0613

90 Percent Confidence Interval for RMSEA (0.0371; 0.0841) P-Value for Test of Close Fit (RMSEA < 0.05) 0.201

As was argued, the RTQ was originally developed to measure a general Risk-

Tolerance factor. However, factor analytic results in the original validation study of

the measure (Grable & Lytton, 1999) revealed that the scale also measures three specific underlying factors reflecting different domains of Risk-Tolerance. Consequently, the data was fitted separately to two models with one and three factors, respectively. Factor analytic results in this research produced greater support for the three-factor model. However, the ideal would have been to successfully fit a model that could reflect a dominant factor whilst simultaneously capturing remaining common variance across items in the three underlying factors. Towards this end, an attempt was made to fit the data to a bifactor model, which

would have provided the best account of the underlying factor structure of the RTQ. Confirmatory bifactor modelling provides a method for evaluating competing structural models in explaining the latent dimensions of an instrument (Canivez, in press). In this instance the bifactor model was specified by modelling all indicator variables onto both a single common latent factor, i.e. Risk-Tolerance, and the specific latent dimensional factor to which it is theoretically related. Therefore, each indicator had one path from a dimensional factor and one from the general factor, i.e.

Risk-Tolerance. Bifactor modelling accommodates the proposed hierarchical

structure of the RTQ by allowing the research to retain the idea of a single common construct whilst acknowledging the multidimensionality of the measure. Unfortunately, when the model was fitted the solution did not converge and was rendered inadmissible.

Consequently, even though the three-factor structure displayed good fit in comparison with the unidimensional factor structure, a decision was made to include

Risk-Tolerance as a single latent variable in the subsequent analyses. This was

done in attempt to protect the original design intention of the scale, which was to produce a single Risk-Tolerance score.

Further to this, consideration was also given to the formation of item parcels prior to the evaluation of the measurement and structural models, which will be discussed in the subsequent chapter. According to Little, Cunningham, Shahar, and Widaman (2002) the law of large numbers typically holds for indicators of constructs and suggests that more items are better than fewer items in estimating a construct centroid. Moreover, when more items are combined and aggregated into parcels non-normal distributions become more normally distributed, and scale intervals increase in number and effectively become both smaller and more equal with regard to distances between points (Little et al., 2002). When fewer items are included, models are more likely to be under identified and may fail to converge. Essentially, models using parcels containing a greater number of items are more desirable as it may improve fit indices and produce a more comprehensive representation of a construct (Little et al., 2002).

For the reasons stated above, a decision against the inclusion of a multidimensional

Risk-Tolerance and Sensation Seeking latent variable was made, as it would have

implications for the success with which the latent variables were operationalised in the measurement and structural models. More specifically, if item parcels had to be formed for Sensation Seeking, it would be possible to combine pairs of items representing each of the four identified dimensions of the BSSS. This would mean that the resultant composites as indicators of Sensation Seeking would consist of only two items. This would also be the case for the third dimension (Speculative

Risk) of the RTQ, which after the removal of poor items consisted of only two items.

The inclusion of only two items in the item parcels may have led to the attenuation of the resulting fit indices.

3.6 Conclusion Regarding the Psychometric Integrity of the Measurement Instruments

The item analyses conducted on the range of scales and subscales used in this study achieved the results presented in table 3.30.

Table 3.30

A summary of the reliability results of the Client Risk-Tolerance Questionnaire latent variable scales/subscales Scale Sample size Number of items Mean Standard deviation Cronbach alpha Number of items deleted Extraversion 205 4 13.39 3.221 .729 0 Agreeableness 205 4 15.30 2.689 .689 0 Neuroticism 205 4 10.55 2.758 .548 0 Conscientiousness 205 4 15.34 2.785 .588 0 Intellect/ Imagination 205 4 14.23 2.842 .650 0 BSSS 205 8 24.64 5.912 .764 0 ESM 205 10 37.44 4.611 .737 0 ESC 205 9 37.72 4.603 .715 1 DGI 205 7 30.98 3.834 .776 0 RTQ 205 11 23.40 3.925 .701 2

The item analyses results revealed that eight out of the ten scales/subscales returned Cronbach’s alpha reliability coefficients above the critical cut-off values33 set for the current study. It is acknowledged that two of the subscales comprising the Mini-IPIP, i.e. Neuroticism and Conscientiousness, yielded concerning results (alpha < .60). Furthermore, completely standardised factor loadings below the cut-off value (.40) were obtained for three items in these two subscales. This included items IPIP09 (Neuroticism), IPIP13 (Conscientiousness) and IPIP19 (Neuroticism) with loadings of .259, .350 and .209, respectively. However, deleting items from these scales were not an option as the subscales already comprised of a limited number of items (m = 4), and no significant increase in the alphas would be incurred from doing so.

The item analysis conducted on the underlying dimensions of the RTQ returned poor reliability coefficients for two of the dimensions (.410 and .295). As mentioned, it needs to be taken into account that the original design intention of the measure was to construct a uni-dimensional Risk-Tolerance construct, and hence Risk-Tolerance was included in the structural model as a single latent variable. The reliability coefficient (.701) obtained in the second instance, with 11 retained items representing the scores on the Risk-Tolerance latent variable, mitigated the unfavourable picture that emerged from the item analysis performed on the three sub-dimensions. Overall, it could be concluded that sufficient evidence was produced to conclude satisfactory internal consistency of most of the scales/subscales utilised in this study.

The primary purpose of the item and dimensionality analysis was to detect and remove poor items. Only three items from the composite questionnaire, containing all scales and subscales intended for this study, were deleted and excluded from further analyses. The results suggested the removal of one item, ER12, from the Emotional

Self-Control subscale. During the EFA only one item, ER12 loaded onto the third

extracted factor, resulting in the decision to delete this item from the final item pool (coupled with the fact that the item analysis results flagged this as a possible

33

Each measured subscale was considered acceptable if the Cronbach’s alpha value exceeded .70. However, due to the fact that the coefficient of internal consistency is attenuated by a limited number of scale items, the acceptable value was set at .60 for the Mini-IPIP with m = 4 per subscale.

problematic item). Two items, RT03 and RT10, were removed from the RTQ. The

Emotional Self-Control subscale was therefore reduced from 10 to nine items and

the RTQ was reduced from 13 to 11 items.

The CFA results for the five factor Mini-IPIP scale, Emotional Self-Management subscale and DGI ranged from adequate to good. For the Emotional Self-Control subscale, dimensionality analyses were performed to determine the underlying factor structure. The results demonstrated that the Emotional Self-Control subscale failed to pass the uni-dimensionality assumption as was originally hypothesised. Initially an unrestricted EFA led to the extraction of three factors. However, only one item loaded onto the third factor and was consequently deleted. A two-factor solution was successfully forced. To strengthen the psychometric support of the scale, CFA analysis were conducted once more on the derived two factor structure from the EFA results. In this instance, it was concluded that the two-factor model provided a better account of the structure of the instrument in this particular sample. Initial inspection of the item content failed to produce meaningful underlying theoretical themes. A closer inspection of the item wording, however, pointed towards the presence of possible method bias. The items loading on the derived two-factor structure could largely be grouped into positive and negatively worded units.

Even though the results of the three dimensional CFA of the RTQ supported good model fit, the one-dimensional analyses did not paint the same positive picture and mediocre fit was concluded. This was, however, anticipated as the measure consisted of variable scales points with as low as two response categories per item, the highest being four. Statistically, scales with a smaller number of response categories, generally two to four, are commonly expected to yield scores that are lower in reliability, validity and discriminatory power compared to those with five or more response categories.

The uni-dimensional BSSS produced undesirable results. Based on the fact that the BSSS was founded on Zuckerman’s Sensation Seeking Scale Form V (SSS-V) and thus reflected four dimensions, it was decided to conduct a CFA on the four underlying dimensions. The range of fit indices produced satisfactory results and statistically, perfect model fit was concluded.

It is undeniable that there exists opportunity for improvement with regards to the

In document Rafael Moneo, la obra de arte y la arquitectura de los museos (página 172-186)