Perfiles de morbilidad y factores de riesgo en las personas mayores

To further study the relationship between the three measures, a confirmatory factor analysis (CFA) -based MTMM analysis was employed with a correlated trait-correlated method (CTCM) model and a correlated trait-correlated uniqueness (CTCU) model being proposed and tested. However, the analysis of the CTCM model showed two major errors: the residual

definite. Therefore, the estimated parameters of the CTCM model were problematic, despite its seemingly acceptable model fit shown in Table 4.13. These errors are common in the CTCM model analysis due to its model complexity and these phenomena have been known as a typical issue with the CTCM model (Brown, 2006). In the rest of this subsection, I focused on the results of the CTCU model analysis.

As shown in Figure 4.3 below, the measures of the same subskill are loaded on the corresponding latent trait variable on the left side of the figure and the unique variance or

measures or measurement errors are correlated on the right side of the figure (Brown, 2006; Pae, 2012). Measurement errors are usually assumed to be random and their magnitudes determine measurement reliability. The CTCU model includes correlations of the measurement errors under the assumption that the indicators are influenced by the shared measurement methods and certain proportion of the measurement errors can be accounted for by this method effect. One of the advantages of using the CFA-based approach is that it comes up with model fit indices so that researchers can empirically evaluate the extent to which the model fits the data. In this study, the CTCU model was empirically identified, meaning that a unique estimate of model parameter was obtained. Overall, the CTCU model showed a marginally acceptable model fit (see Table 4.13). The WSLMV χ2

was 62.019 with a degree of freedom of 23 and it was statistically significant (p

<.001), which suggests that the model did not fit the data well. The value of TLI was .834, below the recommended value of .95. The value of RMSEA was .092 with a 90% confidence interval of 0.065 and .119, which is higher than the recommended values as well. The value of WRMR was 0.696, smaller than one. The value of CFI was .931.

Table 4.13

Model Fit Indices of the Correlated Trait-Correlated Uniqueness (CTCU) and Correlated Trait– Correlated Method (CTCM) Model (n = 202)

Model WSLMV χ2 _(df) p value WLSMV χ2_/df

CFI TLI WRMR RMSEA

90% C.I. Recommended criterion >.05 <2.0 >.95 >.95 <.08 CTCU model 62.019 (23) <.001 2.69 .931 .834 .696 .092 (.065, .119) CTCM model 73.855 (24) <.001 3.08 .913 .800 .513 .100 (.074, .126) Note. WSLMV = mean and variance-adjusted weighted least square estimator, CTCU model = Correlated trait-correlated uniqueness model, CTCM model = Correlated trait-correlated method model, CFI = comparative fit index, TLI = Tucker-Lewis Index, WRMR = Weighted Root Mean square Residual, RMSEA = the Root Mean Square Error of Approximation.

Figure 4.3. Correlated trait-correlated uniqueness (CTCU) model for the MTMM data.

Table 4.14 shows the standardized parameters estimated from the correlated trait- corrected uniqueness (CTCU) model. The standardized loadings on the trait factors were all significantly different from zero. The range of standard factor loadings for the self-assessment sections was from .387 to .453. This factor-loading pattern matches the low to moderate

for the TOEFL iBT was from .474 to .886. The range of the standardized factor loadings for the EPT was from .749 to .892.

Table 4.14

Standardized Parameter for the Correlated Trait–Correlated Uniqueness (CTCU) Model

Trait Factor Loading SMCb Correlated Uniqueness

Rda _{Lsn Spk Wrt Rd Lsn Spk Wrt} SA_Rd .453** .188 1.00 SA_Lsn .387** .150 .743** 1.00 SA_Spk .424** .180 .798** .926** 1.00 SA_Wrt .438** .192 .849** .855** .952** 1.00 EPT_Rd .757** .573 1.00 EPT_Lsn .749** .561 .129 1.00 EPT_Wrt .892** .796 .054 -.159 n/a 1.00 TI_Rd .474** .225 1.00 TI_Lsn .648** .420 .513** 1.00 TI_Spk .866** .750 -.132 -.345 1.00 TI_Wrt .582** .339 .177* -.001 .217 1.00

Trait Factor Correlation

Rd 1.00

Lsn .810** 1.00

Spk .503** .788** 1.00

Wrt .815** .870** .668** 1.00

Note: a. Rd = Reading, Lsn = Listening, Spk = Speaking, Wrt = Writing, SA = the Self-

assessment, EPT = the English Placement Test, TI = the TOEFL iBT. b. SMC, squared multiple correlation (i.e., λ2_{). * significant at p < .05 level, ** significant at p < .01 level.}

The lower part of Table 4.14 shows the correlation between trait factors. All of the trait factor correlations are statistically significant. The highest correlation is between listening and writing (r = .870), followed by the correlation between writing and reading (r = .815). The lowest correlations were between speaking and reading (r = .503) and between speaking and writing (r = .688). The magnitudes of trait factor correlation can serve as a piece of moderate discriminant evidence. These inter-factor correlations suggest that the subskills were closely related with each other, but were still distinguishable in a substantial way.

The existence of statistically significant correlations between unique variances

(uniqueness) or measurement errors suggests significant method effect(s). As shown in Table 4.14, the correlations among the measurement errors in the EPT were not significant, which indicates no method effect in the EPT. This means that the relationship among the individual EPT sections was not noticeably influenced by the test formats used, despite its relatively low reliabilities in the reading and listening section. On the contrary, the self-assessment sections exhibited positive and statistically high correlation, ranging from .743 to .952. This corresponds to the findings from the MTMM correlation matrix analysis and indicates a strong method effect for the self-assessment. The reading and listening sections in the TOEFL iBT had a large positive correlation (r = .513) and the correlation of the residuals between the reading and writing

sections was also statistically significant, but with a smaller magnitude (r = .177). These significant correlations of measurement errors between the TOEFL iBT sections indicated somewhat method effect of the task types used in these three sections, possibly due to the use integrated tasks in the TOEFL iBT, for example, writing an essay based reading and/or listening materials

Overall, the CTCU model showed an acceptable model fit to the data. Similar to the findings from the MTMM correlation matrix, the results of CTCU modeling indicated that the EPT had relatively high factor loadings on the trait factors and measured some shared constructs with the TOEFL iBT and a small portion of constructs tapped by the self-assessment. There was no statistically significant method effect in the EPT test.