All goodness
of fit indices suggested an excellent fit between the models and the data (Table I, models five and six).
For the five - indicator life satisfaction, the goodness - of -
fit indices indicated that the model did not fit well.
For the rejection or acceptance of the model was based on
global fit indices and magnitude of the variance explained by the resulting factors.
Confirmatory factor analysis (CFA) indicated that the current version had the same structure as the original instrument (Tucker — Lewis index = 0.912,
comparative fit index = 0.922, root mean square error of approximation = 0.032, standardized root mean square residual = 0.044).
[jounal] Hu, L. J. / 1999 / Cutoff criteria
for fit indexes in covariance structure analysis: Conventional criteria versus new alternative / Structural Equation Modeling 6: 1 ~ 55
Goodness of
fit indexes in confirmatory factor analysis: the effect of sample size.
Evaluation of
model fit indices for latent variable models with categorical and continuous outcomes
incremental fit index (IFI), and the root mean square error of approximation (RMSEA) were utilized to evaluate the fit of the model.
Overall, this model fits the data extremely well (χ2 = 70.4, P <.001; comparative
fit index = 0.99, Tucker - Lewis index = 0.96, root mean square error of approximation = 0.04, standardized root mean square residual = 0.02).
First, we ran the hypothesized model (χ2 = 133.01, df = 108, p =.05, root mean square error of approximation [RMSEA] =.09,
confirmatory fit index [CFI] =.91, Tucker — Lewis Index [TLI] =.91) and determined whether all predicted paths were significant.
Software of Analysis of Moment Structure (AMOS 18) were used to measure the «good model fit» which means the suitability of the model and
absolute fit indices follow the criteria of (1) Prior theory, model or hypothesis; (2) Variations; (3) Specification of latent variable; (4) relationship among latent variables; and (5) Control conditions (Schermelleh - Engel, Moosbrugger, & Müller, 2003).
Model
fit indices from a confirmatory factor analysis showed mixed support for a three - factor model.
Model fit for this original conceptualization was highly acceptable (χ2 = 1.44, p =.32, comparative fit index [CFI] =.91, root mean square error of approximation [RMSEA] =.07; all paths significance at p <.05).
Fit indices obtained through Confirmatory Factor Analysis indicated that the six - factor structure of the DERS fit the data adequately and that most items loaded strongly on their respective latent factor.
Confirmatory factor analyses revealed adequate to
good fit indices for all three models, although the unitary factor model provided the most parsimonious summary of the data.
The global
fit indices included: The X2 - degrees of freedom (d. f) ratio < 2.0, RMSEA < 0:06, CFI > 0:90, NFI > 0:90, GFI > 0.85, AGFI > 0.85 indicated an acceptable fit.
It also deals with the sample size problems existed in the chi - squared test
normed fit index (Bentler, 1990).
Basically, you'd send a portfolio (text is fine - all that's needed is the full name of all of the investments and dollar amounts), and a time frame, and you'll get a custom benchmark portfolio shell comprised of the best
available fitting indices for each asset class back, with returns looking back over any time frame (as long as the data goes back).
ETFs are also more volatile than their best -
fitting index mutual fund, but have similar covariances.
Root mean square error of approximation and
other fit indices indicated psychoFmetric properties for both versions to be acceptable.
Using confirmatory factor analysis estimated that one - dimensional test reliability method confirmatory factor analysis (Ye & Yang, 2011), model
fit index RMSEA = 0.056, NNFI = 0.921, CFI = 0.931, a good model fit.
The resulting global
fit indices X2 = 113.23, p < 0.0005, chi - square - degrees of freedom (d. f.) ratio = 2.45, RMSEA = 0.102, CFI = 0.72, NFI = 0.68, GFI = 0.59, AGFI = 0.57 showed that the one factor solution proposed by the author should be rejected.
Goodness - of -
fit indices consistent with good fit, logical parameter estimates and a level of explained variability of 38.2 % were found in the final model.
Furthermore, constraining item - factor thresholds equally across time did not
reduce fit indices for the conduct problems and prosocial subscales, demonstrating scalar invariance.
Although the full and partial mediating role of life satisfaction (Model 1 and Model 2) was not supported by the present findings, this is not to say that the mediating role of life satisfaction should be denied — these models still showed
adequate fit indices, but both models were slightly poorer when compared with Model 6.
Results showed that the fifteen - indicator positive youth development fit the data [Satorra — Bentler scaled χ 2 (90, n = 3,987) = 1,580.48; RMSEA = 0.06; GFI = 0.89; SRMR = 0.041; NNFI = 0.99; CFI = 0.99; CVI = 0.95] and that the three - indicator problem behaviour had
excellent fit indices [Satorra — Bentler scaled χ 2 (0, n = 3,987) = 0; CVI = 0.02].
Model 1 is the only one that
displays fit indices of acceptable range indicating that the model fitted the data well.
The nested analyses supported the invariance of the overall structure (χ2 = 665.10, df = 252, p <.01, RMSEA = 0.03, and CFI = 0.93), factor loadings (χ2 = 727.50, df = 265, p <.01, RMSEA = 0.03, and CFI = 0.92), and path coefficients (χ2 = 741.74, df = 272, p <.01, RMSEA = 0.03, and CFI = 0.92) based on
overlapping fit indices.
Cutoff criteria for
fit indexes in covariance structure analysis: Conventional criteria versus new alternatives.
In general,
model fit indexes in confirmatory factor analyses become worse as indicators of latent variables increase (Bandalos, 2002; Coffman & MacCallum, 2005; Gribbons & Hocevar, 1998; Little, Cunningham, Shahar, & Widaman, 2002; Marsh, Hau, Balla, & Grayson, 1998).
[jounal] Hu, L. / 1999 / Cutoff criteria
for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives / Structural Equation Modeling 6: 1 ~ 55
According to Morningstar, in the last three years the Vanguard ETF was most closely matched by the US Core Total Return index, while the iShares ETF's
best fit index was the Dow Jones Industrial Average Price Return index.
Confirmatory factor analysis (CFA): the one - factor model was conducted by confirmatory factor analysis giving unacceptable
global fit indices.
Another criterion of goodness
of fit index (GFI) is employed which determine the discrepancies between the assumed model and the observed covariance matrix.
Where investors can get confused and / or make mistakes, is that many total stock market index funds use the Wilshire 5000 Index or the Russell 3000 Index as the benchmark or, as Morningstar labels it, the «best -
fit index.»
Fit indexes, Lagrange multipliers, constraint changes and incomplete data in structural models.
Still, according to Morningstar the best -
fit index for the fund is the Russell 3000.
In all cases, the Sharpe Ratio of the fundamentally - indexed fund was greater than or equal to that of the ETF that follows the best -
fit index for the fund.
A good rule of thumb is you should be able to
fit your index and your middle finger under the collar pretty easily.
The model fit was confirmed using goodness - of -
fit index (GFI), adjusted GFI (AGFI), confirmatory fit index (CFI), and root mean square error of approximation (RMSEA) values.