**Description of Models**
The seven models fall into the three groups described in the introduction section and are all either hierarchical or non-hierarchical models. Models 1a, 2a, and 3a all represent a multifactor relationship between creativity and intelligence subscores where all factors are intercorrelated. Model 4 is a model where all abilities load directly onto a general factor. Finally, the hybrid models are Models 1b, 2b, and 3b, which all have 2-3 initial factors which then load on a general factor, making them hierarchical models. All other models (i.e., 1a, 2a, 3a, and 4) are non-hierarchical models. Almost all non-hierarchical models have a corresponding hierarchical model with the same number of factors, but with the addition of a general second-order g factor. The exception to this is Model 4, which is a congeneric model where all subscores load directly onto a general factor.
Models 1a and 1b have three first-order factors that are based on the tests, with both forms of the TTCT and the ICAR each forming its own factors based on its subscores. Models 2a and 2b are similar, but form two first-order factors: one for all TTCT subscores and another for ICAR subscores. These models would be appropriate if both forms of the TTCT measure creativity and the ICAR measures a separate cognitive ability (i.e., intelligence). Models 3a and 3b have two second-order factors based on the subtest stimuli, with verbal scores all forming a factor and non-verbal scores forming a separate, correlated factor. These models would support the traditional dichotomization between these types of stimuli, which dates back to David Wechsler. There will be no attempts to modify models in order to improve fit.
Models will be identified with the reference variable strategy, where one variable’s factor loading is set to 1.0. The fluency scores and the matrix reasoning score will always be used for this purpose because these scores tend to have the strongest loadings on TTCT and intelligence factors in exploratory factor analyses (Almeida et al., 2008; Jensen, 1998). For hierarchical models, the factor loading for the first-order ICAR factor on the second-order g factor will be set to 1.0 because if there is a general ability that parsimoniously explains performance on the subtests, then it is likely a general intelligence factor and should have a strong loading from a first-order intelligence factor.
Fit statistics will be used to evaluate model fit and compare models with one another. We intend to use the chi-squared value, the comparative fit index (CFI), Tucker-Lewis Index (TLI), root mean square error of approximation (RMSEA) with 90% confidence interval, standardized root mean square residual (SRMR), Akaike information criterion (AIC), and Bayesian information criterion (BIC). These fit indices are suitable for making comparisons among competing models, and they are a cross-section of fit statistics with compensatory strengths and weaknesses (Fan & Sivo, 2005; Sun, 2005). For this study, models will be judged to have acceptable fit if they have an SRMR value < .08 and at least one of the following: (1) CFI > .90, (2) TLI > .90, or (3) RMSEA < .08. These statistics will also be used to judge the best fitting model(s) among the seven. Models will be favored when their SRMR and RMSEA values are closer to zero and their CFI and TLI values are closer to 1.0.
The AIC and BIC will also be used to compare all models to one another, with lower values of these statistics indicating better model fit. When comparing models with the same degrees of freedom, both fit statistics will favor the same model, and the model with the lowest AIC and/or BIC will be preferred. When models have differing degrees of freedom, the penalty for a more complex model (i.e., fewer degrees of freedom) will be more severe for the BIC than the AIC. Therefore, if a more complex model has a lower BIC than a simpler model, then it will be preferred because this would indicate that the model fits the data much better than the simpler model, despite the loss of parsimony.
Chi-squared difference tests will be used to compare nested models. Table 1 indicates which models are nested within one another. Model 4 is the most general of these models, with Models 2a and 3a nested within it. These latter models will be compared to Model 4 by constraining a correlation between the two first-order factors to 1.0—in order to force these factors to merge—and conducting a chi-squared difference test with 1 degree of freedom. Model 1a is nested within Model 2a, and constraining the correlation between the two TTCT factors will force them to merge. As a result, Model 1a can be compared to Model 2a with another chi-squared difference test with 1 degree of freedom, and Model 1a can be compared to Model 4 with a chi-squared difference test with 2 degrees of freedom. All of these comparisons will be made, and any tests that produce a non-statistically significant result (with p > .05) will indicate that the two nested models are equivalent and that the simpler model with more degrees of freedom should be preferred.
After identifying the best model(s) that fit the data, we will interpret the results in light of the different plausible relationships that creativity and intelligence test scores could have. If Models 1a or 2a fit best, we will interpret this to mean that the TTCT and ICAR measure separate but correlated abilities. If Model 3a fits best, then we will interpret this to indicate that the TTCT and ICAR measure a mix of verbal and non-verbal reasoning ability. A best fitting Model 4 would indicate that all TTCT and ICAR tests are direct measures of g and that there are no separate abilities that these tests measure. If Models 1b or 2b fit the data best, then we will interpret this as indicating that the TTCT and ICAR measure separate first-order factors but that these then combine to form a second-order g factor. Finally, if Model 3b has the best fit indices, then this will mean that the tests measure a mix of verbal and non-verbal abilities which then coalesce into a g factor.
Finally, there is the possibility that no model will have adequate fit. If this occurs, then we will interpret this result to indicate that the factor structure of creativity and intelligence subtest scores does not conform to any a priori theorized structure. The factor structure of these two tests in relation to each other will remain unresolved. We fill not engage in any exploratory analyses (e.g., exploratory factor analysis, modification of confirmatory models to improve fit) if no confirmatory models are found to fit the data.
