The first path model, Model 1, is a CFA model with 2 latent factors and 8 observed variables as shown in Figure 4.1. Model 1 was derived from empirical studies that indicate separate groups of domain specific resources between the verbal and visuospatial memory constructs (Miyake & Shah, 1996; Daneman & Tardiff, 1987) and were assumed to cause the variation and co-variation between the eight observed variables. The verbal factor was linked to four verbal memory measures while the visuospatial factor was associated to four visuospatial memory measures. This 2-factor model does not provide a good fit to the observed data where the chi- square value is highly significant and the fit indices are less than .90 as shown in Table 4.1.
Figure 4.1. A simple path diagram for 2-factor model based on the distinction
The next path model, Model 2, is a CFA model with 2 latent factors and 8 observed (measured) variables as shown in Figure 4.2. Model 2 was derived from the domain specific view of the short-term and working memory measures (Swanson & Luxenberg, 2009). The short-term memory factor was linked to four short-term memory measures while the working memory factor was associated to four working memory measures. Based on the chi-square statistic, this 2-factor model does not provide a satisfactory fit to the observed data where the chi-square value (p<.001) is highly significant, all fit indices are less than .90, and the RMSEA value exceeds .08 as shown in Table 4.1.
Figure 4.2. A simple path diagram for a 2-factor model corresponds to short-term
memory and working memory.
The third path model, Model 3a, is a CFA model with 3 latent factors and 8 observed (measured) variables as shown in Figure 4.3. Model 3a is a three-factor model centred on a single domain general working memory factor (including both the verbal and visuospatial storage and processing tasks) and two distinct storage factors for verbal short-term memory measures and visuospatial short-term memory measures. The Model 3a is consistent with Baddeley & Hitch tripartite working memory model as explained in Chapter 1 (Figure 1.2), as well as that of Engle et. al (1999). Referring to the goodness-of-fit statistic, Model 3a provided a better fit to the data than either Model 1 or Model 2, with a lower chi-square value (although still highly significant, p<0.001). Nonetheless all fit indices were below .90, and the RMSEA = .121, still showing poor fit to data.
Figure 4.3. Path diagram (Model 3a) for a 3-factor model with one domain general
working memory factor and 2 distinct storage factors for verbal and visuospatial short-term memory correspond to Baddeley & Hitch (1974) working memory model.
Figure 4.3 represents Model 3a showing no path lines from the four working memory measures to the corresponding domain storage for either the verbal and visuospatial factors. Since the working memory tasks measure together storage and processing of information in either verbal or visuospatial domain, there should be path lines drawn from the verbal and visuospatial short-term memory factors to their corresponding working memory measured variables. Therefore another model, Model 3b, was constructed and examined but with the appropriate path lines from the domain specific short-term memory factors to the appropriate working memory measures represented in Figure 4.4. Model 3b provide a very good fit of the data with a chi-square value which is in non-significant (p > 0.05) and lower than the other models as indicated in Table 4.1. All fit indices also shows values higher than .90 demonstrating good fit with a lower RMSEA<.05 as well. A chi-square difference test compares the fit of this model with previous theory-derived models. Table 4.2 shows the result of the chi-square difference between Model 3b and Models 3a (Δχ² = 30.82, df = 4, p<.001), Model 3b and Model 2 (Δχ² = 60.47, df = 6, p<.001), and Model 3b and Model 1 (Δχ² =24.1, df =6, p<.001) providing support that Model 3b represent the best account of these observed data.
Figure 4.4. Path diagram (Model 3b) representing a 3-factor model with a single
domain general working memory factor and 2 separable storage factors for verbal and visuospatial short-term memory correspond to Baddeley & Hitch (1974) WM model.
The final path model, Model 4, is a CFA model with 4 latent factors and 8 observed (measured) variables as shown in Figure 4.5. Model 4 is a four-factor model representing the four domain specific constructs; verbal short-term memory (Factor 1), visuospatial short-term memory (Factor 2), verbal working memory (Factor 3) and visuospatial working memory (Factor 4). Model 4 is a model derived from the current theoretical model of working memory based on adult data (e.g Cowan et. al., 2002). While Model 4 seems to provide a good fit to the data as model 3b (refer to Table 4.1), the complexity of the path diagram resulted in multicollinearity problems rendering solution not admissible.
Figure 4.5. Model 4 is a path model with 4 latent factors with separate verbal and
visuospatial working memory and separate short-term memory constructs each co- varies between each other.
Table 4.1 Goodness-of-Fit Statistics for the Different Measurement Models for all the Participants as well as for each Science and Non Science Group
Model Group χ² df p CFI IFI NFI RMSEA
1 All 37.00 19 .008 .91 .91 .83 .094 Science 25.28 19 .152 .91 .92 .74 .080 Non Science 18.32 19 .501 1.0 1.0 .87 .000 2 All 73.37 19 <.001 .72 .73 .67 .164 Science 39.96 19 .003 .69 .73 .58 .147 Non Science 40.43 19 .003 .80 .82 .70 .143 3a All 43.72 17 <.001 .86 .87 .80 .121 Science 26.52 17 .065 .86 .88 .72 .105 Non Science 26.01 17 .074 .92 .93 .81 .098 3b All 12.90 13 .45 1.0 1.0 .94 .000 Science 7.38 13 .89 1.0 1.0 .95 .000 Non Science 11.14 14 .68 1.0 1.0 .88 .000 4 All 14.02 14 .45 1.0 1.0 .94 .004 Science 14.14 14 .44 .99 .99 .85 .014 Non Science 9.02 14 .83 1.0 1.0 .93 .000
Table 4.2 Model Comparison Statistics for Each Group Band Between Models 3b and Model1, and Model 2, and Model 3a
Model 1 Model 2 Model 3a
Group Δχ² df p Δχ² df P Δχ² df p
All 24.1 6 <.001 60.47 6 <.001 30.82 4 <.001 Science 12.38 6 ns 27.06 6 <.001 13.62 4 <.05 Non Science 5.42 5 ns 27.53 5 <.001 13.11 3 <.05 Note: ns = not significant. Δχ² = χ² difference.