Factor Structure of the HLE Measures

Structural equation modelling (SEM) techniques were utilised to analyse the factor structure of the HLE data described in the preceding sections. The measurement model presented here evaluated the hypothesis that storybook exposure and direct literacy instruction are separable aspects of the HLE, as in Sénéchal and LeFevre’s (2002) Home Literacy Model. In addition, children’s interest in books was included as a third factor, as previous authors have suggested that this construct ought to be considered separately from storybook exposure (e.g. Baker et al., 1997). On the basis of the research reviewed in Chapter 1, and the preliminary analyses presented in Sections 3.1 and 3.2, it was predicted that the checklist measures would load onto a ‘storybook exposure’ factor, while the interview items tapping teaching of letters and words would load onto a ‘direct instruction’ factor, and that these two latent factors would be uncorrelated. It was also hypothesised that a ‘child interest’ latent factor, indicated by the relevant interview items, would relate to storybook exposure, but not to direct instruction.

In order to test these hypotheses, a Confirmatory Factor Analysis (CFA) was run on SPSS AMOS, v.20 using maximum likelihood estimation. The resulting measurement model, using data from the whole sample (N=188) is shown in Figure 3.1.

138 Here, ellipses represent latent variables, which are defined by the observed variables shown in rectangular boxes. Factor loadings are indicated above each regression path from the latent variables to their respective observed variables. Finally, the proportion of variance in each observed variable which is accounted for by the relevant latent variable is shown at the top right-hand corner of each observed variable.

Examination of goodness of fit indices revealed good fit to the data: χ2

(27) = 15.20, p=.58; χ2/df ratio= .56; NFI=.95; CFI=1.00; RMSEA=.00 (90% confidence intervals: .00-.06; p=.901). Inspection of the modification indices did not suggest that altering the parameters would improve model fit. Table 3.13 reports the estimated loadings for all latent constructs on their respective indicator variables. All loadings are significant at the .001 level.

The two checklist measures show high loadings onto the storybook exposure latent construct. Adding relevant items from the HLE interview (e.g. frequency of storybook reading) attenuated model fit by adding extra parameters, but these items were only weakly loaded onto by the latent variable. For this reason, only the checklist measures were retained as indicators of storybook exposure.

The factor loadings of the direct instruction and child interest latent constructs are somewhat lower; this is likely due to the fact that indicators represent single items from the HLE interview and that internal consistency for these scales was modest. Teaching children to print letters and words was the most important indicator of direct instruction, while the three indicators of child interest showed equivalently modest

139

χ2 _{(27) = 15.20, p=.58; CFA=1.0; RMSEA = .00 (90% CIs .00-.06), p=.90}

Figure 3.1. One-group CFA model of t2 HLE items

Table 3.13

Factor loadings and covariances for one-group 3-factor CFA

Latent constructs and indicator variables

b (SE b) β Critical ratio p

Storybook Exposure CTC CAC 5.66 (.65) 8.51 (.90) .82 .96 8.71 9.51 <.001 <.001 Direct Instruction Teaching Letters Teaching Reading Teaching Writing .78 (.13) .72 (.15) 1.02 (.15) .59 .44 .74 6.12 4.91 6.95 <.001 <.001 <.001 Child Interest Reading Requests Independent Reading Enjoyment of Reading .61 (.10) .63 (.10) .36 (.06) .55 .59 .58 5.88 6.17 6.07 <.001 <.001 <.001

Covariances between factors

Storybook Exposure – Direct Instruction

Storybook Exposure – Child Interest

Direct Instruction – Child Interest -.23 (.09) .28 (.10) .10 (.12) -.23 .28 .10 -2.57 2.97 .90 .010 .003 .367

140 loadings. Inspection of the modification indices revealed that allowing cross-loadings of indicators onto more than one factor would not improve the model fit.

There was a weak negative correlation between the storybook exposure and direct instruction factors supporting the predictions of the Home Literacy Model (Sénéchal & LeFevre, 2002). As expected, storybook exposure and children’s interest in storybooks were positively correlated but there was no clear relationship between direct literacy instruction and children’s interest in books.

Next, the invariance of the factor structure presented in Figure 3.1 across the FR and TD groups was tested. For the purposes of this analysis, FR-SLI families were included in the FR group. Although this sub-group of families showed lower scores on the HLE measures, the factor structure appeared comparable with the whole sample based on correlational analyses; furthermore removing these 29 families from the two- group CFA analysis yielded a very similar pattern of factor loadings to the full FR group model.

As a first step, baseline models were established for each group separately (Byrne, 2001). These baseline models are displayed in Figures 3.2(a) and (b). The factor structure set out in Figure 3.1 yielded good model fit for each group. For the FR group only, model fit was improved if the teaching letters indicator was allowed to cross-load onto the storybook exposure latent factor. This unique cross-loading meant that the following analyses tested the hypothesis of partial measurement invariance (Kline, 2005).

The second step in this multigroup analysis was to assess the model fit for both groups simultaneously. Chi-square values for the baseline FR and TD groups were summed, thus yielding goodness of fit indices for an unconstrained model. Then a

141 second fully constrained model was created, in which equality constraints on all factor loadings, factor variances, factor covariances and error variances were imposed. Given the cross-loading of teaching letters in the FR group only, this parameter was fixed to zero in the TD group. If these constraints significantly reduced the model fit, variance across groups would be indicated. The results of this fully constrained model indicated a moderate fit to the data, and the difference between the baseline and fully constrained models was not significant (see Table 3.14). Thus, this model appears to be partially invariant across FR and TD groups.

Table 3.14

Multigroup CFA tests of measurement invariance across groups χ2

df  χ2  df p

Baseline model 25.90 33 - - -

Fully constrained model 59.51 52 33.61 19 .221

In summary, the confirmatory factor analyses indicated that storybook exposure, direct instruction of orthographic forms and children’s interest in books are distinct factors in the FR and TD groups, although parental teaching of letter forms is also predicted by storybook exposure in the FR group only. These models provide the rationale for using the three factors as independent predictors of children’s language and literacy development in subsequent chapters.

142

χ2 _{(16) = 13.30, p=.65; CFA=1.0; RMSEA = .00 (90% CIs .00-.07), p=.861}

χ2 _{(17) = 12.60, p=.76; CFA=1.0; RMSEA = .00 (90% CIs .00-.08), p=.87}

Figure 3.2(a). Baseline CFA model for FR group (n=116)

143