Assumptions

Since path analysis is an extension of multiple linear regression, many of the same assumptions hold good for the two techniques. Associations between variables must be linear. Path analysis also requires that there should be no interaction between variables, and for the endogenous variables to be continuous. If variables are ordinal, a minimum of five categories are required (Hox, 2000; Streiner, 2005). For these analyses, educational attainment, social class and parenting practices were included as categorical variables with no fewer than five categories. Furthermore, Streiner (2005) recommends a minimum of 10 cases for every parameter estimated, which the sample size of 1,690 adequately fulfils.

10.3.3 Model generation

A model generating approach was adopted to fit optimal models for each of the four G1 parenting practices – cognitive stimulation, intellectual environment, parental aspirations and coercive discipline. In utilising this technique, the initial theory- driven reference model (figure 10.1) was successively modified and retested until on a combination of statistical and theoretical criteria an optimal fit was obtained. To this end, non-significant paths, as represented by regression coefficients with p- values >0.05 were deleted in accordance with a theory trimming approach to model generation (Anderson, et al., 2002). Model generation and theory trimming was continued in AMOS until an optimal fit was gained.

10.3.4 Model fit

Several criteria were used to assess the fit of the model to the data. The chi- squared statistic is usually applied as a ‘goodness-of-fit’ index, for which a non- significant p-value indicates that the model corresponds to the data. However, with large sample sizes, even trivial discrepancies between data and model can give large chi-squared values, small p-values and unwarranted model rejection (Loehlin, 2004). For this reason, two alternative fit indices were also used to evaluate the fit of the models. The root mean square error of approximation (RMSEA) gives a measure of the discrepancy in fit per degrees of freedom and is therefore insensitive

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to sample size. A value of ≤0.05 is considered to indicate a close fit, ±0.08 a mediocre fit, and ≥0.10 a poor fit (Steiger, 1990). The final index used to asses model fit was the comparative fit index (CFI), which is normally tested against a minimum criterion value of 0.95 (Sacker, et al., 2002).

10.3.5 Stratification by G1 sex

A multi-group analysis was used to examine possible interaction effects in the data. Of specific interest was whether or not the path models varied by parental or offspring sex. To this end, the reference model was estimated separately for G1 men and G1 women with the hypothesis that the regression weights were the same for the two groups. These models allowed the distribution of variables to be different for G1 mothers and fathers and G2 boys and girls while requiring the linear dependencies among the variables to be group-invariant. Significant p-values for the chi-squared test provided evidence that these pathways were not the same for G1 men and women, thus indicating an interaction effect. All models were therefore estimated separately for G1 fathers and G1 mothers. There was no evidence that pathways differed by offspring sex.

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10.4 Results

10.4.1 Overall findings

For three measures of G1 parenting – intellectual environment (figures 10.2 & 10.3), parental aspirations (figures 10.4 & 10.5) and coercive discipline in fathers (figure 10.6) – the models satisfactorily fitted the data and thus provided empirical evidence in support of the theoretical model (RMSEA=0.00-0.04; CFI ≥ 0.99). The ‘goodness- of-fit’ measures for the models of cognitive stimulation and coercive discipline in mothers showed that the data did not fit the theoretical model well, and therefore no results are presented.

The accompanying tables (tables 10.1 to 10.5) present the complete results from the fitted final models including the unstandardised (b) and standardised (β) regression coefficients, the standard error estimates of the unstandardised regression coefficients, and the tests of statistical significance of the null hypothesis that each unstandardised regression coefficient equals zero. The unstandardised b-weights are used with the data in their original units of measurement. The standardised β- weights after each variable has been standardised to have a mean of zero and a standard deviation of one. The arrows in the far left column indicate the direction in which the effect operates. For instance, the first line of results in table 10.1 is for the effect of G0 social class on G1 cognitive ability at age eight. An increase in one standard deviation in G0 social class is associated with an increase in 0.34 standard deviations in G1 ability. The R2 value summarises the proportion of variance in G2 cognitive ability accounted for by the collective set of predictors. The broken lines in the figures denote pathways where the estimates were not significantly different from zero at the 95% level and were therefore omitted from the path model.

The strength of relationship between G1 parental cognitive ability and G2 offspring cognitive ability was approximately 0.2 (p<0.001) for all models. The strongest internal path in all models was from G1 cognitive ability in childhood to G1 educational attainment at age 26, with β-coefficients of approximately 0.5 (p<0.001). In G1 fathers, the path between educational attainment and adult occupation was almost as strong (β=0.39, p<0.001). This was not unexpected, since childhood cognitive ability is a known predictor of educational achievement (Deary, et al., 2007; Kuncel, et al., 2004) and occupational attainment has been shown to be

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largely dependent on academic qualifications (Nettle, 2003). In women, the association between educational attainment and adult social class was less marked (β=0.26, p<0.001) although still significantly positive. This might reflect the fact that the measure used for social class was that of the occupational status of the head of household, which in this cohort was predominantly the husband. As hypothesised, G0 social class was positively associated with G1 cognitive ability, education and occupation, thus indicating an indirect effect of G0 social class on G1 parenting behaviours and subsequently G2 cognitive outcomes.

Consistent with the findings from regression analyses in chapter nine, the quality of the intellectual environment provided by G1 parents and parental cognitive ability exerted approximately equal effects on offspring ability (β=0.20). The effects of maternal education and paternal social class on G2 cognition were almost as great, while the associations between parental aspirations and offspring ability were more modest (β=0.08 and β=0.10), with effect estimates almost one-third of that of parental ability and half that of G1 social class. Overall, the models explained between 19% and 27% of the variance in G2 cognitive ability.

10.4.2 Intellectual environment

Parental cognitive ability and SEP variables were positively associated with the quality of the intellectual environment, as well as with offspring cognitive ability (figures 10.2 & 10.3). One notable exception was that the educational attainment of G1 fathers had no direct influence on offspring cognitive ability. The model revealed that the effect of paternal education on G2 cognition was mediated via the occupation of the fathers as well as the quality of the intellectual environments that they provided for their G2 offspring. The occupational status of the head of household was not related to the intellectual home environment provided by G1 mothers.

10.4.3 Aspirations

For parental aspirations, similar trends were observed. Education of mothers but not fathers was associated with offspring ability, while social class was related to the aspirations of G1 men only. One unexpected finding was that the cognitive ability of fathers was not related to hopes for the educational success of their G2 children.

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Instead, the effects of paternal cognitive ability on this parenting measure operated via education and social class.

10.4.4 Coercive discipline

The model including coercive discipline practices in G1 fathers (figure 10.6) demonstrated a substantive negative effect on cognitive outcomes in G2 offspring (β=-0.16, p<0.001). Low levels of G1 paternal education contributed most to the development of these methods of discipline (β=-0.26, p<0.001), while childhood cognitive ability had insignificant effects.