Analyses

8.4.1 Mobility matrix

Intergenerational occupational and marital mobility were first described by inspecting a mobility matrix of G0 father’s social class and G1 social class, which characterises movement as outflow and inflow mobility (Goldthorpe et al., 1980). Outflow mobility represents the percentage of G1 parents from a given origin class in each destination class, and is interpreted as row percentages. Inflow mobility represents the proportion of G1 parents in a given class at age 26 who originated in each class of origin, and is interpreted as column percentages.

8.4.2 Predictors of intergenerational social mobility

To examine the effect of G1 cognitive ability and educational attainment, as well as maternal age at childbirth, on the chance and direction of intergenerational occupational and marital mobility, odds ratios were calculated using a series of polytomous logistic regression models. The polytomous logistic model is a useful tool for regression analysis with multinomial responses (Agresti, 2002). The two outcomes of interest – occupational and marital mobility – had four categories representing social mobility: stable non-manual, upward, downward and stable manual. Those in the stable manual category were employed as the reference group. Multinomial logistic regression assumes proportional odds, with the impact of predictors assumed to be the same at each possible threshold of the scale (Hosmer & Lemeshow, 2000). Odds ratios greater than one indicated a higher likelihood of the outcome of interest compared with the reference group. Conversely, odds ratios below one indicated a diminished relative probability. The independent variables in these analyses were parental cognitive ability at age eight, parental educational attainment by age 26 (dichotomised to ordinary vs. advanced) and maternal age at childbirth (dichotomised to ≤ 19 years vs. ≥ 20 years).

8.4.3 Social mobility and offspring cognitive ability

Linear regression models were used to examine the effect of parental occupational and marital mobility on offspring cognitive ability. The results were presented as standardised beta coefficients which allowed for comparison of the strength of the relationship across genders and mobility types. Coefficients with a non-significant p-

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value were deemed to be not significantly different from zero – that is, no statistically significant association existed, although proper interpretation of the effect estimate took the magnitude of the standardised coefficient into account.

For these analyses, the two independent variables – occupational and marital mobility – had four categories representing social mobility: stable non-manual, upward, downward and stable manual. Those in the stable manual category were employed as the reference group. The dependent variable was offspring cognitive ability at age eight.

8.4.4 Social mobility and intergenerational associations

Hierarchical linear regression analyses were used to examine the effect of parental social mobility on intergenerational associations in cognitive ability. In hierarchical multiple regression, the number of independent variables entered into the model and the order in which they are entered is predetermined and based upon logical or theoretical considerations (Gelman & Hill, 2007). In these analyses, following unadjusted models examining the intergenerational association between parental and offspring cognitive ability (model 1), parental social mobility was added to the models (model 2). Finally, parental education and maternal age at childbirth were entered as covariates in model 3. These analyses aimed to identify (i) whether or not parental social mobility significantly decreased the unadjusted association between parental and offspring cognitive ability and (ii) whether or not parental educational attainment accounted for any effect of parental mobility on intergenerational relationships in cognitive ability.

Likelihood ratio tests (LRT) examined whether or not there was a statistically significant difference between model 1 and model 2. Significant p-values for the LRT would indicate that parental social mobility significantly reduced the intergenerational association and therefore played a role in the transmission of cognitive ability between G1 parents and G2 offspring.

8.4.4.1 Structural zeros

These regression models may be affected by the fact that certain types of movement are impossible. For example, G1 parents born into classes I & II could not move up and those born into classes IV & V could not move down. Such

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prespecified cell values are known as structural zeros, since data includes cells whose frequencies are known before any data are collected. Structural cells can be avoided when fitting a model so that the calculation of the model table frequencies proceeds as though the structural cells are absent from the table and their values have no influence on the calculation of the other frequencies (Gilbert, 1993).

To determine whether or not the effects of restricted mobility patterns in the extreme classes affected the results, models using structural zeros were calculated. Similar techniques have been employed to examine patterns of mobility related to health selection (Bartley & Plewis, 1997; Manor, et al., 2003). Since the results from models including structural zeros were not markedly different (table 14.3 in appendices), the results from the original regression models are presented.

8.4.5 Stratification by G1 sex

Owing to the marked differences existing in the labour market between men and women during the 1960s when G1 parents were first employed (Halsey & Webb, 2000), it was anticipated that the effects of cognitive ability and educational attainment on social mobility would differ by sex – that is, there would be an interaction effect. Interaction exists when the effect of an independent variable (e.g., cognitive ability) on a dependent variable (e.g., mobility) differs on the value of a third variable (e.g., sex). To analyse interaction, it is necessary to introduce interaction parameters into the regression model to determine whether the terms significantly improve model fit over and above the case where no interaction parameters are included – that is, compared with the model which assumes that the effect of education or cognitive ability is constant between sexes (James, 2001). Statistically this was tested by way of a likelihood ratio test.

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