The Impact of Disability on the Lives of Young Children: Analysis of Growing Up in Scotland Data

Appendix

Multivariate analysis - logistic regression

Many of the factors we are interested in are related to each other as well as being related to the outcome variables of interest. For example, disabled children are more likely to live in lower income households, in areas of high deprivation and have parents who are not working. Simple analysis may identify a relationship between disability and parent-child activities, for example. However, this relationship may be occurring because of the underlying association between disability and household income. Thus, it is actually the lower average income level of families with disabled children which is associated with a lower likelihood of frequent parent-child activities rather than the fact that the child is disabled.

To take these possible confounds into account, in relation to parent-child activities and a range of other experiences and outcomes, multivariate regression analysis was used. This analysis allows the examination of the relationships between an outcome variable and multiple explanatory variables whilst controlling for the inter-relationships between each of the explanatory variables. This means it is possible to identify an independent relationship between any single explanatory variable and the outcome variable; to show, for example, that there is a relationship between disability and parent-child activities that does not simply occur because both income and disability are related.

The logistic regression analysis used employed a stepwise approach. Stepwise regression assesses each variable for significance, entering the most significant variable first and adjusting significance based on variables already entered into the equation, so that the final equation contains only those variables that remain significant when other variables are entered into the model.

All models contained the following independent variables:

• Child's sex
• Mother's age at child's birth
• Household Equivalised income (quintiles)
• Mother's employment status
• Mother's ethnicity
• Housing tenure
• Area deprivation (quintiles of Scottish Index of Multiple Deprivation)

Other independent variables were selected for inclusion depending on the outcome variable of interest. Details of all variables entered in each model are provided alongside the results in the body of the report. As far as possible, all independent variables were selected from the sweep corresponding with the outcome variable, i.e. if the outcome was developmental milestones at age 2, the independent variables were taken from the age 2 survey.

Interpreting regression results

Regression results are given in odds ratios together with the probability that the association is statistically significant. The predictor variable was significantly associated with the outcome variable if p<0.05. The models determined the odds of being in the particular category of the outcome variable (e.g. in the lowest band for mother-child activities) for each category of the independent variable (e.g. household income quintile). Odds are expressed relative to a reference category, which has a given value of 1. Odds ratios greater than 1 indicate higher odds, and odds ratios less than 1 indicate lower odds.

To understand an odds ratio we first need to describe the meaning of odds. The definition of odds is similar but significantly different to that of probability. This is best explained in the form of an example. If 200 mothers out of a population of 1000 breastfed, the probability (p) of breastfeeding is 200/1000, thus p=0.2. The probability of not breastfeeding is therefore 1-p = 0.8. The odds of breastfeeding are calculated as the quotient of these two mutually exclusive events. So, the odds in favour of breastfeeding to not breastfeeding is therefore 0.2/0.8=0.25. Suppose that 150 out of 300 degree-educated mothers breastfeed compared to 50 out of 150 who have no qualifications. The odds of a degree-educated mother breastfeeding are 0.5/0.5=1.0. The odds of mother with no qualifications breastfeeding is 0.3333/0.6666=0.5. The odds ratio of breastfeeding is the ratio of these odds, 1.0/0.5=2.0. Thus the odds of breastfeeding are twice as high among degree-educated mothers (compared to mothers who have no qualifications - the 'reference category').