Keeping Contact with Children: Assessing the Father/Child Post-separation Relationship from the Male Perspective

APPENDIX 1

The data has a hierarchical structure, in that the children (level 1) are "nested" within fathers (level 2), as fathers may have more than one child. The dependent variable (frequency of father/child contact) is measured at the level of each child, while the independent variables are measured either for the children, or for the fathers. This type of data cannot be analyzed using conventional regression models estimated using the ordinary least squares method, for the hierarchical data structure introduces dependency and covariance between observations sharing the same context (i.e. children with the same father); this produces unstable estimates and biased standard errors. Consequently, we used a "multi-level" type of model to correctly estimate the effect of the independent variables (see Bryk and Raudenbaush, 1992; Goldstein, 1995; Marchand, forthcoming). Multi-level models do not assume that observations are independent, and they have the property of producing stable parameter estimates and unbiased standard errors that take into account the covariance between observations (Hox and Kreft, 1994). This method makes it possible to distinguish the proportion of the dependent variable's variation coming from differences between children from that coming from differences between fathers, and to evaluate the contribution made by the independent variables to explaining the variation at each level of the data hierarchy.

The estimation of parameters is based on Goldstein's (1986) iterative generalised least square (IGLS) and is integrated into the software MlwiN (Goldstein et al., 1998). Where they converge, the estimates are those with the maximum likelihood. MlwiN produces standard errors for the fixed and random parts of the model, as well as a deviance value (-2 log-likelihood) that could be used to calculate a likelihood ratio test, the latter having a chi-square distribution with a number of degrees of freedom equal to the additional model parameters (Bryk and Raudenbush, 1992).

The dependent variable included in the regression analysis is the number of days (continuous duration) that fathers spent with children in the course of the year preceding the survey or, more exactly, the square root of this number of days; this transformation was made because the number of days did not follow the normal distribution required by the regression model. Certain independent variables, such as age or the time since separation, are introduced into the model as continuous variables; others, measuring either a state (such as the type of parental union at birth) or a threshold effect (such as level of education), have been entered in the form of dichotomous or polytomous variables, and the reference category is given in brackets (see Table 16).

Tables 16 through 19 present the results of the multi-level regression analyses. They contain the regression coefficients associated with the father and child characteristics, as well as a series of other statistics, among which are the proportion of variation in the number days explained by the independent variables included in the model (R2), and the variance calculated for the fathers (level 2) and children (level 1). For example, the child characteristics taken as a whole (included in model 2 of Table 16) explain 10 percent of the variation between children (R21) and 10 percent of the variation between fathers (R22). This contribution is statistically significant at a threshold of 0.001 (χ2=35.26 with 9 degrees of freedom).

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