Logistic Regression Methods and Tables
Eight of the remaining tables, including the next four, present the results of analyses that apply logistic regression procedures in multivariate models, using data at the level of the individual spell. The dependent variables in these logistic models are binary events -- foster care reunification, reentry to foster care, and completed adoption. The independent variables are a set of child and case attributes that have been considered previously as related to foster care history and exit dynamics.
When interpreting these models, the primary statistics of interest are odds ratios, which indicate the relative effects that are attributed to the different values of each predictive variable, controlling for the influence of other variables in the model. For each variable in the model, one of the possible response attributes (or categories) is arbitrarily selected as the "excluded" category, and is assigned an odds ratio of 1.00. The odds ratios computed for each of the other categories of that variable express the likelihood that a spell with that attribute has the predicted outcome-relative to the likelihood that a spell with the "excluded" attribute has the predicted outcome.
As an example, Table IIC.1 presents the results from two models ¾ one predicting reunification within three years of entry and the other predicting any "family" exit (reunifications plus relative exits) within three years of entry. Each model is computed with nine independent variables.
|Predictor Variable||Category||Reunification within 36 months||Family exit within 36 months|
|Standardized parameter||Odds Ratio||Standardized parameter||Odds Ratio|
|Age at Entry||< 3 months||-0.17||0.39||-0.17||0.39|
|3 -11 months||-0.04||0.78||-0.03||0.79|
|1 - 2 years||-0.01||0.94||0.00||0.96|
|3 - 5 years||0.00||0.98||0.00||0.99|
|6 - 8 years||0.00||0.98||0.00||0.99|
|9 -11 years *||- -||1.00||- -||1.00|
|Female *||- -||1.00||- -||1.00|
|White, Other *||- -||1.00||- -||1.00|
|Primary urban county||-0.12||0.65||-0.12||0.64|
|Remainder of State *||- -||1.00||- -||1.00|
|First Spell in care *||- -||1.00||- -||1.00|
|Other (FC or KC) *||- -||1.00||- -||1.00|
|On placement in spell *||- -||1.00||- -||1.00|
|Michigan *||- -||1.00||- -||1.00|
Year of Entry
|1992 *||- -||1.00||- -||1.00|
|N exits (in type)||176,353||197,682|
|Proportion exit (in type)||0.44||0.49|
Note: Predictors noted with "*" are not contained in model, but are the "excluded" category for their variable. Predetermined odds ratios of 1.00 are assigned to these categories. Odds ratios for other categories of the same variable express effects in relation to that of the excluded category.
Looking at the reunification model, the first independent variable is the age of the child at the time of entry to this spell in foster care. The age category "9-11 years" was selected as the excluded category, and its odds ratio is automatically set at 1.00. The odds ratios for each of the other age categories express the likelihood of reunification of a child entering care at that age, relative to the likelihood of reunification for a child entering care at the age of 9 to 11 years, while controlling for the influence of the other eight variables in the model.
The odds ratio estimated for foster care spells that begin when the child is an infant (<3 months of age) is .39. This should be interpreted as meaning that the relative odds of reunification for a newborn entrant, as compared to a 9-11 year old entrant, are .39 to 1. Conversely, we could take the reciprocal and state that a 9-11 year old entrant is 2.56 times more likely to be reunified within three years than is a newborn. The choice of the excluded category should be unimportant because while numerical values of the odds ratio do depend on which particular category is excluded, the values of the odds ratios relative to each other will be preserved.
The parameters listed in this table are the actual coefficients of the logistic regression model. These are the formal statistics estimated by the model. Because logistic models are not readily interpretable in an intuitively approachable manner, we rely on the odds ratios to express the results of the model. The predictive concordance statistic is a measure of goodness-of-fit for the model. It reports the proportion of outcomes that are correctly predicted by the logistic regression.