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 outcomerelative 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  
1214 years  0.04  0.83  0.05  0.80  
1517 years  0.11  0.57  0.12  0.51  
Gender 
Male  0.00  1.01  0.00  0.99 
Female *     1.00     1.00  
Race/ethnic 
African American  0.12  0.65  0.10  0.69 
Hispanic  0.00  1.00  0.00  1.03  
White, Other *     1.00     1.00  
Region 
Primary urban county  0.12  0.65  0.12  0.64 
Remainder of State *     1.00     1.00  
Sequence 
First Spell in care *     1.00     1.00 
Reentry Spell  0.06  0.72  0.07  0.69  
Placement Type 
Congregate Care  0.03  1.18  0.02  1.12 
Other (FC or KC) *     1.00     1.00  
Stability 
On placement in spell *     1.00     1.00 
2+ placements  0.26  0.40  0.29  0.35  
State: 
Alabama  0.08  0.36  0.01  0.88 
California  0.05  1.19  0.05  0.83  
Illinois  0.07  0.68  0.15  0.45  
Maryland  0.03  0.72  0.00  0.97  
Michigan *     1.00     1.00  
Missouri  0.02  1.17  0.00  0.94  
New Mexico  0.03  1.37  0.01  1.28  
New York  0.01  0.96  0.02  0.91  
Wisconsin  0.05  1.45  0.03  1.27  
Year of Entry 
1990  0.02  1.12  0.02  1.12 
1991  0.01  1.05  0.01  1.06  
1992 *     1.00     1.00  
1993  0.00  0.98  0.00  0.98  
1994  0.02  0.92  0.02  0.93  
Intercept  0.78  1.28  
exp(intercept)  2.18  3.60  
Predictive Concordance  0.70  0.71  
N spells  404,416  404,416  
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 "911 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 911 year old entrant, are .39 to 1. Conversely, we could take the reciprocal and state that a 911 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 goodnessoffit for the model. It reports the proportion of outcomes that are correctly predicted by the logistic regression.

3.1 Reunification From Foster Care

Table IIC.I presents a logistic regression model for the likelihood of reunification within three years of entry and also a parallel model for the likelihood of a family exit within three years of entry. The units of analysis are all spells that started during the years 199094 in the nine study states. Because the spells were observed through 1997, there are no censored observations in these data.
Summary of Logistic Reunification Analysis.
Age Reunification is least likely for children under one year of age at entry, and also for children over twelve years of age at entry. The largest difference is between the ratio for infants and that for 911 year olds, as 911 year olds are 2.56 times more likely to reunify than infants.^{8} Gender Gender has little apparent effect on the likelihood of reunification, with males estimated as being 1 percent more likely than females to exit via reunification. Race The odds of reunification for white and Hispanic children are even. The odds of reunification are 54 percent [(1.00/0.65) 1] more likely for children from either of these groups than for African American children in foster care. Region Reunification is 54 percent [(1.00/0.65) 1] more likely for children living in those portions of these states that are not in the primary urban counties. ^{9} The main urban counties have lower reunification rates.
Sequence Reunification is 39 percent [(1.00/0.72) 1] more likely for children in their first spell in care than it is for children in reentry foster care spells. Placement Reunification is less likely for children in family foster care arrangements (relative or nonrelative) than for children in institutions or group homes.^{10} This result is weakened by the fact that both kinship and nonrelative foster care are included in the foster care category. Stability Reunification is 150 percent more likely [(1.00/0.40)  1] from spells where the child stays in one single placement than in spells where the child moves at least one time between placement settings. Year: Reunification became less likely for each successive annual cohort between 1990 and 1994. The odds for the reunification of 1990 entrants were 22 percent greater [(1.12/0.92)1) for 1990 entrants than they were for 1994 entrants. State: Reunification is most likely in Wisconsin and New Mexico and least likely in Alabama. The largest difference in odds is between Wisconsin and Alabama: entrants in Wisconsin are over 4.0 times as likely [1.45 0.36] as entrants in Alabama to exit foster care via reunification. It is worth restating that these statistics were computed simultaneously in a single multivariate model. Thus, unlike the bivariate results shown earlier, each of these relationships is observed with the influence of all of the other variables in the model being controlled. It is important to note that, for the most part, the basic direction of most of the bivariate results observed in Table IIA. I are largely preserved in the results produced under multivariate controls. Thus, the independent variables we have discussed each appear to contribute independently to the prediction of reunification levels.
8. The following are equivalent expressions: 911 year olds are 2.56 times more likely to reunify than infants. Infants are 156 percent less likely to reunify than 911 year olds. The odds ratio of reunification between infants and 911 year olds is .39 to 1.
9. Primary urban counties have been as follows: AL (Jefferson), CA (Los Angeles), IL (Cook), MD (Baltimore City), MI (Wayne), MO (Jackson and St. Louis City), NM (Bernalillo), NY (New York City), and WI (Milwaukee).
10. Because kinship care cannot be identified in all states, relative and nonrelative foster care are combined into one category for the ninestate analysis tables that follow, a category for kinship care will be reported separately. For states where kinship cannot be identified, relative and nonrelative care will continue to be combined, and the value for kinship care is reported as "missing."
