Small Area Estimation of Dependency: Final Report. Regression-Adjusted Results

01/13/1989

A model including demographic and contextual variables was fit to the dependent variable, functional dependency. Table 5 presents the survey-weighted results of the log-linear regression analysis. Race, sex, age, age-squared and the categorical variable reflecting the percent of the elderly (65 and older) population who reside in poverty were significant (p<.001) predictors of functional dependency in the overall model. Assuming a true log-linear relationship, the continuous form of the contextual variable (percent elderly population in poverty) statistically would be preferable. However, as we found negligible statistical differences between the continuous and the categorical use of the contextual variable, and as we felt results and examples could more easily be presented with the categorical variable, our results focus on the latter. (Survey-weighted results for the continuous variable are presented in Table 6.)

TABLE 5: Regression Results: Demographic and Categorical Contextual Variables
Variable   Chi-Square     d.f.     p-value  
Race 28.56 2 0.001
Sex 217.76 2 0.001
Age Group 654.65 2 0.001
Age Group-Squared   29.23 2 0.001
Poverty 36.66 2 0.001
Intercept 1920.81 2 0.001
Lack of fit chi-square = 128.13, df = 108, p = 0.0906
Model chi-square = 959.14, df = 10, p = 0.001
Log   Probability of being not dependent
 Probability of being ADL dependent
Variable Coefficient Standard Error Chi-Square d.f. p-value
Race -0.41 0.13 12.60 1 0.001
Sex -0.17 0.08 4.84 1 0.028
Age Group -0.59 0.03 478.96 1 0.001
Age Group-Squared -0.11 0.02 26.03 1 0.001
Poverty -0.35 0.07 25.57 1 0.001
Intercept 2.51 0.08 1030.29 1 0.001
Log   Probability of being IADL dependent
 Probability of being ADL dependent
Variable Coefficient Standard Error Chi-Square d.f. p-value
Race -0.02 0.13 0.02 1 0.877
Sex 0.71 0.09 62.80 1 0.001
Age Group -0.20 0.03 44.47 1 0.001
Age Group-Squared -0.07 0.02 7.23 1 0.007
Poverty -0.15 0.08 3.51 1 0.061
Intercept 0.44 0.09 22.15 1 0.001

 

TABLE 6: Regression Results: Demographic and Continuous Contextual Variables
Variable   Chi-Square     d.f.     p-value  
Race 31.94 2 0.001
Sex 219.28 2 0.001
Age Group 652.69 2 0.001
Age Group-Squared   28.79 2 0.001
Poverty 32.19 2 0.001
Intercept 998.66 2 0.001
Lack of fit chi-square = 1232.45, df = 1176, p = 0.1231
Model chi-square = 956.07, df = 10, p = 0.001
Log   Probability of being not dependent
 Probability of being ADL dependent
Variable Coefficient Standard Error Chi-Square d.f. p-value
Race -0.46 0.12 15.78 1 0.001
Sex -0.17 0.08 4.96 1 0.026
Age Group -0.59 0.03 476.88 1 0.001
Age Group-Squared -0.11 0.02 25.59 1 0.001
Poverty -0.02 0.01 12.50 1 0.001
Intercept 2.75 0.12 492.68 1 0.001
Log   Probability of being IADL dependent
 Probability of being ADL dependent
Variable Coefficient Standard Error Chi-Square d.f. p-value
Race -0.06 0.13 0.21 1 0.650
Sex 0.71 0.09 63.09 1 0.001
Age Group -0.20 0.03 43.73 1 0.001
Age Group-Squared -0.07 0.02 7.04 1 0.008
Poverty 0.00 0.01 0.00 1 0.971
Intercept 0.39 0.14 7.40 1 0.007

In our analysis we found that three additional contextual variables (both in their continuous and categorical forms) were significant predictors of functional dependency: the number of heating degree days (a variable reflective of climate and a proxy for geographic region); the ratio of Medicaid recipients to the population below poverty (a measure of access to health care services); and the number of unoccupied nursing home beds per 1000 elderly (a measure of the supply of beds relative to the demand for them). When each of these variables was added to the model with race, sex, age, and age-squared each was significant (p<.02). However, when more than one of the community variables was included in the model, only the poverty variable remained significant (p<.10).

The fit of the model which included the categorical poverty variable as the only contextual variable was evaluated with the log-likelihood ratio chi-square statistic. Since the statistic was nonsignificant, the use of the model was supported. The need for pairwise interactions of the variables was evaluated and determined to be unnecessary.

Further evaluation of the fit of the model was done by plotting the observed age-specific rates of dependency and the regression-predicted rates of dependency. As can be seen from Figure 1 and Figure 2, the predicted rate of both ADL (Figure 1) and IADL (Figure 2) dependency closely approximate the observed rates. However, when the population is divided into smaller subgroups, such as nonwhite females, the model fits somewhat less well (Figure 3).

FIGURE 1: ADL Dependent Population
Line Chart: Observed and Predicted Percent Dependent by Age Group 65-69, 70-74, 75-79, 80-84, 85+.

 

FIGURE 2: IADL Dependent Population
Line Chart: Observed and Predicted Percent Dependent by Age Group 65-69, 70-74, 75-79, 80-84, 85+.

 

FIGURE 3: ADL Dependent Nonwhite Female Population
Line Chart: Observed and Predicted Percent Dependent by Age Group 65-69, 70-74, 75-79, 80-84, 85+.

Table 7 presents the regression-adjusted estimates of the prevalence of ADL dependency and Table 8 of IADL dependency. As the poverty variable has 3 values (less than 8%, between 8 and 15%, and over 15% of the elderly population residing in poverty), 3 sets of estimates are produced--one for communities with low rates of poverty, one for communities with moderate rates, and one for communities with high rates of poverty among the elderly. As can be seen in the tables, results showed the likelihood of ADL and IADL dependency increases quadratically with age, and also increases with being nonwhite, and with an increasing percent of the elderly population residing in poverty. The likelihood of IADL dependency also increases with being female, but the likelihood of being ADL dependent does not increase uniformly with being female. Although the likelihood of being ADL dependent is in general higher for females than males until age 80 in communities of low and moderate levels of poverty, and until age 75 for those in high poverty communities, after these ages the percent of noninstitutionalized males with an ADL impairment is either equal to or greater than that of females.

TABLE 7: Regression-Adjusted Estimates of the Percentage of ADL Dependent Elderly Americans Living in the Community by Age, Sex and Race
Race Sex   65-69     70-74     75-79     80-84     85 & Over     65 & Over  
LOW POVERTY COMMUNITY
White Male 2.5 3.2 4.9 9.1 18.8 4.3
Female   2.8 3.4 5.1 9.0 17.4 5.6
Both 2.7 3.4 5.1 9.0 17.7 5.1
NonWhite Male 3.7 4.6 7.0 12.4 24.1 6.5
Female 3.9 4.8 7.0 11.7 21.1 6.1
Both 3.8 4.8 7.0 11.8 23.0 6.2
All Races   Male 2.7 3.3 5.1 9.3 19.9 4.5
Female 2.9 3.6 5.3 9.3 17.5 5.6
Both 2.8 3.5 5.2 9.3 18.1 5.2
MODERATE POVERTY COMMUNITY
White Male 3.5 4.4 6.7 12.1 23.9 6.4
Female 3.8 4.7 6.9 11.7 21.5 7.2
Both 3.7 4.6 6.8 11.8 22.2 6.9
NonWhite Male 5.1 6.3 9.4 16.2 29.7 7.9
Female 5.3 6.4 9.1 14.8 25.5 9.0
Both 5.2 6.4 9.3 15.3 26.4 8.5
All Races Male 3.7 4.6 6.9 12.4 24.0 6.5
Female 3.9 4.8 7.0 11.9 21.7 7.3
Both 3.8 4.7 6.9 12.0 22.4 7.0
HIGH POVERTY COMMUNITY
White Male 4.9 6.1 9.1 15.9 29.7 8.4
Female 5.2 6.3 9.1 14.9 26.2 9.0
Both 5.1 6.2 9.1 15.3 27.3 8.8
NonWhite Male 7.0 8.5 12.5 20.7 35.9 11.4
Female 7.1 8.4 11.8 18.4 30.2 11.3
Both 7.1 8.5 12.0 19.0 32.3 11.3
All Races Male 5.2 6.4 9.7 16.4 30.6 8.9
Female 55 6.7 9.5 15.5 26.7 9.4
Both 5.3 6.6 9.6 15.8 28.0 9.2

 

TABLE 8: Regression-Adjusted Estimates of the Percentage of IADL Dependent Elderly Americans Living in the Community by Age, Sex and Race
Race Sex   65-69     70-74     75-79     80-84     85 & Over     65 & Over  
LOW POVERTY COMMUNITY
White Male 5.2 6.6 8.9 12.5 17.3 7.3
Female   11.7 14.4 18.8 25.2 32.5 17.5
Both 8.7 11.5 14.5 22.0 29.4 13.5
NonWhite Male 7.5 9.3 12.3 16.7 21.7 10.3
Female 16.2 19.7 25.0 32.0 38.7 21.1
Both 12.0 17.0 17.7 29.3 27.7 16.7
All Races   Male 5.5 6.8 9.2 12.7 18.2 7.6
Female 12.2 15.2 19.2 25.9 32.8 17.9
Both 9.1 12.2 14.7 22.7 29.2 13.8
MODERATE POVERTY COMMUNITY
White Male 6.3 7.8 10.4 14.4 18.9 9.0
Female 13.8 16.9 21.7 28.2 34.8 19.9
Both 10.4 13.1 17.3 23.5 29.9 15.5
NonWhite Male 8.9 11.0 14.3 18.8 23.1 11.8
Female 18.9 22.7 28.2 35.0 40.4 25.2
Both 13.8 17.6 21.4 28.9 36.6 19.1
All Races Male 6.5 8.1 10.7 14.6 19.1 9.2
Female 14.1 17.3 22.0 28.6 35.1 20.2
Both 10.6 13.4 17.5 23.8 30.2 15.7
HIGH POVERTY COMMUNITY
White Male 7.5 9.3 12.2 16.3 20.3 10.5
Female 16.2 19.6 24.7 31.1 36.5 22.1
Both 12.4 15.2 19.7 25.9 31.1 17.3
NonWhite Male 10.5 12.8 16.3 20.8 24.1 14.1
Female 21.7 25.8 31.4 37.6 41.3 28.3
Both 17.3 21.1 25.5 33.5 35.0 23.1
All Races Male 7.9 9.8 12.9 16.8 20.9 11.0
Female 17.0 20.8 25.9 32.3 37.1 23.2
Both 13.1 16.2 20.7 27.1 31.6 18.3

 

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