Appendix
It is trivially obvious that some of the variables included in the dataset are
intercorrelated. Age strongly correlates to income as people progress through their
careers; the relationship of education is more complicated, as older cohorts may have
fewer college-educated individuals, but as cohorts grow older their education levels rise
as individuals return to school. Quadratic terms for black and Latino populations are
similarly obviously intercorrelated with the values for population. But the question is
whether there is sufficient intercorrelation to support factor analysis (Cerny and Kaiser
1977). Figure 1 demonstrates that the Bartlett’s test demonstrates statistically significant
intercorrelation, while the KMO shows that the factorability is “mediocre.” However, the
“kitchen sink” model with all variables separately regressed is moving in too many
directions to support any inferences. Thus, a confirmatory factor analysis is appropriate
to determine if the variables intercorrelate in the way they are expected to do.
FIGURE 1 ABOUT HERE
Racial groupings are expected to intercorrelate, and Table A1, the rotated
orthogonal factor loading matrix, demonstrates that they do. However, the non-racial
demographic factors either need to load onto one factor, or the proxy for education
needs to be excluded, and age and income need to be broken out as separate control
variables. This is so because while age and income can be expected to intercorrelate,
education presents a more complicated picture. Earning a bachelor’s degree is more
frequent among younger cohorts, but older cohorts have lower rates of attainment. The
picture for income is even more complicated, with some skilled trades having high
incomes with minimal formal education, and conversely, some bachelor’s degree
holders working in positions with lower incomes. Table A2 shows the least-squares
regression to check for the effect of age and education on income. While age is strongly
correlated, education is extremely weak. As a check for nonlinearity, a quadratic term
for age is included, but is not significant. Thus, since the three non-racial demographic
variables do not all load onto one factor, then age and income should be broken out and
education should be jettisoned. In Table A1, precisely that result is what is seen. While
age loads onto the second factor (in this table, not yet labeled as anything other than
“Factor2”), income and education load separately onto “Factor4”. Thus, we can
conclude that education is not an appropriate control variable and exclude it.
TABLE A2 ABOUT HERE
TABLE A3 ABOUT HERE
Tables and Figures
Figure 1: Test for Factorability
Determinant of the correlation matrix
Det = 0.002
Bartlett test of sphericity:
Chi-square = 1.42e+05
Degrees of freedom = 28
p-value = 0.000
H0: variables are not intercorrelated
Kaiser-Meyer-Olkin Measure of Sampling Adequacy:
KMO = 0.634
Table A1: Orthogonally-Rotated Factor Loading Matrix
-------------------------------------------------------------------------------
Variable Factor1 Factor2 Factor3 Factor4 Factor5 Uniqueness
-------------+--------------------------------------------------+--------------
Bachelors Degrees 0.0627 -0.1965 0.0911 0.5116 -0.0286 0.6866
Median Age -0.1435 0.9672 -0.1738 -0.0248 0.0122 0.013
Percent White -0.8204 0.2448 -0.2054 -0.1982 0.1178 0.1717
Percent Black 0.9636 -0.1292 -0.0295 -0.0233 -0.015 0.0532
Percent Latino 0.0277 -0.203 0.9355 0.0835 -0.0463 0.0737
Mean Adjusted Gross Income -0.1188 0.0749 -0.0673 0.403 0.0425 0.8115
Black Quadratic Term 0.9322 -0.0562 -0.0628 -0.0857 0.08 0.1101
Latino Quadratic Term -0.0064 -0.1335 0.9374 -0.055 0.0354 0.0992
Age Quadratic Term -0.1324 0.9739 -0.1416 -0.0257 -0.0018 0.0132
-------------------------------------------------------------------------------
Table A2: Effect of age and education on income
Mean Adjusted Gross
Income Coef.
Bachelors Degrees
Age Quadratic Term
Significance: .05 > * > .01 > **.
Std.
Err. T P>t
0.0064
2
0.8704
9 0.3176 2.74 0.006**
0.0035
8
8.6076
5
0.0001
4 45.26 0.000**
0.0037
4 0.96
6.6985
4 1.29
0.338_
0.199_
Cerny, B.A. and Kaiser, H.F. (1977). “A Study of a Measure of Sampling Adequacy For
Factor-Analytic Correlation Matrices,” Multivariate Behavioral Research 12(1): 43-47.