The standard independent variables, described in Appendix 2, are zAFQT89, the 1989 scoring of the AFQT; zSES, the socioeconomic background of the NLSY subjects; and zAge, based on the age of the NLSY subjects as of December 31, 1990. All are expressed as standard scores with a mean of 0 and a standard deviation of 1.
All dependent variables are binary. The coefficients are parameter estimates when the dependent variable = “yes.” The linear logistic model has the form
logit(p) = log(p/(1−p)) = α + ß′x
where α is the intercept parameter and ß is the vector of slope parameters for a vector of independent variables x. Take as an example the first set of results presented subsequently, involving poverty. Suppose you want to know the probability that a person is under the poverty line in 1989 (Poverty = “Yes”), stipulating that the person in question has an IQ (zAFQT) 1.5 standard deviations below the mean, socioeconomic background (zSES) .3 standard deviation above the mean, and is exactly of mean age. Using the parameters in the basic analysis for poverty rounded to four decimal places, and a computationally convenient re-expression of p, the probability is computed as follows:
The probability we set out to compute is 18.37 percent.
“The High School Sample” consists of those who received a high school diploma through the normal route (not a GED) and reported exactly twelve years of education as of the 1990 interview.
“The College Sample” consists of those who completed a bachelor’s degree and reported exactly sixteen years of education as of the 1990 interview.
The software used for the analyses is JMP Version 3, by SAS Institute Inc. JMP treats nominal independent variables differently from other major software packages such as SAS and SPSS. In those packages, a parameter for a nominal variable represents the difference between that level of the nominal variable and an omitted level serving as a reference group. In JMP, a parameter represents the difference of a given level from the average over all levels of the nominal variable. The implied parameter for the remaining level is the negative sum of the other levels (i.e., the parameters sum to zero over all the effect levels). For example, suppose Race were being used as a nominal variable, with categories of Black, Latino, and White. In the JMP printout, the coefficients would appear as
Race[Black-White] x1
Race [Latino-White] x2
The order is determined by the alphabetical order of the categories. In this case, the coefficient x1 applies to blacks, x2 to Latinos. The implied White coefficient is −1 × (x1 + x2). In the case of a binary independent variable such as Sex, the printout would show a single line
Sex [Female-Male] x1
which applies to females. The coefficient for Male equals −x1.
CHAPTER 5: POVERTY
DEPENDENT VARIABLE: Under the official poverty line in 1989.
SAMPLE RESTRICTIONS: Excludes those who reported they were out of the labor force because they were in school in either the 1989 or 1990 interviews.
Basic Analysis:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prot>ChiSq
Model 3 90.94009 181.8802 0.000000
Error 3363 784.40179
C Total 3366 875.34188
RSquare (U) 0.1039
Observations 3367
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept −2.6487288 0.0768803 1187 0.0000
zAFQT89 −0.8376338 0.0935061 80.25 0.0000
zSES −0.3300720 0.0900996 13.42 0.0002
zAge −0.0238375 0.0723735 0.11 0.7419
The High School Sample:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 22.01811 44.03622 0.000000
Error 1232 325.26939
C Total 1235 347.28750
RSquare (U) 0.0634
Observations 1236
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept −2.7237775 0.1290286 445.63 0.0000
zAFQT89 −0.8267293 0.1627358 25.81 0.0000
zSES −0.3619703 0.1499855 5.82 0.0158
zAge +0.1049227 0.1094603 0.92 0.3378
The College Sampk: Omitted. Only six persons in the cross-sectional College Sample were in poverty.
For Mothers Married as of the 1989 Interview:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 17.14553 34.29106 0.000000
Error 786 179.84999
C Total 789 196.99552
RSquare (U) 0.0870
Observations 790
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept −2.7732817 0.1646023 283.87 0.0000
zAFQT89 −0.6437797 0.2140132 9.05 0.0026
zSES −0.3910629 0.2020317 3.75 0.0529
zAge −0.3338674 0.1587605 4.42 0.0355
For MothersWho Were Separated, Divorced, or Never Married as of the1989 Interview:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 8.07114 16.14228 0.001060
Error 211 135.77658
C Total 214 143.84772
RSquare (U) 0.0561
Observations 215
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept −0.7449132 0.1713794 18.89 0.0000
zAFQT89 −0.6722121 0.2277019 8.72 0.0032
zSES −0.1597461 0.1952709 0.67 0.4133
zAge −0.1524315 0.1530986 0.99 0.3194
CHAPTER 6: SCHOOLING
DEPENDENT VARIABLE: Permanently dropped out of high school.
SAMPLE RESTRICTIONS: Excludes those who obtained a GED.
Basic Analysis:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 393.8978 787.7956 0.000000
Error 3568 779.9904
C Total 3571 1173.8882
RSquare (U) 0.3355
Observations 3572
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept −2.85322606 0.0939659 922.00 0.0000
zAFQT89 −1.72295934 0.1028145 280.83 0.0000
zSES −0.64776232 0.0896658 52.19 0.0000
zAge +0.05695640 0.0688286 0.68 0.4079
Basic Analysis, Adding an Interaction Term for zAFQT and zSES:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 4 399.9876 799.9751 0.000000
Error 3567 773.9006
C Total 3571 1173.8882
RSquare (U) 0.3407
Observations 3572
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept −2.9143231 0.1029462 801.41 0.0000
zAFQT89 −1.8937642 0.1188518 253.89 0.0000
zSES −0.9402389 0.1250634 56.52 0.0000
zAge +0.0522667 0.0682755 0.59 0.4440
zAFQT89*zSES −0.4133224 0.1187879 12.11 0.0005
DEPENDENT VARIABLE: Received a GED instead of a high school diploma.
SAMPLE RESTRICTIONS: Excludes those who obtained neither a high school diploma nor a GED.
Basic Analysis:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 72.06475 144.1295 0.000000
Error 3490 915.28145
C Total 3493 987.34620
RSquare (U) 0.0730
Observations 3494
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept −2.3548461 0.0653867 1297 0.0000
zAFQT89 −0.4325254 0.0851185 25.82 0.0000
zSES −0.6082151 0.0837515 52.74 0.0000
zAge− 0.0416441 0.0662445 0.40 0.5296
DEPENDENT VARIABLE: Received a ba
chelor’s degree.
SAMPLE RESTRICTIONS: Excludes those who had less than a bachelor’s degree and were in postsecondary education in either the 1989 or 1990 interview.
Basic Analysis:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 807.9072 1615.814 0.000000
Error 3817 1364.3417
C Total 3820 2172.2489
RSquare (U) 0.3719
Observations 3821
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept −2.41992250 0.0786991 945.50 0.0000
zAFQT89 +1.80771403 0.0795537 516.34 0.0000
zSES +1.04818417 0.0690372 230.52 0.0000
zAge −0.29777760 0.0516373 33.25 0.0000
CHAPTER 7: UNEMPLOYMENT, IDLENESS, AND INJURY
DEPENDENT VARIABLE: Out of the labor force for four weeks or more in 1989.
SAMPLE RESTRICTIONS: Civilian males who did not respond “unable to work” or “in school” to the question on labor force participation in the 1989 or 1990 interview.
Basic Analysis:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 9.44293 18.88586 0.000289
Error 1682 548.25144
C Total 1685 557.69437
RSquare (U) 0.0169
Observations 1686
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept −2.20264085 0.0868001 643.94 0.0000
zAFQT89 −0.36246881 0.0992802 13.33 0.0003
zSES +0.21788340 0.1075722 4.10 0.0428
zAge −0.12815393 0.0864018 2.20 0.1380
The High School Sample:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 4.45831 8.916625 0.030420
Error 617 156.98046
C Total 620 161.43878
RSquare (U) 0.0276
Observations 621
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept −2.69780012 0.1767563 232.95 0.0000
zAFQT89 −0.42151253 0.2264362 3.47 0.0627
zSES +0.56489480 0.230053 6.03 0.0141
zAge −0.14556950 0.1672623 0.76 0.3841
The College Sample:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 6.794337 13.58867 0.003522
Error 264 56.536860
C Total 267 63.331196
RSquare (U) 0.1073
Observation 268
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>Sq
Intercept −3.12957075 0.6081769 26.48 0.0000
zAFQT89 −0.84324247 0.4526768 3.47 0.0625
zSES +0.94514750 0.3875388 5.95 0.0147
zAge −0.46061574 0.299044 2.37 0.1235
DEPENDENT VARIABLE: Unemployed for four weeks or more in 1989.
SAMPLE RESTRICTIONS: Civilian males who did not respond “unable to work” or “in school” to the question on labor force participation in the 1989 or 1990 interview and were in the labor force throughout 1989.
Basic Analysis:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 11.30841 22.61682 0.000049
Error 1393 348.71511
C Total 1396 360.02353
RSquare(U) 0.0314
Observations 1397
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept −2.53577016 0.1076083 555.30 0.0000
zAFQT89 −0.49486463 0.1298967 14.51 0.0001
zSES −0.02534849 0.1383889 0.03 0.8547
zAge −0.02181428 0.1108396 0.04 0.8440
The High School Sample:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 1.86533 3.730657 0.292056
Error 533 140.49123
C Total 536 142.35656
RSquare(U) 0.0131
Observations 537
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept −2.59878187 0.1766146 216.51 0.0000
zAFQT89 −039353140 0.2368752 2.76 0.0966
zSES +0.13951940 0.2353179 0.35 0.5532
zAge −0.10510566 0.1762471 0.36 0.5509
The College Sample:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 3.570096 7.140193 0.067561
Error 224 40.506133
C Total 227 44.076230
RSquare (U) 0.0810
Observations 228
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept −3.1686886 0.7276735 18.96 0.0000
zAFQT89 −0.9196886 0.5641635 2.66 0.1031
zSES +1.0039255 0.5015717 4.01 0.0453
zAge +0.2941965 0.3311174 0.79 0.3743
CHAPTER 8: FAMILY MATTERS
DEPENDENT VARIABLE: Ever married before the age of 30.
SAMPLE RESTRICTIONS: Persons who turned thirty by the 1990 interview.
Basic Analysis:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 6.43345 12.8669 0.004933
Error 1630 839.76747
C Total 1633 846.20092
RSquare (U) 0.0076
Observations 1634
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept +1.19841361 0.128902 86.44 0.0000
zAFQT89 −0.0473587 0.0757854 0.39 0.5320
zSES −0.1905526 0.0786307 5.87 0.0154
zAge +0.20403379 0.1290545 2.50 0.1139
The High School Sample:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 6.92871 13.857 0.003106
Error 601 259.40296
C Total 604 266.33168
RSquare (U) 0.0260
Observations 605
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept +1.41494853 0.2342703 36.48 0.0000
zAFQT89 +0.51424443 0.1598383 10.35 0.0013
zSES −0.1128845 0.1582799 .51 0.4757
zAge +0.36827169 0.2422543 2.31 0.1285
The College Sample:
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 3 0.17181 0.343616 0.951627
Error 233 145.35748
C Total 236 145.52929
RSquare (U) 0.0012
Observations 237
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept +0.71372375 0.3946174 3.27 0.0705
zAFQT89 +0.05013859 0.2237528 0.05 0.8227
zSES +0.0968295 0.1833680 0.28 0.5975
zAge −0.0177807 0.2950863 0.00 0.9520
DEPENDENT VARIABLE: Divorced within the first five years of marriage.
SAMPLE RESTRICTIONS: Persons married prior to January 1, 1986.
Basic Analysis, Adding Date of First Marriage (MarDate 1):
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 4 21.8881 43.77626 0.000000
Error 2026 991.3719
C Total 2030 1013.2600
RSquare (U) 0.0216
Observations 2031
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept +5.70860970 1.9858067 8.26 0.0040
zAFQT89 −0.35734009 0.0781258 20.92 0.0000
zSES +0.22195410 0.0787612 7.94 0.0048
zAge −0.17766944 0.0741478 5.74 0.0166
MarDatel −0.08677335 0.0243113 12.74 0.0004
<
br /> The High School Sample, Adding Date of First Marriage (MarDate 1):
Whole-Model Test
Source DF −LogLikihood ChiSquare Prob>ChiSq
Model 4 3.54304 7.086073 0.131409
Error 870 428.70643
C Total 874 432.24947
RSquare (U) 0.0082
Observations 875
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept +5.4451395 3.1286887 3.03 0.0818
zAFQT89 −0.0379171 0.1348129 1.08 0.7785
zSES +0.2206925 0.1288222 2.93 0.0867
zAge −0.1078057 0.1146773 0.88 0.3472
MarDatel −0.0839950 0.0383236 4.80 0.0284
The College Sample, Adding Date of First Marriage (MarDate 1):
Whole-Model Test
Source DF -LogLikelihood ChiSquare Prob>ChiSq
Model 4 5.548154 11.09631 0.025503
Error 204 48.414468
C Total 208 53.962623
RSquare (U) 0.1028
Observations 209
Parameter Estimates
Term Estimate Std Error ChiSquare Prob>ChiSq
Intercept +32.392875 13.508886 5.75 0.0165
zAFQT89 −0.75619367 0.4502182 2.82 0.0930
zAge −0.55875424 0.4046911 1.91 0.1674
MarDatel −0.41113710 0.1629791 6.36 0.0116
Basic analysis, Adding Parental Living Arrangements at Age 14 (Adultl4):
The Bell Curve: Intelligence and Class Structure in American Life Page 71
