... formulation are discussed. 8 1 2011 © Population Association of America 1977 1977 Compositional Variable Mathematical Relationship Saturated Model Ordinary Regression Multiplicative Model References Duncan , O. D. ( 1968 ). Inheritance of Poverty or Inheritance of Race...

... obtained by constructing a life table. This model is known as the fully saturated model be- cause it completely reproduces the data in the sense that the expected deaths exactly equal the observed (JlijkEijk = Dijk = Dijk)' There are as many parame- ters (/1K) as cells in the model. The fully saturated...

... ser comparado uno con otro y con criterios externos, tales como series de tiempo empíricas. Summary The demographic model is a program for representing births, deaths, migration, and social mobility as social processes in a non-stationary stochastic process (Markovian). Transition probabilities...

... in the degree of segregation. Our models (Charles and Grusky 1995) properly refocus attention on the underlying profile itself. Although the task of modeling such profiles is not always easy, we can simplify matters for illustrative pur- poses by relying, without loss of generality, on the following saturated...

... addresses this gap by comparing the trajectories of higher education expansion with those experienced at other levels on their course to universal or near-universal access. We demonstrate that a population-level model of expansion toward universal access fits higher education as well as lower levels...

... group (4). This model is the best-fitting homogamy model in terms of the BIC. However, it is slightly worse fitting than the saturated model, which allows for a saturated association between wives' and husbands' educational achievement ( Ψ i j H W ) (−126.4; results not shown...

... for this situation may be con- sidered as a three-way I X J X K cross- table with expected proportions 1rt)k. We will assume that 1rtJk > 0 for all i,j, and k, and we let VIJk = log (1rtJk)' A "saturated" multiplicative model with zero degrees of freedom may be written as _ C G D CG CD GD CGD (1) 1rtJk - 1/Tt TJ Tk...

... test to test whether the target models (i.e., the various biometric and psychometric models) fit significantly less well than a satu- rated model. The test statistic equals the difference between the chi-squares of the saturated model and target model, and is chi-square distributed with the degrees...

... impetus to estimate the bequest model by including both earnings and occupation. In the reestimation of the model, we tested the shift parameters for occupations that are independent of earnings (Model B), a structured model based on priors about particular occupations (Model C), and a saturated model...

... the significant effect, if any, of the interaction between Y and the parity and spacing factors of the reproductive process. The saturated model (Table 3) presents the second-order interaction of Y and the linear and quadratic effects of P and A. The main effect of year (period change between 1965 and 1970...

...Fig. 2 Bayesian information criterion (BIC) statistic compared with the saturated models for different log-linear models fit to Brazilian marriage data. Lower values indicate superior fit. Black bars indicate the case where browns and blacks are collapsed into a single category. Gray bars...

... in completed months. d Omitted category (captured by main effect). e l against fully saturated model (the full data matrix defined by Model V). f Degrees of freedom = number of nonempty cells in the full data matrix defined by Model V. associated with very short birth intervals (see Miller 1989...

... the modeling by comparing bivariate with saturated models to test the assumption of twin modeling. When using raw data, it is necessary to estimate a saturated model with free covariances to evaluate the fit of the ACE and other subset models. The ACE model did not differ from the saturated model for education...

.... To analyze whether the fulfillment of residential preference is affected by the factors we considered important, two saturated logit models were formulated, each of which examines one of the sets of explanatory factors. In table 2, the hypothesis that the fulfillment of residential preference would...

... < HS diploma e1 e1 n/a HS diploma e2 ij1 HRWRHE + e2 ij1 HRWRHE Some college e3 ij1 HRWRHE + ij 2 HRWRHE + e3 ij 2 HRWRHE BA or more e4 ij1 HRWRHE + ij 2 HRWRHE + ij 3 HRWRHE + e4 ij 3 HRWRHE Notes: The models for each minority group include four sets of exchange parameters. These sets of parameters compare (1) the schooling of white wives minority husbands with the schooling of minority wives minority husbands; (2) the schooling of white wives white husbands with the schooling of minority wives white husbands; (3) the schooling of white husbands minority wives with the schooling of minority husbands minority wives; and (4) the schooling of white husbands white wives with the schooling of minority husbands white wives. aThe local odds ratio is the ratio of the odds for adjacent rows that a minority wife s (husband s) spouse has the higher level of schooling to the odds that a white wife s (husband s) spouse has the higher level of schooling. Negative values for the log local odds ratios in the top panel suggest that wives of minority husbands have less schooling than wives of white husbands; negative values for log local odds ratios in the bottom panel suggest that husbands of minority wives have less schooling than husbands of white wives. RACIAL INTERMARRIAGE PAIRINGS 153 of respondent s race on spouse s schooling. The first is a column-effects model with unit-spaced scores for the rows (Agresti 1990:287 90; Ishii-Kuntz 1994). The second is an R + C model (Clogg and Shihadeh 1994:44 45), which generalizes the column-effects model by estimating the row scores as parameters. For both models, the estimated effects can be interpreted in terms of local odds ratios, which are odds ratios for 2 × 2 tables formed by the intersection of two adjacent rows and two adjacent columns. Thus the ij1 HRWRWE effects represent the log of the ratio of the odds of having a high school diploma versus having less than a high school diploma for minority husbands wives to the same odds for white husbands wives. The ij 2 HRWRWE and ij 3 HRWRWE parameters represent the effects for higher pairs of adjacent schooling categories; the ij1 HRWRHE , ij 2 HRWRHE , and ij 3 HRWRHE pa- rameters represent the corresponding effects of wife s racial group on husband s schooling. The column-effects model constrains the exchange parameters in each set, and hence the local odds ratios, to be equal. The R + C model allows the exchange parameters in each set to vary. In every case, a negative value for these exchange pa- rameters suggests that minority respondents spouses have less schooling than whites spouses. If all the exchange pa- rameters for a particular comparison are negative, we can conclude that the minority members spouses have less schooling than whites spouses. RESULTS The sample restrictions yielded a total of 488,673 marriages. Table 2 presents a cross-classification of husband s and wife s schooling by husband s and wife s race. The first col- umn of coefficients in Table 3 presents crude odds ratios rep- resenting the likelihood of marrying members of one s own group. For blacks, Japanese Americans, and Mexican Ameri- cans, the odds of marrying a member of one s own group rather than a white spouse are much larger than the odds that a white individual would marry a member of the minority group rather than a white spouse. The odds that a black man or woman is married to a black spouse rather than a white spouse is 11,222 times the odds that a white man or woman is married to a black spouse rather than a white spouse. For Mexican Americans, the corresponding odds ratio is 270; for Japanese Americans, 873. These odds ratios do not account for group differences in schooling, and should be considered only crude indicators of intermarriage tendencies. They sug- gest, however, that group boundaries between Mexican Americans and whites are weakest, followed by those be- tween whites and Japanese Americans. Boundaries between blacks and whites are very strong. Log-Linear Models Table 4 lists the goodness-of-fit chi-square and BIC statistics for the log-linear models analyzing these marriages.7 Let us begin by discussing the models for marriages between whites and blacks. Model 1a is the endogamous intermarriage model, which assumes that the only determinants of marriage pat- terns are educational assortative mating, marginal group dif- ferences in education, and an overall tendency to intermarry. For blacks, the endogamous intermarriage model clearly does not fit the data as well as the saturated model (P[ 29 > 311.1541] < .0001), although the BIC statistic indicates that it is more plausible than the saturated model. Model 2a, the column-effects model, adds a set of con- strained exchange parameters (described in Table 1) to the endogamous intermarriage model. A likelihood-ratio test re- ports...

... was simply the change in the wording of the census item on education, because that hypothesis implies no re- gional pattern. The direction of the changes in educational attainment is shown in Table 5, which reports estimated parameters from the saturated model for interactions with education and year...

...": 1988U.S. BIRTH COHORTb Unsaturated Model With Gestational Age and Intrauterine Growth Frisbie Hadlock Saturated Model Parameter et al. et al. With BirthWeight Race/Ethnicity White (R) Black 0.416* 0.339* 0.350* Gestational Age Full-Term (R) Preterm 1.234* 2.058* Intrauterine Growth Not IUGR (R) IUGR 1.286...

... 4,335.75 938.76 4,997.03 Log-Likelihood Test Chi-Square vs. Saturated Modela 1,447.53 4,951.89 1,143.25 Note: Numbers in parentheses are standard errors. aSpecific sets of covariates are tested against saturated model (Model 3). For Model 1, the two immigration covariates are tested; for Model 2...

... are constrained separately to equal 0 (not shown). The likelihood ratio of the saturated model (model 4 in Tables 4 and 5) is then used as a standard against which to judge the change in the fit obtained when the effects of selected variable(s) are constrained to equal 0.8 The likelihood ratio chi-squares...