### Abstract

Regression coefficients specify the partial effect of a regressor on the dependent variable. Sometimes the bivariate or limited multivariate relationship of that regressor variable with the dependent variable is known from populationlevel data. We show here that such populationlevel data can be used to reduce variance and bias about estimates of those regression coefficients from sample survey data. The method of constrained MLE is used to achieve these improvements. Its statistical properties are first described. The method constrains the weighted sum of all the covariatespecific associations partial effects of the regressors on the dependent variable to equal the overall association of one or more regressors, where the latter is known exactly from the population data. We refer to those regressors whose bivariate or limited multivariate relationships with the dependent variable are constrained by population data as being "directly constrained." Our study investigates the improvements in the estimation of directly constrained variables as well as the improvements in the estimation of other regressor variables that may be correlated with the directly constrained variables, and thus "indirectly constrained" by the population data. The example application is to the marital fertility of black versus white women. The difference between white and black women's rates of marital fertility, available from populationlevel data, gives the overall association of race with fertility. We show that the constrained MLE technique both provides a far more powerful statistical test of the partial effect of being black and purges the test of a bias that would otherwise distort the estimated magnitude of this effect. We find only trivial reductions, however, in the standard errors of the parameters for indirectly constrained regressors.

Original language | English (US) |
---|---|

Pages (from-to) | 303-346 |

Number of pages | 44 |

Journal | Sociological Methodology |

Volume | 35 |

Issue number | 1 |

DOIs | |

State | Published - Aug 1 2005 |

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### ASJC Scopus subject areas

- Sociology and Political Science

### Cite this

*Sociological Methodology*,

*35*(1), 303-346. https://doi.org/10.1111/j.0081-1750.2006.00169.x

**Improved regression estimation of a multivariate relationship with population data on the bivariate relationship.** / Handcock, Mark S.; Rendall, Michael S.; Cheadle, Jacob E.

Research output: Contribution to journal › Review article

*Sociological Methodology*, vol. 35, no. 1, pp. 303-346. https://doi.org/10.1111/j.0081-1750.2006.00169.x

}

TY - JOUR

T1 - Improved regression estimation of a multivariate relationship with population data on the bivariate relationship

AU - Handcock, Mark S.

AU - Rendall, Michael S.

AU - Cheadle, Jacob E.

PY - 2005/8/1

Y1 - 2005/8/1

N2 - Regression coefficients specify the partial effect of a regressor on the dependent variable. Sometimes the bivariate or limited multivariate relationship of that regressor variable with the dependent variable is known from populationlevel data. We show here that such populationlevel data can be used to reduce variance and bias about estimates of those regression coefficients from sample survey data. The method of constrained MLE is used to achieve these improvements. Its statistical properties are first described. The method constrains the weighted sum of all the covariatespecific associations partial effects of the regressors on the dependent variable to equal the overall association of one or more regressors, where the latter is known exactly from the population data. We refer to those regressors whose bivariate or limited multivariate relationships with the dependent variable are constrained by population data as being "directly constrained." Our study investigates the improvements in the estimation of directly constrained variables as well as the improvements in the estimation of other regressor variables that may be correlated with the directly constrained variables, and thus "indirectly constrained" by the population data. The example application is to the marital fertility of black versus white women. The difference between white and black women's rates of marital fertility, available from populationlevel data, gives the overall association of race with fertility. We show that the constrained MLE technique both provides a far more powerful statistical test of the partial effect of being black and purges the test of a bias that would otherwise distort the estimated magnitude of this effect. We find only trivial reductions, however, in the standard errors of the parameters for indirectly constrained regressors.

AB - Regression coefficients specify the partial effect of a regressor on the dependent variable. Sometimes the bivariate or limited multivariate relationship of that regressor variable with the dependent variable is known from populationlevel data. We show here that such populationlevel data can be used to reduce variance and bias about estimates of those regression coefficients from sample survey data. The method of constrained MLE is used to achieve these improvements. Its statistical properties are first described. The method constrains the weighted sum of all the covariatespecific associations partial effects of the regressors on the dependent variable to equal the overall association of one or more regressors, where the latter is known exactly from the population data. We refer to those regressors whose bivariate or limited multivariate relationships with the dependent variable are constrained by population data as being "directly constrained." Our study investigates the improvements in the estimation of directly constrained variables as well as the improvements in the estimation of other regressor variables that may be correlated with the directly constrained variables, and thus "indirectly constrained" by the population data. The example application is to the marital fertility of black versus white women. The difference between white and black women's rates of marital fertility, available from populationlevel data, gives the overall association of race with fertility. We show that the constrained MLE technique both provides a far more powerful statistical test of the partial effect of being black and purges the test of a bias that would otherwise distort the estimated magnitude of this effect. We find only trivial reductions, however, in the standard errors of the parameters for indirectly constrained regressors.

UR - http://www.scopus.com/inward/record.url?scp=33744954656&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33744954656&partnerID=8YFLogxK

U2 - 10.1111/j.0081-1750.2006.00169.x

DO - 10.1111/j.0081-1750.2006.00169.x

M3 - Review article

AN - SCOPUS:33744954656

VL - 35

SP - 303

EP - 346

JO - Sociological Methodology

JF - Sociological Methodology

SN - 0081-1750

IS - 1

ER -