Using an accessible approach perfect for social and behavioral science students (requiring minimal use of matrix and vector algebra), Holmes examines how propensity scores can be used to both reduce bias with different kinds of quasi-experimental designs and fix or improve broken experiments. This unique book covers the causal assumptions of propensity score estimates and their many uses, linking these uses with analysis appropriate for different designs. Thorough coverage of bias assessment, propensity score estimation, and estimate improvement is provided, along with graphical and statistical methods for this process. Applications are included for analysis of variance and covariance, maximum likelihood and logistic regression, two-stage least squares, generalized linear regression, and general estimation equations. The examples use public data sets that have policy and programmatic relevance across a variety of social and behavioral science disciplines.

Propensities and Weighted Least Squares Regression

This chapter presents the use of propensity scores in weighted least squares (WLS) regression. It presents different approaches to weighting and examines the trade-offs between them. Criteria for assessing the results of the regression, as well as judging the adequacy of the results of the weighting in reducing bias in the comparisons, are presented.

Weighted regression may be done using multiple regression (ordinary least squares regression (OLS), maximum likelihood solutions, or generalized least squares) or using logistic regression. The former is used when weighting is necessary and the outcomes are continuous variables. The latter is used when weighting is necessary and the outcomes are dichotomous or polychotomous variables.

Propensities as Weights

When one has a sample of cases and wants it ...

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