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2 results

  • 14 - Multiple Regression and General Linear Models

  • Jan Lepš, University of South Bohemia, Czech Republic, Petr Šmilauer, University of South Bohemia, Czech Republic
  • Book:
    Biostatistics with R
    Published online:
    18 September 2020
    Print publication:
    30 July 2020, pp 219-238

  • Summary

    We explain linear regression models with multiple predictors, including an overview of partial regression coefficients. The related concept of partial correlation is discussed in a separate section. We also contrast the overall model test using the F-ratio statistic and the t tests of partial effects of individual predictors. The adjusted coefficient of determination is presented as a more accurate way of conveying the explanatory power of a regression model. Finally, we characterise the family of general linear models, focusing specifically on analysis of covariance (ANCOVA). We provide examples of ANCOVA models and demonstrate their usefulness when applied to the analysis of biological experiments. The methods described in this chapter are accompanied by a carefully-explained guide to the R code needed for their use, including the effects and ppcor packages.

  • Regression Discontinuity with Multiple Running Variables Allowing Partial Effects

  • Jin-young Choi, Myoung-jae Lee
  • Journal:
    Political Analysis / Volume 26 / Issue 3 / July 2018
    Published online by Cambridge University Press:
    31 July 2018, pp. 258-274
    • Article
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  • In regression discontinuity (RD), a running variable (or “score”) crossing a cutoff determines a treatment that affects the mean-regression function. This paper generalizes this usual “one-score mean RD” in three ways: (i) considering multiple scores, (ii) allowing partial effects due to each score crossing its own cutoff, not just the full effect with all scores crossing all cutoffs, and (iii) accommodating quantile/mode regressions. This generalization is motivated by (i) many multiple-score RD cases, (ii) the full-effect identification needing the partial effects to be separated, and (iii) informative quantile/mode regression functions. We establish identification for multiple-score RD (MRD), and propose simple estimators that become “local difference in differences” in case of double scores. We also provide an empirical illustration where partial effects exist.